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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 76 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1440.3398.1.a1.a1 $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_1$ $1$ ✓
1440.3398.2.a1.a1 $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.2.a1.b1 $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.2.b1.a1 $C_{24}:C_{30}$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.2.b1.b1 $C_{24}:C_{30}$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.2.c1.a1 $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.2.d1.a1 $C_{120}:S_3$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.2.e1.a1 $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.4.a1.a1 $C_{15}\times D_{12}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.a1.b1 $C_{15}\times D_{12}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.b1.a1 $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.c1.a1 $C_{12}.C_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.c1.b1 $C_{12}.C_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.d1.a1 $C_3\times C_{120}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.e1.a1 $C_3^2:C_{40}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.5.a1.a1 $C_{24}.D_6$ $2^{5} \cdot 3^{2}$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_5$ $5$ ✓
1440.3398.6.a1.a1 $C_{120}:C_2$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.3398.6.a1.b1 $C_{120}:C_2$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.3398.8.a1.a1 $C_{30}:S_3$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_4$ $2^{3}$
1440.3398.8.b1.a1 $C_3\times C_{60}$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^3$ $2^{3}$ ✓
1440.3398.8.c1.a1 $C_3^2:C_{20}$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_4$ $2^{3}$
1440.3398.10.a1.a1 $D_{12}:S_3$ $2^{4} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.10.a1.b1 $D_{12}:S_3$ $2^{4} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.10.b1.a1 $C_{24}:C_6$ $2^{4} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.10.b1.b1 $C_{24}:C_6$ $2^{4} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.10.c1.a1 $D_{12}:S_3$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.10.d1.a1 $C_{24}:S_3$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.10.e1.a1 $C_3^2:Q_{16}$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
1440.3398.12.a1.a1 $C_5\times D_{12}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
1440.3398.12.a1.b1 $C_5\times D_{12}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
1440.3398.12.b1.a1 $C_{15}:Q_8$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
1440.3398.12.b1.b1 $C_{15}:Q_8$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
1440.3398.12.c1.a1 $C_{120}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
1440.3398.12.c1.b1 $C_{120}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
1440.3398.16.a1.a1 $C_3\times C_{30}$ $2 \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times D_4$ $2^{4}$
1440.3398.20.a1.a1 $C_3\times D_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.20.a1.b1 $C_3\times D_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.20.b1.a1 $C_{12}:S_3$ $2^{3} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.20.c1.a1 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.20.c1.b1 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.20.d1.a1 $C_3\times C_{24}$ $2^{3} \cdot 3^{2}$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.20.e1.a1 $C_3^2:C_8$ $2^{3} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
1440.3398.24.a1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times D_6$ $2^{3} \cdot 3$
1440.3398.24.a1.b1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2\times D_6$ $2^{3} \cdot 3$
1440.3398.30.a1.a1 $C_{24}:C_2$ $2^{4} \cdot 3$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_5\times S_3$ $2 \cdot 3 \cdot 5$
1440.3398.30.a1.b1 $C_{24}:C_2$ $2^{4} \cdot 3$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_5\times S_3$ $2 \cdot 3 \cdot 5$
1440.3398.32.a1.a1 $C_3\times C_{15}$ $3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_8:C_2$ $2^{5}$
1440.3398.36.a1.a1 $C_{40}$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3^2$ $2^{2} \cdot 3^{2}$
1440.3398.40.a1.a1 $C_6:S_3$ $2^{2} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_5\times D_4$ $2^{3} \cdot 5$
1440.3398.40.b1.a1 $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2\times C_{10}$ $2^{3} \cdot 5$ ✓
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