↑

Learn more

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

Refine search

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
Sort order Select

Results (1-50 of at least 1000)

Next   To download results, determine the number of results.
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
20.2.1.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_{20}$ $2^{2} \cdot 5$ $C_1$ $1$ ✓
40.1.2.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_5:C_8$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.2.2.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ ✓ $C_{40}$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.4.2.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_5:Q_8$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.5.2.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_4\times D_5$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.6.2.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $D_{20}$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.9.2.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_2\times C_{20}$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.9.2.b1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_2\times C_{20}$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.10.2.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_5\times D_4$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.11.2.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5\times Q_8$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.11.2.a1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5\times Q_8$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
40.11.2.a1.c1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5\times Q_8$ $2^{3} \cdot 5$ $C_2$ $2$ ✓
60.1.3.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_3:C_{20}$ $2^{2} \cdot 3 \cdot 5$ $3$ $-$
60.4.3.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ ✓ $C_{60}$ $2^{2} \cdot 3 \cdot 5$ $C_3$ $3$ ✓
80.1.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:C_{16}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.2.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_{80}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.3.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:C_{16}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.4.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_8\times D_5$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.5.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{40}:C_2$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.6.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{40}:C_2$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.7.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $D_{40}$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.8.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:Q_{16}$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.9.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{10}:C_8$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.9.4.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{10}:C_8$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.10.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:\OD_{16}$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.10.4.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:\OD_{16}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.11.4.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}:C_4$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.11.4.c1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}:C_4$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.12.4.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_{10}.D_4$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.13.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}:C_4$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.13.4.b1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_{20}:C_4$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.14.4.f1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $D_{10}:C_4$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.15.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:D_8$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.16.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:\SD_{16}$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.17.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $Q_8:D_5$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.17.4.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $Q_8:D_5$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.18.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_5:Q_{16}$ $2^{4} \cdot 5$ $C_2^2$ $2^{2}$ ✓
80.18.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_5:Q_{16}$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.20.4.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_4\times C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.20.4.a1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_4\times C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.20.4.a1.c1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_4\times C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.20.4.a1.d1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_4\times C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.20.4.a1.e1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_4\times C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.20.4.a1.f1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_4\times C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.21.4.d1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_2^2:C_{20}$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.21.4.d1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_2^2:C_{20}$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.22.4.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_4:C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.22.4.b1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ $C_4:C_{20}$ $2^{4} \cdot 5$ $C_4$ $2^{2}$ ✓
80.22.4.c1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_4:C_{20}$ $2^{4} \cdot 5$ $2^{2}$ $-$
80.22.4.c1.b1 $C_{20}$ $2^{2} \cdot 5$ ✓ $C_4:C_{20}$ $2^{4} \cdot 5$ $2^{2}$ $-$
Next   To download results, determine the number of results.