↑

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 78 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
480.38.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.48.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.49.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.129.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.135.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.143.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.382.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\SD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.383.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.393.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\SD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.394.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:Q_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.396.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:Q_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.397.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.405.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}.(S_3\times D_4)$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.408.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{15}:(C_4\times Q_8)$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.420.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{15}:(C_4\times Q_8)$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.435.2.c1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.444.2.c1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.451.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.452.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.459.2.c1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.461.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.497.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $(C_3\times D_{10}):Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.500.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.531.2.f1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{10}.(S_3\times D_4)$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.747.2.c1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.748.2.c1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{60}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.754.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.757.2.f1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $(C_2\times C_{30}):Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.764.2.g1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_5\times C_2^3.D_6$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.766.2.c1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_3:(Q_8\times C_{20})$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.767.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{60}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.767.2.d1.b1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{60}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.775.2.g1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_5\times D_6:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.776.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.781.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{40}:D_6$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.784.2.a1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}:Q_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.784.2.a1.b1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{30}:Q_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.788.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{20}.D_{12}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.803.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.812.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:\SD_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.815.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.822.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{30}:Q_{16}$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.823.2.c1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.830.2.b1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1073.2.c1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1075.2.e1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{20}:D_6$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1076.2.d1.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{20}.D_6$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1082.2.c1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{30}:Q_8$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1085.2.e1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $D_{60}:C_2^2$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
480.1150.2.a1 $C_{30}:Q_8$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $C_{60}.C_2^3$ $2^{5} \cdot 3 \cdot 5$ $C_2$ $2$ ✓
Next   displayed columns for results