Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 136 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×C5×Dic3 | C2 | semidirect |
| 4. C5×Dic3⋊Dic3 | C2 | semidirect |
| 13. C3×C4×C5×D3 | C4 | semidirect |
| 14. #63855 | C5 | direct (N × H) |
| 25. C4×C5×Dic3 | D3 | semidirect |
| 35. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 36. C3×C4×Dic3 | C2×C5 | semidirect |
| 37. Dic3⋊Dic3 | C2×C5 | semidirect |
| 52. C4×C5×D3 | Dic3 | semidirect |
| 68. C3×C4×D3 | C4×C5 | semidirect |
| 96. C4×Dic3 | C5×D3 | semidirect |
| 97. C32×C5 | #117 | semidirect |
| 133. C4×D3 | C5×Dic3 | semidirect |
| 150. C3×C5 | #872 | semidirect |
| 151. C3×C5 | #926 | semidirect |
| 172. C32 | C5×#117 | semidirect |
| 187. C5 | #63855 | direct (N × H) |
| 196. C3 | C5×#872 | semidirect |
| 197. C3 | C5×#926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#926 | 3 |
| C5×#872 | 3 |
| #63855 | 5 |