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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 332 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
360.106.360.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
720.351.360.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{120}:S_3$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
720.352.360.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{120}:S_3$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
720.358.360.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4\times C_3^2:C_{20}$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
720.359.360.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times C_{20})$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
720.361.360.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{30}.D_{12}$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
720.740.360.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{60}:D_6$ $2^{4} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1080.224.360.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{180}:S_3$ $2^{3} \cdot 3^{3} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1080.227.360.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^2:S_3\times C_{20}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1080.412.360.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{30}.S_3^2$ $2^{3} \cdot 3^{3} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1080.414.360.b1 $C_3$ $3$ ✓ ✓ ✓ $C_{30}.S_3^2$ $2^{3} \cdot 3^{3} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1080.465.360.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3:S_3\times C_{60}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1080.475.360.a1 $C_3$ $3$ ✓ ✓ $C_3^2:S_3\times C_{20}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓
1440.1356.360.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{240}:S_3$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1357.360.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{240}:S_3$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1361.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{10}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1362.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2.C_{10}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1364.360.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1365.360.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_6^2.D_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1366.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_6^2.D_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1367.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_6^2.D_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1368.360.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{60}.D_{12}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1369.360.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{60}.D_{12}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1372.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_8\times C_3^2:C_{20}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1372.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_8\times C_3^2:C_{20}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1373.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6.(S_3\times C_{40})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1374.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_3\times C_{120}):C_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1374.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_3\times C_{120}):C_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1378.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{60}.D_{12}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1379.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{30}.D_{24}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1380.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_6^2.D_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1381.360.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_6^2.Q_8$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1382.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{60}.D_{12}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1383.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{60}.D_{12}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1384.360.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_6^2.D_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.1390.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_6\times C_{12}):C_{20}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4368.360.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{12}^2.C_{10}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4371.360.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4372.360.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4373.360.c1 $C_4$ $2^{2}$ ✓ ✓ $C_{60}:D_{12}$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4377.360.b1 $C_2^2$ $2^{2}$ ✓ ✓ $C_6.(D_6\times C_{20})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4381.360.b1 $C_2^2$ $2^{2}$ ✓ ✓ $(C_2\times C_{60}):D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4382.360.b1 $C_2^2$ $2^{2}$ ✓ ✓ $C_6^2:(C_2\times C_{20})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4387.360.b1 $C_4$ $2^{2}$ ✓ ✓ $C_3^2:(Q_8\times C_{20})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4392.360.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{12}:(S_3\times C_{20})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4393.360.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{12}.(S_3\times C_{20})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4394.360.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{12}:(S_3\times C_{20})$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4399.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{120}:D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4399.360.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{120}:D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
1440.4400.360.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{120}:D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$
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