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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 82 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2000.152.1.a1.a1 $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_1$ $1$ ✓
2000.152.2.a1.a1 $C_{100}:C_{10}$ $2^{3} \cdot 5^{3}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
2000.152.2.b1.a1 $C_{25}:C_{40}$ $2^{3} \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
2000.152.2.b1.b1 $C_{25}:C_{40}$ $2^{3} \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2$ $2$ ✓
2000.152.4.a1.a1 $C_{50}:C_{10}$ $2^{2} \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_4$ $2^{2}$ ✓
2000.152.4.b1.a1 $C_{100}:C_5$ $2^{2} \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_4$ $2^{2}$ ✓
2000.152.4.c1.a1 $C_{100}:C_5$ $2^{2} \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2^2$ $2^{2}$ ✓
2000.152.5.a1.a1 $C_{50}:C_8$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_5$ $5$ ✓
2000.152.5.b1.a1 $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $5$ $-$
2000.152.8.a1.a1 $C_{25}:C_{10}$ $2 \cdot 5^{3}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_8$ $2^{3}$ ✓
2000.152.8.a1.b1 $C_{25}:C_{10}$ $2 \cdot 5^{3}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_8$ $2^{3}$ ✓
2000.152.8.b1.a1 $C_{25}:C_{10}$ $2 \cdot 5^{3}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2\times C_4$ $2^{3}$ ✓
2000.152.10.a1.a1 $C_{10}\times C_{20}$ $2^{3} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $D_5$ $2 \cdot 5$
2000.152.10.b1.a1 $C_2\times C_{100}$ $2^{3} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{10}$ $2 \cdot 5$ ✓
2000.152.10.c1.a1 $C_{25}:C_8$ $2^{3} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{10}$ $2 \cdot 5$ ✓
2000.152.10.c1.b1 $C_{25}:C_8$ $2^{3} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{10}$ $2 \cdot 5$ ✓
2000.152.10.d1.a1 $C_2\times C_{100}$ $2^{3} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
2000.152.10.d1.b1 $C_2\times C_{100}$ $2^{3} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
2000.152.10.e1.a1 $C_5:C_{40}$ $2^{3} \cdot 5^{2}$ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
2000.152.10.e1.b1 $C_5:C_{40}$ $2^{3} \cdot 5^{2}$ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2 \cdot 5$ $-$
2000.152.16.a1.a1 $C_{25}:C_5$ $5^{3}$ $5$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2\times C_8$ $2^{4}$ ✓
2000.152.20.a1.a1 $C_{10}^2$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_5:C_4$ $2^{2} \cdot 5$
2000.152.20.b1.a1 $C_2\times C_{50}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{20}$ $2^{2} \cdot 5$ ✓
2000.152.20.c1.a1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_5:C_4$ $2^{2} \cdot 5$
2000.152.20.d1.a1 $C_{100}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{20}$ $2^{2} \cdot 5$ ✓
2000.152.20.e1.a1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $D_{10}$ $2^{2} \cdot 5$
2000.152.20.f1.a1 $C_{100}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓
2000.152.20.g1.a1 $C_2\times C_{50}$ $2^{2} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
2000.152.20.g1.b1 $C_2\times C_{50}$ $2^{2} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
2000.152.20.h1.a1 $C_{100}$ $2^{2} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
2000.152.20.h1.b1 $C_{100}$ $2^{2} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
2000.152.20.i1.a1 $C_{100}$ $2^{2} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
2000.152.20.i1.b1 $C_{100}$ $2^{2} \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{2} \cdot 5$ $-$
2000.152.25.a1.a1 $C_{10}:C_8$ $2^{4} \cdot 5$ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $5^{2}$ $-$
2000.152.25.b1.a1 $C_2\times C_{40}$ $2^{4} \cdot 5$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $5^{2}$ $-$
2000.152.40.a1.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_5:C_8$ $2^{3} \cdot 5$
2000.152.40.a1.b1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_5:C_8$ $2^{3} \cdot 5$
2000.152.40.b1.a1 $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{40}$ $2^{3} \cdot 5$ ✓
2000.152.40.b1.b1 $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{40}$ $2^{3} \cdot 5$ ✓
2000.152.40.c1.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_{10}:C_4$ $2^{3} \cdot 5$
2000.152.40.d1.a1 $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓
2000.152.40.e1.a1 $C_{50}$ $2 \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
2000.152.40.e1.b1 $C_{50}$ $2 \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
2000.152.40.e1.c1 $C_{50}$ $2 \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
2000.152.40.e1.d1 $C_{50}$ $2 \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
2000.152.40.f1.a1 $C_{50}$ $2 \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
2000.152.40.f1.b1 $C_{50}$ $2 \cdot 5^{2}$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2^{3} \cdot 5$ $-$
2000.152.50.a1.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ ✓ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $C_5\times D_5$ $2 \cdot 5^{2}$
2000.152.50.b1.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2 \cdot 5^{2}$ $-$
2000.152.50.c1.a1 $C_5:C_8$ $2^{3} \cdot 5$ $C_{50}:C_{40}$ $2^{4} \cdot 5^{3}$ $2 \cdot 5^{2}$ $-$
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