| Label |
Name |
Order |
Exponent |
Nilp. class |
Der. length |
Comp. length |
Rank |
$\card{\mathrm{conj}(G)}$ |
Subgroups |
Subgroup classes |
Normal subgroups |
Center |
Central quotient |
Commutator |
Abelianization |
$\card{\mathrm{Aut}(G)}$ |
$\card{\mathrm{Out}(G)}$ |
Tr. deg |
Perm. deg |
$\C$-irrep deg |
$\R$-irrep deg |
$\Q$-irrep deg |
$\C$-rep deg |
$\R$-rep deg |
$\Q$-rep deg |
Type - length |
| 294.16 |
$C_7^2:C_6$ |
$2 \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$38$ |
$232$ |
$40$ |
$22$ |
$C_2$ |
$C_7^2:C_3$ |
$C_7^2$ |
$C_{6}$ |
$2^{5} \cdot 3^{2} \cdot 7^{3}$ |
$2^{5} \cdot 3 \cdot 7$ |
$98$ |
$16$ |
$-$ |
$-$ |
$-$ |
$6$ |
$12$ |
$12$ |
Solvable - 2 |
| 294.19 |
$C_{21}:D_7$ |
$2 \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$78$ |
$232$ |
$40$ |
$22$ |
$C_3$ |
$C_7:D_7$ |
$C_7^2$ |
$C_{6}$ |
$2^{6} \cdot 3^{2} \cdot 7^{3}$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$147$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$14$ |
Solvable - 2 |
| 294.20 |
$S_3\times C_7^2$ |
$2 \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$147$ |
$60$ |
$40$ |
$30$ |
$C_7^2$ |
$S_3$ |
$C_3$ |
$C_{7} \times C_{14}$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$147$ |
$17$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$14$ |
Solvable - 2 |
| 294.22 |
$C_7:D_{21}$ |
$2 \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$75$ |
$444$ |
$40$ |
$21$ |
$C_1$ |
$C_7:D_{21}$ |
$C_7\times C_{21}$ |
$C_{2}$ |
$2^{6} \cdot 3^{3} \cdot 7^{3}$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$147$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$14$ |
Solvable - 2 |
| 300.17 |
$C_5^2:C_{12}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$84$ |
$144$ |
$48$ |
$34$ |
$C_6$ |
$C_5:D_5$ |
$C_5^2$ |
$C_{12}$ |
$2^{7} \cdot 3 \cdot 5^{3}$ |
$2^{6} \cdot 3 \cdot 5$ |
$300$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$12$ |
Solvable - 2 |
| 300.18 |
$C_{15}:C_{20}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$150$ |
$64$ |
$48$ |
$40$ |
$C_5\times C_{10}$ |
$S_3$ |
$C_3$ |
$C_{5} \times C_{20}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{6} \cdot 3 \cdot 5$ |
$300$ |
$17$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$12$ |
Solvable - 2 |
| 300.20 |
$C_{10}.D_{15}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$78$ |
$256$ |
$48$ |
$33$ |
$C_2$ |
$C_5:D_{15}$ |
$C_5\times C_{15}$ |
$C_{4}$ |
$2^{7} \cdot 3^{2} \cdot 5^{3}$ |
$2^{6} \cdot 3 \cdot 5$ |
$300$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$12$ |
Solvable - 2 |
| 300.42 |
$A_4\times C_5^2$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$100$ |
$80$ |
$40$ |
$24$ |
$C_5^2$ |
$A_4$ |
$C_2^2$ |
$C_{5} \times C_{15}$ |
$2^{8} \cdot 3^{2} \cdot 5$ |
$2^{6} \cdot 3 \cdot 5$ |
$100$ |
$14$ |
$-$ |
$-$ |
$-$ |
$4$ |
$7$ |
$11$ |
Solvable - 2 |
| 300.45 |
$C_{15}:D_{10}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$84$ |
$368$ |
$80$ |
$38$ |
$C_6$ |
$C_5:D_5$ |
$C_5^2$ |
$C_{2} \times C_{6}$ |
$2^{7} \cdot 3 \cdot 5^{3}$ |
$2^{6} \cdot 3 \cdot 5$ |
$150$ |
$15$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$10$ |
Solvable - 2 |
| 300.46 |
$D_6\times C_5^2$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$150$ |
$128$ |
$80$ |
$56$ |
$C_5\times C_{10}$ |
$S_3$ |
$C_3$ |
$C_{10}^{2}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{6} \cdot 3 \cdot 5$ |
$150$ |
$15$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$10$ |
Solvable - 2 |
| 300.48 |
$C_5:D_{30}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$78$ |
$704$ |
$80$ |
$35$ |
$C_2$ |
$C_5:D_{15}$ |
$C_5\times C_{15}$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3^{2} \cdot 5^{3}$ |
$2^{6} \cdot 3 \cdot 5$ |
$150$ |
$15$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$10$ |
Solvable - 2 |
| 350.5 |
$D_7\times C_5^2$ |
$2 \cdot 5^{2} \cdot 7$ |
$2 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$125$ |
$80$ |
$32$ |
$24$ |
$C_5^2$ |
$D_7$ |
$C_7$ |
$C_{5} \times C_{10}$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$175$ |
$17$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$14$ |
Solvable - 2 |
| 350.8 |
$C_{35}:D_5$ |
$2 \cdot 5^{2} \cdot 7$ |
$2 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$98$ |
$128$ |
$32$ |
$18$ |
$C_7$ |
$C_5:D_5$ |
$C_5^2$ |
$C_{14}$ |
$2^{6} \cdot 3^{2} \cdot 5^{3}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$175$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$14$ |
Solvable - 2 |
| 350.9 |
$C_5:D_{35}$ |
$2 \cdot 5^{2} \cdot 7$ |
$2 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$89$ |
$464$ |
$32$ |
$17$ |
$C_1$ |
$C_5:D_{35}$ |
$C_5\times C_{35}$ |
$C_{2}$ |
$2^{6} \cdot 3^{2} \cdot 5^{3} \cdot 7$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$175$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$14$ |
Solvable - 2 |
| 414.5 |
$C_3^2\times D_{23}$ |
$2 \cdot 3^{2} \cdot 23$ |
$2 \cdot 3 \cdot 23$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$117$ |
$156$ |
$24$ |
$18$ |
$C_3^2$ |
$D_{23}$ |
$C_{23}$ |
$C_{3} \times C_{6}$ |
$2^{5} \cdot 3 \cdot 11 \cdot 23$ |
$2^{4} \cdot 3 \cdot 11$ |
$207$ |
$29$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$26$ |
Solvable - 2 |
| 414.8 |
$C_{69}:S_3$ |
$2 \cdot 3^{2} \cdot 23$ |
$2 \cdot 3 \cdot 23$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$138$ |
$56$ |
$24$ |
$14$ |
$C_{23}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{46}$ |
$2^{5} \cdot 3^{3} \cdot 11$ |
$2^{4} \cdot 3 \cdot 11$ |
$207$ |
$29$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$26$ |
Solvable - 2 |
| 414.9 |
$C_3:D_{69}$ |
$2 \cdot 3^{2} \cdot 23$ |
$2 \cdot 3 \cdot 23$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$105$ |
$540$ |
$24$ |
$13$ |
$C_1$ |
$C_3:D_{69}$ |
$C_3\times C_{69}$ |
$C_{2}$ |
$2^{5} \cdot 3^{3} \cdot 11 \cdot 23$ |
$2^{4} \cdot 3 \cdot 11$ |
$207$ |
$29$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$26$ |
Solvable - 2 |
| 450.15 |
$C_{45}:D_5$ |
$2 \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$126$ |
$192$ |
$48$ |
$27$ |
$C_9$ |
$C_5:D_5$ |
$C_5^2$ |
$C_{18}$ |
$2^{6} \cdot 3^{2} \cdot 5^{3}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$225$ |
$19$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$14$ |
Solvable - 2 |
| 450.16 |
$D_9\times C_5^2$ |
$2 \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$150$ |
$128$ |
$48$ |
$32$ |
$C_5^2$ |
$D_9$ |
$C_9$ |
$C_{5} \times C_{10}$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$225$ |
$19$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$14$ |
Solvable - 2 |
| 450.18 |
$C_5:D_{45}$ |
$2 \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$114$ |
$752$ |
$48$ |
$25$ |
$C_1$ |
$C_5:D_{45}$ |
$C_5\times C_{45}$ |
$C_{2}$ |
$2^{6} \cdot 3^{4} \cdot 5^{3}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$225$ |
$19$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$14$ |
Solvable - 2 |
| 450.28 |
$C_{15}:C_{30}$ |
$2 \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$225$ |
$112$ |
$72$ |
$48$ |
$C_5\times C_{15}$ |
$S_3$ |
$C_3$ |
$C_{5} \times C_{30}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{6} \cdot 3 \cdot 5$ |
$150$ |
$16$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$12$ |
Solvable - 2 |
| 450.30 |
$C_{15}:D_{15}$ |
$2 \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$117$ |
$496$ |
$72$ |
$34$ |
$C_3$ |
$C_5:D_{15}$ |
$C_5\times C_{15}$ |
$C_{6}$ |
$2^{7} \cdot 3^{2} \cdot 5^{3}$ |
$2^{6} \cdot 3 \cdot 5$ |
$150$ |
$16$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$12$ |
Solvable - 2 |
| 468.23 |
$C_{39}:C_{12}$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$144$ |
$108$ |
$36$ |
$30$ |
$C_3\times C_6$ |
$D_{13}$ |
$C_{13}$ |
$C_{3} \times C_{12}$ |
$2^{7} \cdot 3^{2} \cdot 13$ |
$2^{6} \cdot 3^{2}$ |
$468$ |
$23$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$18$ |
Solvable - 2 |
| 468.26 |
$C_3^2:C_{52}$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$156$ |
$68$ |
$36$ |
$26$ |
$C_{26}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{52}$ |
$2^{7} \cdot 3^{4}$ |
$2^{6} \cdot 3^{2}$ |
$468$ |
$23$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$18$ |
Solvable - 2 |
| 468.27 |
$C_6.D_{39}$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$120$ |
$332$ |
$36$ |
$25$ |
$C_2$ |
$C_3:D_{39}$ |
$C_3\times C_{39}$ |
$C_{4}$ |
$2^{7} \cdot 3^{4} \cdot 13$ |
$2^{6} \cdot 3^{2}$ |
$468$ |
$23$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$18$ |
Solvable - 2 |
| 468.50 |
$C_3^2\times D_{26}$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$2 \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$144$ |
$276$ |
$60$ |
$42$ |
$C_3\times C_6$ |
$D_{13}$ |
$C_{13}$ |
$C_{6}^{2}$ |
$2^{7} \cdot 3^{2} \cdot 13$ |
$2^{6} \cdot 3^{2}$ |
$234$ |
$21$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$16$ |
Solvable - 2 |
| 468.53 |
$C_{78}:S_3$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$2 \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$156$ |
$156$ |
$60$ |
$30$ |
$C_{26}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{2} \times C_{26}$ |
$2^{7} \cdot 3^{4}$ |
$2^{6} \cdot 3^{2}$ |
$234$ |
$21$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$16$ |
Solvable - 2 |
| 468.54 |
$C_3:D_{78}$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$2 \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$120$ |
$948$ |
$60$ |
$27$ |
$C_2$ |
$C_3:D_{39}$ |
$C_3\times C_{39}$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3^{4} \cdot 13$ |
$2^{6} \cdot 3^{2}$ |
$234$ |
$21$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$16$ |
Solvable - 2 |
| 522.5 |
$C_3^2\times D_{29}$ |
$2 \cdot 3^{2} \cdot 29$ |
$2 \cdot 3 \cdot 29$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$144$ |
$192$ |
$24$ |
$18$ |
$C_3^2$ |
$D_{29}$ |
$C_{29}$ |
$C_{3} \times C_{6}$ |
$2^{6} \cdot 3 \cdot 7 \cdot 29$ |
$2^{5} \cdot 3 \cdot 7$ |
$261$ |
$35$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$32$ |
Solvable - 2 |
| 522.8 |
$C_{87}:S_3$ |
$2 \cdot 3^{2} \cdot 29$ |
$2 \cdot 3 \cdot 29$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$174$ |
$56$ |
$24$ |
$14$ |
$C_{29}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{58}$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2^{5} \cdot 3 \cdot 7$ |
$261$ |
$35$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$32$ |
Solvable - 2 |
| 522.9 |
$C_3:D_{87}$ |
$2 \cdot 3^{2} \cdot 29$ |
$2 \cdot 3 \cdot 29$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$132$ |
$672$ |
$24$ |
$13$ |
$C_1$ |
$C_3:D_{87}$ |
$C_3\times C_{87}$ |
$C_{2}$ |
$2^{6} \cdot 3^{3} \cdot 7 \cdot 29$ |
$2^{5} \cdot 3 \cdot 7$ |
$261$ |
$35$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$32$ |
Solvable - 2 |
| 525.3 |
$C_{35}:C_{15}$ |
$3 \cdot 5^{2} \cdot 7$ |
$3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$125$ |
$80$ |
$32$ |
$24$ |
$C_5^2$ |
$C_7:C_3$ |
$C_7$ |
$C_{5} \times C_{15}$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{6} \cdot 3 \cdot 5$ |
$175$ |
$17$ |
$-$ |
$-$ |
$-$ |
$4$ |
$8$ |
$14$ |
Solvable - 2 |
| 558.11 |
$C_3^2\times D_{31}$ |
$2 \cdot 3^{2} \cdot 31$ |
$2 \cdot 3 \cdot 31$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$153$ |
$204$ |
$24$ |
$18$ |
$C_3^2$ |
$D_{31}$ |
$C_{31}$ |
$C_{3} \times C_{6}$ |
$2^{5} \cdot 3^{2} \cdot 5 \cdot 31$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$279$ |
$37$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$34$ |
Solvable - 2 |
| 558.14 |
$C_{93}:S_3$ |
$2 \cdot 3^{2} \cdot 31$ |
$2 \cdot 3 \cdot 31$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$186$ |
$56$ |
$24$ |
$14$ |
$C_{31}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{62}$ |
$2^{5} \cdot 3^{4} \cdot 5$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$279$ |
$37$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$34$ |
Solvable - 2 |
| 558.15 |
$C_3:D_{93}$ |
$2 \cdot 3^{2} \cdot 31$ |
$2 \cdot 3 \cdot 31$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$141$ |
$716$ |
$24$ |
$13$ |
$C_1$ |
$C_3:D_{93}$ |
$C_3\times C_{93}$ |
$C_{2}$ |
$2^{5} \cdot 3^{4} \cdot 5 \cdot 31$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$279$ |
$37$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$34$ |
Solvable - 2 |
| 588.22 |
$C_7^2:C_{12}$ |
$2^{2} \cdot 3 \cdot 7^{2}$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$28$ |
$444$ |
$60$ |
$24$ |
$C_2$ |
$C_7:F_7$ |
$C_7^2$ |
$C_{12}$ |
$2^{6} \cdot 3^{2} \cdot 7^{3}$ |
$2^{5} \cdot 3 \cdot 7$ |
$196$ |
$18$ |
$-$ |
$-$ |
$-$ |
$12$ |
$14$ |
$14$ |
Solvable - 2 |
| 588.25 |
$C_7^2:C_{12}$ |
$2^{2} \cdot 3 \cdot 7^{2}$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$76$ |
$348$ |
$60$ |
$33$ |
$C_4$ |
$C_7^2:C_3$ |
$C_7^2$ |
$C_{12}$ |
$2^{6} \cdot 3^{2} \cdot 7^{3}$ |
$2^{6} \cdot 3 \cdot 7$ |
$196$ |
$18$ |
$-$ |
$-$ |
$-$ |
$6$ |
$12$ |
$14$ |
Solvable - 2 |
| 588.45 |
$C_{14}:F_7$ |
$2^{2} \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$28$ |
$868$ |
$100$ |
$28$ |
$C_2$ |
$C_7:F_7$ |
$C_7^2$ |
$C_{2} \times C_{6}$ |
$2^{6} \cdot 3^{2} \cdot 7^{3}$ |
$2^{5} \cdot 3 \cdot 7$ |
$98$ |
$16$ |
$-$ |
$-$ |
$-$ |
$12$ |
$12$ |
$12$ |
Solvable - 2 |
| 588.51 |
$C_{21}:D_{14}$ |
$2^{2} \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$78$ |
$1120$ |
$100$ |
$34$ |
$C_1$ |
$C_{21}:D_{14}$ |
$C_7\times C_{21}$ |
$C_{2}^{2}$ |
$2^{6} \cdot 3^{3} \cdot 7^{3}$ |
$2^{4} \cdot 3^{2} \cdot 7$ |
$147$ |
$17$ |
$-$ |
$-$ |
$-$ |
$6$ |
$6$ |
$14$ |
Solvable - 2 |
| 588.59 |
$C_{14}^2:C_3$ |
$2^{2} \cdot 3 \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$68$ |
$580$ |
$50$ |
$21$ |
$C_1$ |
$C_{14}^2:C_3$ |
$C_{14}^2$ |
$C_{3}$ |
$2^{7} \cdot 3^{3} \cdot 7^{3}$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$196$ |
$18$ |
$-$ |
$-$ |
$-$ |
$6$ |
$12$ |
$15$ |
Solvable - 2 |
| 612.13 |
$C_{51}:C_{12}$ |
$2^{2} \cdot 3^{2} \cdot 17$ |
$2^{2} \cdot 3 \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$180$ |
$132$ |
$36$ |
$30$ |
$C_3\times C_6$ |
$D_{17}$ |
$C_{17}$ |
$C_{3} \times C_{12}$ |
$2^{9} \cdot 3 \cdot 17$ |
$2^{8} \cdot 3$ |
$612$ |
$27$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$22$ |
Solvable - 2 |
| 612.16 |
$C_3^2:C_{68}$ |
$2^{2} \cdot 3^{2} \cdot 17$ |
$2^{2} \cdot 3 \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$204$ |
$68$ |
$36$ |
$26$ |
$C_{34}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{68}$ |
$2^{9} \cdot 3^{3}$ |
$2^{8} \cdot 3$ |
$612$ |
$27$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$22$ |
Solvable - 2 |
| 612.17 |
$C_6.D_{51}$ |
$2^{2} \cdot 3^{2} \cdot 17$ |
$2^{2} \cdot 3 \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$156$ |
$420$ |
$36$ |
$25$ |
$C_2$ |
$C_3:D_{51}$ |
$C_3\times C_{51}$ |
$C_{4}$ |
$2^{9} \cdot 3^{3} \cdot 17$ |
$2^{8} \cdot 3$ |
$612$ |
$27$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$22$ |
Solvable - 2 |
| 612.31 |
$C_3^2\times D_{34}$ |
$2^{2} \cdot 3^{2} \cdot 17$ |
$2 \cdot 3 \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$180$ |
$348$ |
$60$ |
$42$ |
$C_3\times C_6$ |
$D_{17}$ |
$C_{17}$ |
$C_{6}^{2}$ |
$2^{9} \cdot 3 \cdot 17$ |
$2^{8} \cdot 3$ |
$306$ |
$25$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$20$ |
Solvable - 2 |
| 612.34 |
$C_{102}:S_3$ |
$2^{2} \cdot 3^{2} \cdot 17$ |
$2 \cdot 3 \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$204$ |
$156$ |
$60$ |
$30$ |
$C_{34}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{2} \times C_{34}$ |
$2^{9} \cdot 3^{3}$ |
$2^{8} \cdot 3$ |
$306$ |
$25$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$20$ |
Solvable - 2 |
| 612.35 |
$C_3:D_{102}$ |
$2^{2} \cdot 3^{2} \cdot 17$ |
$2 \cdot 3 \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$156$ |
$1212$ |
$60$ |
$27$ |
$C_2$ |
$C_3:D_{51}$ |
$C_3\times C_{51}$ |
$C_{2}^{2}$ |
$2^{9} \cdot 3^{3} \cdot 17$ |
$2^{8} \cdot 3$ |
$306$ |
$25$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$20$ |
Solvable - 2 |
| 630.21 |
$C_{21}:C_{30}$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$2 \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$225$ |
$120$ |
$48$ |
$36$ |
$C_3\times C_{15}$ |
$D_7$ |
$C_7$ |
$C_{3} \times C_{30}$ |
$2^{7} \cdot 3^{2} \cdot 7$ |
$2^{6} \cdot 3^{2}$ |
$315$ |
$18$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$14$ |
Solvable - 2 |
| 630.22 |
$C_{15}:C_{42}$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$2 \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$252$ |
$96$ |
$48$ |
$36$ |
$C_3\times C_{21}$ |
$D_5$ |
$C_5$ |
$C_{3} \times C_{42}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{6} \cdot 3^{2}$ |
$315$ |
$18$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$14$ |
Solvable - 2 |
| 630.23 |
$C_3^2\times D_{35}$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$2 \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$171$ |
$312$ |
$48$ |
$30$ |
$C_3^2$ |
$D_{35}$ |
$C_{35}$ |
$C_{3} \times C_{6}$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{6} \cdot 3^{2}$ |
$315$ |
$18$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$14$ |
Solvable - 2 |
| 630.28 |
$C_{105}:S_3$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$2 \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$210$ |
$112$ |
$48$ |
$28$ |
$C_{35}$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{70}$ |
$2^{7} \cdot 3^{4}$ |
$2^{6} \cdot 3^{2}$ |
$315$ |
$18$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$14$ |
Solvable - 2 |
