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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 270 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 $C_{60}.D_6$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.3398.3.a1.a1 $C_{40}.D_6$ $2^{5} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $3$ $-$
1440.3398.3.a1.b1 $C_{40}.D_6$ $2^{5} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $3$ $-$
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 $C_3^2:C_{40}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
1440.3398.4.f1.a1 $C_{15}:D_{12}$ $2^{3} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2}$ $-$
1440.3398.4.f1.b1 $C_{15}:D_{12}$ $2^{3} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2}$ $-$
1440.3398.4.g1.a1 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2}$ $-$
1440.3398.4.g1.b1 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2}$ $-$
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 $C_{120}:C_2$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.3398.6.b1.a1 $C_{20}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.b1.b1 $C_{20}.D_6$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.c1.a1 $C_{15}\times \SD_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.c1.b1 $C_{15}\times \SD_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.d1.a1 $D_{12}:C_{10}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.d1.b1 $D_{12}:C_{10}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.e1.a1 $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.e1.b1 $C_{15}:D_8$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.f1.a1 $S_3\times C_{40}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.f1.b1 $S_3\times C_{40}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.g1.a1 $S_3\times C_{40}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.h1.a1 $C_{15}:Q_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.3398.6.h1.b1 $C_{15}:Q_{16}$ $2^{4} \cdot 3 \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
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 $C_3^2:C_{20}$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $D_4$ $2^{3}$
1440.3398.8.d1.a1 $S_3\times C_{30}$ $2^{2} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3}$ $-$
1440.3398.8.d1.b1 $S_3\times C_{30}$ $2^{2} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3}$ $-$
1440.3398.8.e1.a1 $C_3:C_{60}$ $2^{2} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3}$ $-$
1440.3398.8.e1.b1 $C_3:C_{60}$ $2^{2} \cdot 3^{2} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3}$ $-$
1440.3398.9.a1.a1 $D_8:C_{10}$ $2^{5} \cdot 5$ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $3^{2}$ $-$
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 $D_{12}:S_3$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{120}.D_6$ $2^{5} \cdot 3^{2} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
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