Note: Search results may be incomplete due to uncomputed quantities: Outer aut. group order (4830 objects)
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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
120.1 | $C_3:C_{40}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $60$ | $C_{20}$ | Solvable - 2 |
120.2 | $C_5:C_{24}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $48$ | $C_{12}$ | Solvable - 2 |
120.3 | $C_{15}:C_8$ | $2^{3} \cdot 3 \cdot 5$ | $2^{3} \cdot 3 \cdot 5$ | $36$ | $C_4$ | Solvable - 2 |
120.8 | $C_6.D_{10}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $24$ | $C_2$ | Solvable - 2 |
120.9 | $C_6.D_{10}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $24$ | $C_2$ | Solvable - 2 |
120.10 | $D_{15}:C_4$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $24$ | $C_2$ | Solvable - 2 |
120.11 | $C_{15}:D_4$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $21$ | $C_2$ | Solvable - 2 |
120.12 | $C_3:D_{20}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $21$ | $C_2$ | Solvable - 2 |
120.13 | $C_5:D_{12}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $21$ | $C_2$ | Solvable - 2 |
120.14 | $C_{15}:Q_8$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $21$ | $C_2$ | Solvable - 2 |
120.15 | $C_5\times \SL(2,3)$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $35$ | $C_{10}$ | Solvable - 3 |
120.16 | $C_{15}:Q_8$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $39$ | $C_6$ | Solvable - 2 |
120.17 | $D_5\times C_{12}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $48$ | $C_{12}$ | Solvable - 2 |
120.18 | $C_3\times D_{20}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $39$ | $C_6$ | Solvable - 2 |
120.19 | $C_{10}:C_{12}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $48$ | $C_2\times C_6$ | Solvable - 2 |
120.20 | $C_{15}:D_4$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $39$ | $C_6$ | Solvable - 2 |
120.21 | $C_{15}:Q_8$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_{10}$ | Solvable - 2 |
120.22 | $S_3\times C_{20}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $60$ | $C_{20}$ | Solvable - 2 |
120.23 | $C_5\times D_{12}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_{10}$ | Solvable - 2 |
120.24 | $C_6:C_{20}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $60$ | $C_2\times C_{10}$ | Solvable - 2 |
120.25 | $C_{15}:D_4$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $45$ | $C_{10}$ | Solvable - 2 |
120.26 | $C_{15}:Q_8$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $33$ | $C_2$ | Solvable - 2 |
120.27 | $C_4\times D_{15}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $36$ | $C_4$ | Solvable - 2 |
120.28 | $D_{60}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $33$ | $C_2$ | Solvable - 2 |
120.29 | $C_{30}:C_4$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $36$ | $C_2^2$ | Solvable - 2 |
120.30 | $C_{15}:D_4$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $33$ | $C_2$ | Solvable - 2 |
120.32 | $D_4\times C_{15}$ | $2^{3} \cdot 3 \cdot 5$ | $2^{2} \cdot 3 \cdot 5$ | $75$ | $C_{30}$ | Nilpotent - 2 |
120.42 | $S_3\times D_{10}$ | $2^{3} \cdot 3 \cdot 5$ | $2 \cdot 3 \cdot 5$ | $24$ | $C_2$ | Solvable - 2 |
120.43 | $C_{10}\times A_4$ | $2^{3} \cdot 3 \cdot 5$ | $2 \cdot 3 \cdot 5$ | $40$ | $C_{10}$ | Solvable - 2 |
168.2 | $C_7:C_{24}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{3} \cdot 3 \cdot 7$ | $40$ | $C_8$ | Solvable - 2 |
168.3 | $C_3:C_{56}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{3} \cdot 3 \cdot 7$ | $84$ | $C_{28}$ | Solvable - 2 |
168.4 | $C_7:C_{24}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{3} \cdot 3 \cdot 7$ | $60$ | $C_{12}$ | Solvable - 2 |
168.5 | $C_{21}:C_8$ | $2^{3} \cdot 3 \cdot 7$ | $2^{3} \cdot 3 \cdot 7$ | $48$ | $C_4$ | Solvable - 2 |
168.10 | $C_{14}:C_{12}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $28$ | $C_2^2$ | Solvable - 2 |
168.12 | $C_6.D_{14}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $30$ | $C_2$ | Solvable - 2 |
168.13 | $C_6.D_{14}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $30$ | $C_2$ | Solvable - 2 |
168.14 | $D_{21}:C_4$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $30$ | $C_2$ | Solvable - 2 |
168.15 | $C_{21}:D_4$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $27$ | $C_2$ | Solvable - 2 |
168.16 | $C_3:D_{28}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $27$ | $C_2$ | Solvable - 2 |
168.17 | $C_7:D_{12}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $27$ | $C_2$ | Solvable - 2 |
168.18 | $C_{21}:Q_8$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $27$ | $C_2$ | Solvable - 2 |
168.19 | $C_{14}:C_{12}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $40$ | $C_2\times C_4$ | Solvable - 2 |
168.21 | $C_{28}.C_6$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $25$ | $C_2$ | Solvable - 2 |
168.22 | $C_7\times \SL(2,3)$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $49$ | $C_{14}$ | Solvable - 3 |
168.24 | $C_{21}:Q_8$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $51$ | $C_6$ | Solvable - 2 |
168.25 | $C_{12}\times D_7$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $60$ | $C_{12}$ | Solvable - 2 |
168.26 | $C_3\times D_{28}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $51$ | $C_6$ | Solvable - 2 |
168.28 | $C_{21}:D_4$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $51$ | $C_6$ | Solvable - 2 |
168.29 | $C_{21}:Q_8$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $63$ | $C_{14}$ | Solvable - 2 |
168.30 | $S_3\times C_{28}$ | $2^{3} \cdot 3 \cdot 7$ | $2^{2} \cdot 3 \cdot 7$ | $84$ | $C_{28}$ | Solvable - 2 |