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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 330 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
240.102.1.a1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_1$ $1$ ✓
480.967.2.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $\SL(2,3).D_{10}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.969.2.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $\SL(2,3).D_{10}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.971.2.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{10}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.973.2.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{10}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1016.2.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_2\times C_{10}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1016.2.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_2\times C_{10}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1018.2.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $\GL(2,3):C_{10}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1019.2.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1019.2.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1020.2.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $\GL(2,3):C_{10}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
720.526.3.a1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}.S_4$ $2^{4} \cdot 3^{2} \cdot 5$ $C_3$ $3$ ✓
720.532.3.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{30}.S_4$ $2^{4} \cdot 3^{2} \cdot 5$ $3$ $-$
720.532.3.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{30}.S_4$ $2^{4} \cdot 3^{2} \cdot 5$ $3$ $-$
720.532.3.b1.c1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{30}.S_4$ $2^{4} \cdot 3^{2} \cdot 5$ $3$ $-$
960.5783.4.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.5783.4.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.5785.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5789.4.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.5789.4.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.5792.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $(C_5\times Q_8).D_{12}$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5799.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $(C_5\times Q_8).D_{12}$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5801.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5810.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $(C_5\times \GL(2,3)):C_4$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.5812.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $(C_5\times \GL(2,3)):C_4$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.5815.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{20}.(C_2\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5817.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{20}.(C_2\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5822.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.5826.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6253.4.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_4\times C_{10}.S_4$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.6253.4.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_4\times C_{10}.S_4$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.6254.4.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_2.(C_{20}\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.6254.4.b1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_2.(C_{20}\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.6256.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_5\times Q_8.D_{12}$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6256.4.c1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_5\times Q_8.D_{12}$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6261.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $(Q_8\times C_{20}):S_3$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6269.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{40}.S_4$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6269.4.c1.b1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{40}.S_4$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6270.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,3):C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.6271.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,3):C_{20}$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.6272.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{40}.S_4$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6285.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6291.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6294.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.6296.4.d1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ $C_{10}.\GL(2,\mathbb{Z}/4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2}$ $-$
960.10895.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.10897.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.10898.4.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $F_5\times C_2.S_4$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.10899.4.b1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{10}.(C_4\times S_4)$ $2^{6} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
960.10954.4.c1.a1 $C_{10}.S_4$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_2\times \SL(2,3).D_{10}$ $2^{6} \cdot 3 \cdot 5$ $C_2^2$ $2^{2}$ ✓
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