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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 (48 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1600.1933.1.a1 $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_1$ $1$ ✓
1600.1933.2.a1 $C_{20}^2.C_2$ $2^{5} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_2$ $2$ ✓
1600.1933.2.b1 $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_2$ $2$ ✓
1600.1933.2.c1 $C_{20}.D_{20}$ $2^{5} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_2$ $2$ ✓
1600.1933.4.a1 $C_{20}^2$ $2^{4} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_2^2$ $2^{2}$ ✓
1600.1933.4.b1 $C_{20}:C_{20}$ $2^{4} \cdot 5^{2}$ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_4$ $2^{2}$ ✓
1600.1933.8.a1 $C_{10}\times C_{20}$ $2^{3} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $D_4$ $2^{3}$
1600.1933.8.b1 $C_{10}\times C_{20}$ $2^{3} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $D_4$ $2^{3}$
1600.1933.8.c1 $C_{10}\times C_{20}$ $2^{3} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_2\times C_4$ $2^{3}$ ✓
1600.1933.10.a1 $C_{20}:Q_8$ $2^{5} \cdot 5$ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $D_5$ $2 \cdot 5$
1600.1933.16.a1 $C_{10}^2$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_2^2:C_4$ $2^{4}$
1600.1933.16.b1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $D_8$ $2^{4}$
1600.1933.16.c1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $\SD_{16}$ $2^{4}$
1600.1933.16.d1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $\SD_{16}$ $2^{4}$
1600.1933.16.e1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $Q_{16}$ $2^{4}$
1600.1933.20.a1 $C_4\times C_{20}$ $2^{4} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $D_{10}$ $2^{2} \cdot 5$
1600.1933.20.b1 $C_4:C_{20}$ $2^{4} \cdot 5$ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:C_4$ $2^{2} \cdot 5$
1600.1933.32.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $D_4:C_4$ $2^{5}$
1600.1933.32.b1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $Q_8:C_4$ $2^{5}$
1600.1933.32.c1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_4.D_4$ $2^{5}$
1600.1933.40.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:D_4$ $2^{3} \cdot 5$
1600.1933.40.b1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:D_4$ $2^{3} \cdot 5$
1600.1933.40.c1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_4$ $2^{3} \cdot 5$
1600.1933.50.a1 $C_4:Q_8$ $2^{5}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:D_5$ $2 \cdot 5^{2}$
1600.1933.64.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_4.D_8$ $2^{6}$
1600.1933.80.a1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}.D_4$ $2^{4} \cdot 5$
1600.1933.80.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:D_8$ $2^{4} \cdot 5$
1600.1933.80.c1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:\SD_{16}$ $2^{4} \cdot 5$
1600.1933.80.d1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $Q_8:D_5$ $2^{4} \cdot 5$
1600.1933.80.e1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:Q_{16}$ $2^{4} \cdot 5$
1600.1933.100.a1 $C_4^2$ $2^{4}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5:D_{10}$ $2^{2} \cdot 5^{2}$
1600.1933.100.b1 $C_4:C_4$ $2^{4}$ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5^2:C_4$ $2^{2} \cdot 5^{2}$
1600.1933.160.a1 $C_{10}$ $2 \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}.D_8$ $2^{5} \cdot 5$
1600.1933.160.b1 $C_{10}$ $2 \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}.Q_{16}$ $2^{5} \cdot 5$
1600.1933.160.c1 $C_{10}$ $2 \cdot 5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{20}.D_4$ $2^{5} \cdot 5$
1600.1933.200.a1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}^2:C_2$ $2^{3} \cdot 5^{2}$
1600.1933.200.b1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}^2:C_2$ $2^{3} \cdot 5^{2}$
1600.1933.200.c1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}.D_{10}$ $2^{3} \cdot 5^{2}$
1600.1933.320.a1 $C_5$ $5$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{20}.D_8$ $2^{6} \cdot 5$ ✓
1600.1933.400.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}^2:C_4$ $2^{4} \cdot 5^{2}$
1600.1933.400.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5^2:D_8$ $2^{4} \cdot 5^{2}$
1600.1933.400.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{20}.D_{10}$ $2^{4} \cdot 5^{2}$
1600.1933.400.d1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{20}.D_{10}$ $2^{4} \cdot 5^{2}$
1600.1933.400.e1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_5^2:Q_{16}$ $2^{4} \cdot 5^{2}$
1600.1933.800.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}^2.D_4$ $2^{5} \cdot 5^{2}$ ✓
1600.1933.800.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}^2.D_4$ $2^{5} \cdot 5^{2}$ ✓
1600.1933.800.c1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $(C_{10}\times C_{20}).C_4$ $2^{5} \cdot 5^{2}$ ✓
1600.1933.1600.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$
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