Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 3. C3×C4×Dic15 | C2 | semidirect |
| 4. #10623831 | C2 | semidirect |
| 13. C3×C4×D15 | C4 | semidirect |
| 17. C4×Dic15 | D3 | semidirect |
| 35. C4×C3⋊Dic3 | D5 | semidirect |
| 46. C4×D15 | Dic3 | semidirect |
| 97. C32×C5 | #117 | semidirect |
| 150. C3×C5 | #872 | semidirect |
| 151. C3×C5 | #926 | semidirect |
| 172. C32 | #4018 | semidirect |
| 187. C5 | #63855 | semidirect |
| 196. C3 | #91357 | semidirect |
| 197. C3 | #91386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C4×Dic15 | 2 |
| #10623831 | 2 |
| #10623829 | 2 |
| #91386 | 3 |
| #91357 | 3 |
| #63855 | 5 |