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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
480.60.1.a1.a1 $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_1$ $1$ ✓
480.60.2.a1.a1 $C_{12}:C_{20}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.60.2.b1.a1 $C_{10}:C_{24}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.60.2.c1.a1 $C_{30}:C_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.60.3.a1.a1 $C_{20}:C_8$ $2^{5} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $3$ $-$
480.60.4.a1.a1 $C_2\times C_{60}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2^2$ $2^{2}$ ✓
480.60.4.b1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
480.60.4.c1.a1 $C_6:C_{20}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_4$ $2^{2}$ ✓
480.60.4.d1.a1 $C_5:C_{24}$ $2^{3} \cdot 3 \cdot 5$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2}$ $-$
480.60.4.e1.a1 $C_{15}:C_8$ $2^{3} \cdot 3 \cdot 5$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2}$ $-$
480.60.5.a1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $5$ $-$
480.60.6.a1.a1 $C_{10}:C_8$ $2^{4} \cdot 5$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $S_3$ $2 \cdot 3$
480.60.6.b1.a1 $C_4\times C_{20}$ $2^{4} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 3$ $-$
480.60.6.c1.a1 $C_{10}:C_8$ $2^{4} \cdot 5$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 3$ $-$
480.60.8.a1.a1 $C_2\times C_{30}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
480.60.8.b1.a1 $C_3:C_{20}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_8$ $2^{3}$ ✓
480.60.8.b1.b1 $C_3:C_{20}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_8$ $2^{3}$ ✓
480.60.8.c1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $D_4$ $2^{3}$
480.60.8.d1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $Q_8$ $2^{3}$
480.60.8.e1.a1 $C_3:C_{20}$ $2^{2} \cdot 3 \cdot 5$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{3}$ $-$
480.60.10.a1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $D_5$ $2 \cdot 5$
480.60.10.b1.a1 $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
480.60.10.c1.a1 $C_6:C_8$ $2^{4} \cdot 3$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 5$ $-$
480.60.12.a1.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $D_6$ $2^{2} \cdot 3$
480.60.12.b1.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3$ $-$
480.60.12.c1.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3$ $-$
480.60.12.d1.a1 $C_5:C_8$ $2^{3} \cdot 5$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3$ $-$
480.60.12.e1.a1 $C_5:C_8$ $2^{3} \cdot 5$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3$ $-$
480.60.15.a1.a1 $C_4:C_8$ $2^{5}$ $2$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $3 \cdot 5$ $-$
480.60.16.a1.a1 $C_{30}$ $2 \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_2\times C_8$ $2^{4}$ ✓
480.60.16.b1.a1 $C_{30}$ $2 \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $\OD_{16}$ $2^{4}$
480.60.16.c1.a1 $C_{30}$ $2 \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_4:C_4$ $2^{4}$
480.60.20.a1.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $D_{10}$ $2^{2} \cdot 5$
480.60.20.b1.a1 $C_6:C_4$ $2^{3} \cdot 3$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_5:C_4$ $2^{2} \cdot 5$
480.60.20.c1.a1 $C_6:C_4$ $2^{3} \cdot 3$ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_5:C_4$ $2^{2} \cdot 5$
480.60.20.d1.a1 $C_{24}$ $2^{3} \cdot 3$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 5$ $-$
480.60.20.e1.a1 $C_3:C_8$ $2^{3} \cdot 3$ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 5$ $-$
480.60.24.a1.a1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_4\times S_3$ $2^{3} \cdot 3$
480.60.24.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_3:D_4$ $2^{3} \cdot 3$
480.60.24.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_3:Q_8$ $2^{3} \cdot 3$
480.60.24.d1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3$ $-$
480.60.24.d1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3$ $-$
480.60.24.e1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3$ $-$
480.60.30.a1.a1 $C_4^2$ $2^{4}$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $-$
480.60.30.b1.a1 $C_2\times C_8$ $2^{4}$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $-$
480.60.30.c1.a1 $C_2\times C_8$ $2^{4}$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $-$
480.60.32.a1.a1 $C_{15}$ $3 \cdot 5$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_4:C_8$ $2^{5}$
480.60.40.a1.a1 $C_2\times C_6$ $2^{2} \cdot 3$ ✓ ✓ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_{10}:C_4$ $2^{3} \cdot 5$
480.60.40.b1.a1 $C_3:C_4$ $2^{2} \cdot 3$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_5:C_8$ $2^{3} \cdot 5$
480.60.40.b1.b1 $C_3:C_4$ $2^{2} \cdot 3$ ✓ $C_{12}.D_{20}$ $2^{5} \cdot 3 \cdot 5$ $C_5:C_8$ $2^{3} \cdot 5$
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