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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 120 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1120.880.1.a1.a1 $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_1$ $1$ ✓
1120.880.2.a1.a1 $D_{140}:C_2$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.2.b1.a1 $Q_8\times C_{70}$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.2.c1.a1 $C_{140}.C_4$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.2.d1.a1 $Q_8:D_{35}$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.2.d1.b1 $Q_8:D_{35}$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.2.e1.a1 $C_{35}:Q_{16}$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.2.e1.b1 $C_{35}:Q_{16}$ $2^{4} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2$ $2$ ✓
1120.880.4.a1.a1 $C_2\times C_{140}$ $2^{3} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.b1.a1 $D_{140}$ $2^{3} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.c1.a1 $Q_8\times C_{35}$ $2^{3} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.c1.b1 $Q_8\times C_{35}$ $2^{3} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.d1.a1 $C_{35}:Q_8$ $2^{3} \cdot 5 \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.e1.a1 $C_{35}:C_8$ $2^{3} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.e1.b1 $C_{35}:C_8$ $2^{3} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1120.880.4.f1.a1 $C_{35}:D_4$ $2^{3} \cdot 5 \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{2}$ $-$
1120.880.4.g1.a1 $C_2\times C_{140}$ $2^{3} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{2}$ $-$
1120.880.4.h1.a1 $C_4\times D_{35}$ $2^{3} \cdot 5 \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{2}$ $-$
1120.880.4.i1.a1 $Q_8\times C_{35}$ $2^{3} \cdot 5 \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{2}$ $-$
1120.880.5.a1.a1 $C_{28}.D_4$ $2^{5} \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $5$ $-$
1120.880.7.a1.a1 $C_{20}.D_4$ $2^{5} \cdot 5$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $7$ $-$
1120.880.8.a1.a1 $C_2\times C_{70}$ $2^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_4$ $2^{3}$
1120.880.8.b1.a1 $C_{140}$ $2^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_4$ $2^{3}$
1120.880.8.c1.a1 $C_{140}$ $2^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1120.880.8.d1.a1 $D_{70}$ $2^{2} \cdot 5 \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{3}$ $-$
1120.880.8.e1.a1 $C_{140}$ $2^{2} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{3}$ $-$
1120.880.8.e1.b1 $C_{140}$ $2^{2} \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{3}$ $-$
1120.880.8.f1.a1 $C_{35}:C_4$ $2^{2} \cdot 5 \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{3}$ $-$
1120.880.10.a1.a1 $Q_8\times C_{14}$ $2^{4} \cdot 7$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_5$ $2 \cdot 5$
1120.880.10.b1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 5$ $-$
1120.880.10.c1.a1 $C_7:\OD_{16}$ $2^{4} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 5$ $-$
1120.880.10.d1.a1 $Q_8:D_7$ $2^{4} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 5$ $-$
1120.880.10.d1.b1 $Q_8:D_7$ $2^{4} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 5$ $-$
1120.880.10.e1.a1 $C_7:Q_{16}$ $2^{4} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 5$ $-$
1120.880.10.e1.b1 $C_7:Q_{16}$ $2^{4} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 5$ $-$
1120.880.14.a1.a1 $Q_8\times C_{10}$ $2^{4} \cdot 5$ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_7$ $2 \cdot 7$
1120.880.14.b1.a1 $D_{20}:C_2$ $2^{4} \cdot 5$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
1120.880.14.c1.a1 $C_5:\OD_{16}$ $2^{4} \cdot 5$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
1120.880.14.d1.a1 $Q_8:D_5$ $2^{4} \cdot 5$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
1120.880.14.d1.b1 $Q_8:D_5$ $2^{4} \cdot 5$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
1120.880.14.e1.a1 $C_5:Q_{16}$ $2^{4} \cdot 5$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
1120.880.14.e1.b1 $C_5:Q_{16}$ $2^{4} \cdot 5$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2 \cdot 7$ $-$
1120.880.16.a1.a1 $C_{70}$ $2 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_2\times D_4$ $2^{4}$
1120.880.16.b1.a1 $C_{70}$ $2 \cdot 5 \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{4}$ $-$
1120.880.16.c1.a1 $D_{35}$ $2 \cdot 5 \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{4}$ $-$
1120.880.20.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_{10}$ $2^{2} \cdot 5$
1120.880.20.b1.a1 $C_7\times Q_8$ $2^{3} \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_{10}$ $2^{2} \cdot 5$
1120.880.20.b1.b1 $C_7\times Q_8$ $2^{3} \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $D_{10}$ $2^{2} \cdot 5$
1120.880.20.c1.a1 $C_7:D_4$ $2^{3} \cdot 7$ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{2} \cdot 5$ $-$
1120.880.20.d1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $2^{2} \cdot 5$ $-$
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