Finite Group DatabasebetaFinite Group DatabasebetaOrder 7200.
4312 conjugacy classes of subgroups; only the 460 normal subgroups are shown.
This group has 4312 conjugacy classes of subgroups — too many to draw. Only its 460 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×C5⋊D5 |
| commutator, cosocle | C2×C32×C52 | C24 |
| Frattini | C2 | C2×D32×C5⋊D5 |
| Fitting, socle | C22×C32×C52 | C23 |
| hypocenter | C32×C52 | C22×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊(C5⋊D5) | 2 |
| C2×#14268293 | 2 |
| C2×C3×#10597115 | 2 |
| C2×C52×#624 | 2 |
| #72231388 | 2 |
| C2×D3×C4⋊(C5⋊D5) | 3 |
| C22×C3⋊D3×C5⋊D5 | 2 |
| C2×#10624031 | 5 |