↑

Learn more

Refine search

Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central Non-trivial proper
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient Maximal quotient
Sort order Select

Results (5 matches)

  displayed columns for results
Label Subgroup Ambient Quotient
Name Order norm char cyc ab solv max perf cent Name Order Name Size cyc ab solv max
25920.a.25920.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ ✓ ✓ ✓ $C(2,3)$ $2^{6} \cdot 3^{4} \cdot 5$ $C(2,3)$ $2^{6} \cdot 3^{4} \cdot 5$
51840.a.25920.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ ✓ $\Sp(4,3)$ $2^{7} \cdot 3^{4} \cdot 5$ $C(2,3)$ $2^{6} \cdot 3^{4} \cdot 5$ ✓
51840.i.25920.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ ✓ $C_2\times C(2,3)$ $2^{7} \cdot 3^{4} \cdot 5$ $C(2,3)$ $2^{6} \cdot 3^{4} \cdot 5$ ✓
77760.a.25920.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ ✓ $\GU(4,2)$ $2^{6} \cdot 3^{5} \cdot 5$ $C(2,3)$ $2^{6} \cdot 3^{4} \cdot 5$ ✓
4199040.a.25920.a1 $C_3^3:S_3$ $2 \cdot 3^{4}$ ✓ ✓ ✓ $C_3^4:\Sp(4,3)$ $2^{7} \cdot 3^{8} \cdot 5$ $C(2,3)$ $2^{6} \cdot 3^{4} \cdot 5$
  displayed columns for results