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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 101 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
80.4.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_8\times D_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.5.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_{40}:C_2$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.28.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_5:C_8$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.29.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_5:\OD_{16}$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.30.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_4\times F_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.31.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_{20}:C_4$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.36.2.d1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $C_4\times D_{10}$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.36.2.d1.b1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $C_4\times D_{10}$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.36.2.d1.c1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $C_4\times D_{10}$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.36.2.d1.d1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $C_4\times D_{10}$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.38.2.c1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $D_{20}:C_2$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.38.2.c1.b1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $D_{20}:C_2$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.39.2.d1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_4\times D_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.40.2.d1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_4:D_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.41.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $Q_8\times D_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.41.2.a1.b1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $Q_8\times D_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.41.2.a1.c1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $Q_8\times D_5$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.42.2.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $D_{20}:C_2$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.42.2.a1.b1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $D_{20}:C_2$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
80.42.2.a1.c1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ $D_{20}:C_2$ $2^{4} \cdot 5$ $C_2$ $2$ ✓
120.8.3.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_6.D_{10}$ $2^{3} \cdot 3 \cdot 5$ $3$ $-$
120.10.3.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $D_{15}:C_4$ $2^{3} \cdot 3 \cdot 5$ $3$ $-$
120.17.3.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_5\times C_{12}$ $2^{3} \cdot 3 \cdot 5$ $C_3$ $3$ ✓
120.27.3.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_4\times D_{15}$ $2^{3} \cdot 3 \cdot 5$ $3$ $-$
200.5.5.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_4\times D_{25}$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.22.5.b1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{10}.D_{10}$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.23.5.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{10}.D_{10}$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.23.5.a1.b1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{10}.D_{10}$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.28.5.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_5\times C_{20}$ $2^{3} \cdot 5^{2}$ $C_5$ $5$ ✓
200.33.5.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{20}:D_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.33.5.a1.b1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{20}:D_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.33.5.a1.c1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{20}:D_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.33.5.a1.d1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{20}:D_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.33.5.a1.e1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{20}:D_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.33.5.a1.f1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{20}:D_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
200.41.5.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $D_5\times F_5$ $2^{3} \cdot 5^{2}$ $5$ $-$
240.92.6.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_4\times A_5$ $2^{4} \cdot 3 \cdot 5$ $2 \cdot 3$ $-$
240.93.6.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $\SL(2,5):C_2$ $2^{4} \cdot 3 \cdot 5$ $2 \cdot 3$ $-$
280.8.7.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{10}.D_{14}$ $2^{3} \cdot 5 \cdot 7$ $7$ $-$
280.9.7.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $D_{35}:C_4$ $2^{3} \cdot 5 \cdot 7$ $7$ $-$
280.20.7.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_5\times C_{28}$ $2^{3} \cdot 5 \cdot 7$ $C_7$ $7$ ✓
280.25.7.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_4\times D_{35}$ $2^{3} \cdot 5 \cdot 7$ $7$ $-$
360.130.9.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_3^2:C_4\times D_5$ $2^{3} \cdot 3^{2} \cdot 5$ $3^{2}$ $-$
440.18.11.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{10}.D_{22}$ $2^{3} \cdot 5 \cdot 11$ $11$ $-$
440.19.11.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $D_{55}:C_4$ $2^{3} \cdot 5 \cdot 11$ $11$ $-$
440.30.11.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_5\times C_{44}$ $2^{3} \cdot 5 \cdot 11$ $C_{11}$ $11$ ✓
440.35.11.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_4\times D_{55}$ $2^{3} \cdot 5 \cdot 11$ $11$ $-$
520.12.13.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $C_{10}.D_{26}$ $2^{3} \cdot 5 \cdot 13$ $13$ $-$
520.13.13.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ $D_{65}:C_4$ $2^{3} \cdot 5 \cdot 13$ $13$ $-$
520.24.13.a1.a1 $C_4\times D_5$ $2^{3} \cdot 5$ ✓ ✓ ✓ $D_5\times C_{52}$ $2^{3} \cdot 5 \cdot 13$ $C_{13}$ $13$ ✓
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