Finite Group DatabasebetaFinite Group DatabasebetaOrder 27900.
352 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D32×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C32×C31 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C31 | C22×C5 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C5 | |
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 |
|---|---|
| C5×C3⋊D3×ΓL(1,𝔽32) | 2 |
| C3×C5×D3×ΓL(1,𝔽32) | 2 |
| C2×C5×D3×ΓL(1,𝔽32) | 3 |
| C5×D32×C31 | 5 |
| D32×ΓL(1,𝔽32) | 5 |
| C52×D32 | 31 |