Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator, Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C22×C3×C5×D3 | C22 |
| hypocenter | C32×C5 | #126 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10623832 | C2 | semidirect |
| 2. #10623814 | C2 | semidirect |
| 5. #10623774 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 32. Dic3×Dic5 | D3 | semidirect |
| 127. C32×C5 | #126 | semidirect |
| 196. C3×C5 | #876 | semidirect |
| 197. C3×C5 | #879 | semidirect |
| 226. C32 | #4025 | semidirect |
| 245. C5 | #63859 | semidirect |
| 257. C3 | #91372 | semidirect |
| 258. C3 | #91531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623832 | 2 |
| #10623814 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| #10623774 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| C3×Dic3×Dic5 | 2 |
| #91531 | 3 |
| #91372 | 3 |
| #63859 | 5 |