Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 274 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⋊D15 | 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. #10623828 | C2 | semidirect |
| 4. C5×Dic3⋊Dic3 | C2 | semidirect |
| 6. C3×Dic3⋊Dic5 | C2 | semidirect |
| 7. C3×#6668 | C2 | semidirect |
| 24. Dic3⋊Dic5 | D3 | semidirect |
| 25. #6668 | D3 | semidirect |
| 47. Dic3⋊Dic3 | D5 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #898 | semidirect |
| 200. C3×C5 | #898 | semidirect |
| 231. C32 | #4044 | semidirect |
| 251. C5 | #63848 | semidirect |
| 263. C3 | #91337 | semidirect |
| 264. C3 | #91345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623828 | 2 |
| #10623813 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| #10623772 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6668 | 2 |
| #91345 | 3 |
| #91337 | 3 |
| #63848 | 5 |