| 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 |
| 360.2 |
$C_5:C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$144$ |
$36$ |
$24$ |
$21$ |
$C_{36}$ |
$D_5$ |
$C_5$ |
$C_{72}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{4} \cdot 3$ |
$360$ |
$22$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$14$ |
Solvable - 2 |
| 360.5 |
$C_5:C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$90$ |
$48$ |
$24$ |
$18$ |
$C_{18}$ |
$F_5$ |
$C_5$ |
$C_{72}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3$ |
$360$ |
$22$ |
$4$ |
$8$ |
$24$ |
$4$ |
$6$ |
$14$ |
Solvable - 2 |
| 360.14 |
$Q_8:C_{45}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$105$ |
$42$ |
$22$ |
$14$ |
$C_{30}$ |
$A_4$ |
$Q_8$ |
$C_{45}$ |
$2^{5} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$360$ |
$22$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$14$ |
Solvable - 3 |
| 360.16 |
$D_5\times C_{36}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$144$ |
$108$ |
$48$ |
$33$ |
$C_{36}$ |
$D_5$ |
$C_5$ |
$C_{2} \times C_{36}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{4} \cdot 3$ |
$180$ |
$18$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 360.19 |
$C_{45}:D_4$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$117$ |
$120$ |
$48$ |
$27$ |
$C_{18}$ |
$D_{10}$ |
$C_{10}$ |
$C_{2} \times C_{18}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3$ |
$180$ |
$18$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 360.31 |
$D_4\times C_{45}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$2$ |
$2$ |
$6$ |
$2$ |
$225$ |
$60$ |
$48$ |
$36$ |
$C_{90}$ |
$C_2^2$ |
$C_2$ |
$C_{2} \times C_{90}$ |
$2^{6} \cdot 3$ |
$2^{4} \cdot 3$ |
$180$ |
$18$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$12$ |
Nilpotent - 2 |
| 360.34 |
$C_3:C_{120}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$180$ |
$52$ |
$38$ |
$28$ |
$C_{60}$ |
$S_3$ |
$C_3$ |
$C_{120}$ |
$2^{6} \cdot 3$ |
$2^{5}$ |
$120$ |
$19$ |
$2$ |
$4$ |
$32$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 360.43 |
$C_{18}\times F_5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$90$ |
$120$ |
$48$ |
$30$ |
$C_{18}$ |
$F_5$ |
$C_5$ |
$C_{2} \times C_{36}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3$ |
$90$ |
$16$ |
$4$ |
$8$ |
$24$ |
$4$ |
$6$ |
$10$ |
Solvable - 2 |
| 360.46 |
$C_2^2:C_{90}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$120$ |
$84$ |
$40$ |
$20$ |
$C_{30}$ |
$A_4$ |
$C_2^2$ |
$C_{90}$ |
$2^{5} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$90$ |
$20$ |
$3$ |
$6$ |
$24$ |
$3$ |
$5$ |
$10$ |
Solvable - 2 |
| 360.51 |
$C_3\times \SL(2,5)$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$27$ |
$202$ |
$28$ |
$6$ |
$C_6$ |
$A_5$ |
$\SL(2,5)$ |
$C_{3}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{2}$ |
$72$ |
$27$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Non-Solvable - 3 |
| 360.53 |
$C_{15}:C_{24}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$54$ |
$108$ |
$38$ |
$22$ |
$C_6$ |
$C_{15}:C_4$ |
$C_{15}$ |
$C_{24}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3}$ |
$120$ |
$19$ |
$4$ |
$8$ |
$16$ |
$4$ |
$8$ |
$10$ |
Solvable - 2 |
| 360.95 |
$C_{12}.C_{30}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$135$ |
$84$ |
$54$ |
$36$ |
$C_{30}$ |
$D_6$ |
$C_6$ |
$C_{2} \times C_{30}$ |
$2^{7} \cdot 3$ |
$2^{5}$ |
$120$ |
$19$ |
$2$ |
$4$ |
$32$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 360.96 |
$S_3\times C_{60}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$180$ |
$116$ |
$70$ |
$44$ |
$C_{60}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{60}$ |
$2^{6} \cdot 3$ |
$2^{5}$ |
$120$ |
$15$ |
$2$ |
$4$ |
$32$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 360.97 |
$C_{15}\times D_{12}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$135$ |
$148$ |
$70$ |
$36$ |
$C_{30}$ |
$D_6$ |
$C_6$ |
$C_{2} \times C_{30}$ |
$2^{7} \cdot 3$ |
$2^{5}$ |
$120$ |
$15$ |
$2$ |
$4$ |
$32$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 360.98 |
$C_6:C_{60}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$180$ |
$108$ |
$74$ |
$52$ |
$C_2\times C_{30}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{60}$ |
$2^{7} \cdot 3$ |
$2^{6}$ |
$120$ |
$17$ |
$-$ |
$-$ |
$-$ |
$3$ |
$4$ |
$8$ |
Solvable - 2 |
| 360.99 |
$D_6:C_{30}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$135$ |
$140$ |
$74$ |
$36$ |
$C_{30}$ |
$D_6$ |
$C_6$ |
$C_{2} \times C_{30}$ |
$2^{6} \cdot 3$ |
$2^{4}$ |
$60$ |
$15$ |
$2$ |
$4$ |
$16$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 360.119 |
$C_3\times S_5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$21$ |
$362$ |
$41$ |
$6$ |
$C_3$ |
$S_5$ |
$A_5$ |
$C_{6}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2$ |
$15$ |
$8$ |
$4$ |
$8$ |
$8$ |
$4$ |
$6$ |
$6$ |
Non-Solvable - 3 |
| 360.122 |
$C_6\times A_5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$30$ |
$388$ |
$50$ |
$8$ |
$C_6$ |
$A_5$ |
$A_5$ |
$C_{6}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{2}$ |
$30$ |
$10$ |
$3$ |
$6$ |
$8$ |
$3$ |
$5$ |
$6$ |
Non-Solvable - 3 |
| 360.126 |
$D_{15}:C_{12}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$45$ |
$292$ |
$70$ |
$28$ |
$C_3$ |
$S_3\times F_5$ |
$C_{15}$ |
$C_{2} \times C_{12}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2$ |
$30$ |
$11$ |
$8$ |
$16$ |
$16$ |
$6$ |
$8$ |
$8$ |
Solvable - 2 |
| 360.138 |
$C_{15}\times S_4$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$75$ |
$140$ |
$48$ |
$16$ |
$C_{15}$ |
$S_4$ |
$A_4$ |
$C_{30}$ |
$2^{6} \cdot 3$ |
$2^{3}$ |
$60$ |
$12$ |
$3$ |
$6$ |
$24$ |
$3$ |
$5$ |
$9$ |
Solvable - 3 |
| 360.146 |
$C_{30}:C_{12}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$54$ |
$276$ |
$74$ |
$34$ |
$C_6$ |
$C_{15}:C_4$ |
$C_{15}$ |
$C_{2} \times C_{12}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3}$ |
$60$ |
$13$ |
$4$ |
$8$ |
$16$ |
$4$ |
$8$ |
$8$ |
Solvable - 2 |
| 504.1 |
$C_7:C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$84$ |
$60$ |
$24$ |
$18$ |
$C_{12}$ |
$F_7$ |
$C_7$ |
$C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$504$ |
$24$ |
$6$ |
$12$ |
$72$ |
$6$ |
$8$ |
$16$ |
Solvable - 2 |
| 504.2 |
$C_7:C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$120$ |
$48$ |
$24$ |
$20$ |
$C_{24}$ |
$C_7:C_3$ |
$C_7$ |
$C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3$ |
$504$ |
$24$ |
$3$ |
$6$ |
$144$ |
$3$ |
$6$ |
$16$ |
Solvable - 2 |
| 504.8 |
$C_{28}:C_{18}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$84$ |
$156$ |
$48$ |
$30$ |
$C_{12}$ |
$F_7$ |
$C_7$ |
$C_{2} \times C_{36}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$252$ |
$20$ |
$6$ |
$12$ |
$72$ |
$6$ |
$8$ |
$14$ |
Solvable - 2 |
| 504.11 |
$D_{14}:C_{18}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$57$ |
$180$ |
$48$ |
$24$ |
$C_6$ |
$C_2\times F_7$ |
$C_{14}$ |
$C_{2} \times C_{18}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3$ |
$252$ |
$20$ |
$6$ |
$12$ |
$72$ |
$6$ |
$10$ |
$14$ |
Solvable - 2 |
| 504.22 |
$Q_8:C_{63}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$147$ |
$42$ |
$22$ |
$14$ |
$C_{42}$ |
$A_4$ |
$Q_8$ |
$C_{63}$ |
$2^{4} \cdot 3^{3}$ |
$2^{2} \cdot 3^{2}$ |
$504$ |
$24$ |
$2$ |
$4$ |
$72$ |
$2$ |
$4$ |
$16$ |
Solvable - 3 |
| 504.40 |
$D_4\times C_{63}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2$ |
$2$ |
$6$ |
$2$ |
$315$ |
$60$ |
$48$ |
$36$ |
$C_{126}$ |
$C_2^2$ |
$C_2$ |
$C_{2} \times C_{126}$ |
$2^{5} \cdot 3^{2}$ |
$2^{3} \cdot 3^{2}$ |
$252$ |
$20$ |
$2$ |
$4$ |
$72$ |
$2$ |
$4$ |
$14$ |
Nilpotent - 2 |
| 504.47 |
$C_3:C_{168}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$252$ |
$52$ |
$38$ |
$28$ |
$C_{84}$ |
$S_3$ |
$C_3$ |
$C_{168}$ |
$2^{5} \cdot 3^{2}$ |
$2^{4} \cdot 3$ |
$168$ |
$21$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 504.52 |
$F_8:C_9$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$24$ |
$129$ |
$18$ |
$7$ |
$C_3$ |
$F_8:C_3$ |
$F_8$ |
$C_{9}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$3$ |
$72$ |
$17$ |
$7$ |
$14$ |
$42$ |
$7$ |
$9$ |
$13$ |
Solvable - 3 |
| 504.61 |
$C_2^2:C_{126}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$168$ |
$84$ |
$40$ |
$20$ |
$C_{42}$ |
$A_4$ |
$C_2^2$ |
$C_{126}$ |
$2^{4} \cdot 3^{3}$ |
$2^{2} \cdot 3^{2}$ |
$126$ |
$22$ |
$3$ |
$6$ |
$36$ |
$3$ |
$5$ |
$12$ |
Solvable - 2 |
| 504.134 |
$S_3\times C_{84}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$252$ |
$116$ |
$70$ |
$44$ |
$C_{84}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{84}$ |
$2^{5} \cdot 3^{2}$ |
$2^{4} \cdot 3$ |
$168$ |
$17$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 504.137 |
$D_6:C_{42}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$189$ |
$140$ |
$74$ |
$36$ |
$C_{42}$ |
$D_6$ |
$C_6$ |
$C_{2} \times C_{42}$ |
$2^{5} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$84$ |
$17$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 504.174 |
$C_{21}\times S_4$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$105$ |
$140$ |
$48$ |
$16$ |
$C_{21}$ |
$S_4$ |
$A_4$ |
$C_{42}$ |
$2^{5} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$84$ |
$14$ |
$3$ |
$6$ |
$36$ |
$3$ |
$5$ |
$11$ |
Solvable - 3 |
| 540.5 |
$F_5\times C_{27}$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$135$ |
$56$ |
$24$ |
$16$ |
$C_{27}$ |
$F_5$ |
$C_5$ |
$C_{108}$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2 \cdot 3^{2}$ |
$135$ |
$32$ |
$4$ |
$8$ |
$72$ |
$4$ |
$6$ |
$22$ |
Solvable - 2 |
| 540.17 |
$C_3:C_{180}$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$270$ |
$64$ |
$44$ |
$30$ |
$C_{90}$ |
$S_3$ |
$C_3$ |
$C_{180}$ |
$2^{5} \cdot 3^{2}$ |
$2^{4} \cdot 3$ |
$180$ |
$21$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$14$ |
Solvable - 2 |
| 540.19 |
$C_9:C_{60}$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$100$ |
$92$ |
$40$ |
$24$ |
$C_{10}$ |
$C_9:C_6$ |
$C_9$ |
$C_{60}$ |
$2^{4} \cdot 3^{3}$ |
$2^{3}$ |
$180$ |
$18$ |
$6$ |
$12$ |
$24$ |
$6$ |
$8$ |
$12$ |
Solvable - 2 |
| 540.30 |
$C_9:C_{60}$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$2$ |
$2$ |
$6$ |
$2$ |
$220$ |
$60$ |
$48$ |
$42$ |
$C_{60}$ |
$C_3^2$ |
$C_3$ |
$C_{3} \times C_{60}$ |
$2^{4} \cdot 3^{3}$ |
$2^{4} \cdot 3$ |
$180$ |
$18$ |
$3$ |
$6$ |
$48$ |
$3$ |
$6$ |
$12$ |
Nilpotent - 2 |
| 540.66 |
$S_3\times C_{90}$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$270$ |
$112$ |
$68$ |
$42$ |
$C_{90}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{90}$ |
$2^{5} \cdot 3^{2}$ |
$2^{4} \cdot 3$ |
$180$ |
$19$ |
$2$ |
$4$ |
$48$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 540.68 |
$C_{18}:C_{30}$ |
$2^{2} \cdot 3^{3} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$100$ |
$196$ |
$64$ |
$32$ |
$C_{10}$ |
$C_9:C_6$ |
$C_9$ |
$C_{2} \times C_{30}$ |
$2^{4} \cdot 3^{3}$ |
$2^{3}$ |
$90$ |
$16$ |
$6$ |
$12$ |
$24$ |
$6$ |
$8$ |
$10$ |
Solvable - 2 |
| 600.1 |
$C_3:C_{200}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$300$ |
$30$ |
$24$ |
$21$ |
$C_{100}$ |
$S_3$ |
$C_3$ |
$C_{200}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{4} \cdot 5$ |
$600$ |
$36$ |
$2$ |
$4$ |
$80$ |
$2$ |
$4$ |
$24$ |
Solvable - 2 |
| 600.14 |
$C_{25}\times \SL(2,3)$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$175$ |
$45$ |
$21$ |
$12$ |
$C_{50}$ |
$A_4$ |
$Q_8$ |
$C_{75}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3} \cdot 5$ |
$200$ |
$33$ |
$2$ |
$4$ |
$40$ |
$2$ |
$4$ |
$24$ |
Solvable - 3 |
| 600.21 |
$S_3\times C_{100}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$300$ |
$78$ |
$48$ |
$33$ |
$C_{100}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{100}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{4} \cdot 5$ |
$300$ |
$32$ |
$2$ |
$4$ |
$80$ |
$2$ |
$4$ |
$24$ |
Solvable - 2 |
| 600.24 |
$D_6:C_{50}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$225$ |
$90$ |
$48$ |
$27$ |
$C_{50}$ |
$D_6$ |
$C_6$ |
$C_{2} \times C_{50}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3} \cdot 5$ |
$300$ |
$32$ |
$2$ |
$4$ |
$80$ |
$2$ |
$4$ |
$24$ |
Solvable - 2 |
| 600.31 |
$D_4\times C_{75}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$2$ |
$2$ |
$6$ |
$2$ |
$375$ |
$60$ |
$48$ |
$36$ |
$C_{150}$ |
$C_2^2$ |
$C_2$ |
$C_{2} \times C_{150}$ |
$2^{6} \cdot 5$ |
$2^{4} \cdot 5$ |
$300$ |
$32$ |
$2$ |
$4$ |
$80$ |
$2$ |
$4$ |
$24$ |
Nilpotent - 2 |
| 600.34 |
$S_4\times C_{25}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$125$ |
$90$ |
$33$ |
$12$ |
$C_{25}$ |
$S_4$ |
$A_4$ |
$C_{50}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{2} \cdot 5$ |
$100$ |
$29$ |
$3$ |
$6$ |
$60$ |
$3$ |
$5$ |
$23$ |
Solvable - 3 |
| 600.40 |
$A_4\times C_{50}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5^{2}$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$200$ |
$78$ |
$36$ |
$18$ |
$C_{50}$ |
$A_4$ |
$C_2^2$ |
$C_{150}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3} \cdot 5$ |
$150$ |
$31$ |
$3$ |
$6$ |
$60$ |
$3$ |
$5$ |
$23$ |
Solvable - 2 |
| 600.54 |
$C_5\times \SL(2,5)$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$45$ |
$200$ |
$28$ |
$6$ |
$C_{10}$ |
$A_5$ |
$\SL(2,5)$ |
$C_{5}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3}$ |
$120$ |
$29$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Non-Solvable - 3 |
| 600.72 |
$C_5:C_{120}$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$150$ |
$80$ |
$36$ |
$24$ |
$C_{30}$ |
$F_5$ |
$C_5$ |
$C_{120}$ |
$2^{6} \cdot 5$ |
$2^{4}$ |
$120$ |
$21$ |
$4$ |
$8$ |
$32$ |
$4$ |
$6$ |
$12$ |
Solvable - 2 |
| 600.144 |
$C_5\times S_5$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$35$ |
$336$ |
$39$ |
$6$ |
$C_5$ |
$S_5$ |
$A_5$ |
$C_{10}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{2}$ |
$25$ |
$10$ |
$4$ |
$8$ |
$16$ |
$4$ |
$6$ |
$8$ |
Non-Solvable - 3 |
| 600.147 |
$C_{10}\times A_5$ |
$2^{3} \cdot 3 \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$50$ |
$376$ |
$48$ |
$8$ |
$C_{10}$ |
$A_5$ |
$A_5$ |
$C_{10}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3}$ |
$50$ |
$12$ |
$3$ |
$6$ |
$12$ |
$3$ |
$5$ |
$8$ |
Non-Solvable - 3 |
