↑

Learn more

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 125 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
400.81.400.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
800.287.400.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{20}:C_{40}$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
800.287.400.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{20}:C_{40}$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
800.289.400.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}:C_{40}$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
800.296.400.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{10}:C_{80}$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
800.297.400.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{20}.C_{40}$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
800.315.400.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{10}^2:C_8$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
800.813.400.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{10}^2:C_8$ $2^{5} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
1200.285.400.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{60}.D_{10}$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
1200.390.400.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{10}:C_{120}$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
1200.438.400.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{30}:C_{40}$ $2^{4} \cdot 3 \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$ ✓
1600.1717.400.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{40}:C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1719.400.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{40}:C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1720.400.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{40}:C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1721.400.d1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{40}:C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1722.400.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}:C_{80}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1722.400.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}:C_{80}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1723.400.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{40}.C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1723.400.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{40}.C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1724.400.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}:C_{80}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1725.400.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{40}.C_{40}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1762.400.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{10}:C_{160}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1763.400.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{20}.C_{80}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1788.400.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2.C_4^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1789.400.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2.\OD_{16}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1792.400.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2.\OD_{16}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1798.400.e1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1799.400.e1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1813.400.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{10}^2:C_{16}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1817.400.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_5\times C_{40}.D_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.1825.400.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2.\OD_{16}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4533.400.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4533.400.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4536.400.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4536.400.h1 $C_4$ $2^{2}$ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4538.400.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4538.400.b1.b1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4538.400.c1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4538.400.c1.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4538.400.d1.a1 $C_4$ $2^{2}$ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4538.400.d1.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{20}^2.C_4$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4623.400.d1.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4623.400.d1.b1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4623.400.d1.c1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4623.400.d1.d1 $C_2^2$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4623.400.e1.a1 $C_4$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4623.400.e1.b1 $C_4$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4636.400.d1 $C_4$ $2^{2}$ ✓ ✓ $C_{20}^2.C_2^2$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4709.400.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2:C_{16}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
1600.4709.400.c1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{10}^2:C_{16}$ $2^{6} \cdot 5^{2}$ $C_{10}:C_{40}$ $2^{4} \cdot 5^{2}$
Next   displayed columns for results