Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
406 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×D3×Dic15 | C2 | semidirect |
| 3. C4×C3⋊Dic15 | C2 | semidirect |
| 4. C3×C4⋊Dic15 | C2 | semidirect |
| 5. (C2×D3)⋊Dic15 | C2 | semidirect |
| 13. C3×C5×D12 | C4 | semidirect |
| 21. C4⋊Dic15 | D3 | semidirect |
| 30. C2×C3×C5×D3 | C2×C4 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 33. C3⋊Dic15 | D4 | semidirect |
| 55. C5×D12 | Dic3 | semidirect |
| 74. C3×D12 | Dic5 | semidirect |
| 84. C2×C5×D3 | C2×Dic3 | semidirect |
| 86. C3×C4×C5 | C4×D3 | semidirect |
| 87. C3×C4×C5 | C2×Dic3 | semidirect |
| 107. C32×C5 | C4×D4 | semidirect |
| 118. C2×C3×D3 | C2×Dic5 | semidirect |
| 119. C32×C4 | C2×Dic5 | semidirect |
| 150. D12 | Dic15 | semidirect |
| 156. C4×C5 | D3×Dic3 | semidirect |
| 170. C3×C5 | #893 | semidirect |
| 171. C3×C5 | D4×Dic3 | semidirect |
| 180. C2×D3 | C2×Dic15 | semidirect |
| 183. C3×C4 | D3×Dic5 | semidirect |
| 184. C3×C4 | C2×Dic15 | semidirect |
| 196. C32 | D4×Dic5 | semidirect |
| 215. C5 | #63898 | semidirect |
| 223. C4 | D3×Dic15 | semidirect |
| 225. C3 | #91435 | semidirect |
| 226. C3 | D4×Dic15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D12 | 2 |
| C2×D3×Dic15 | 2 |
| C4×C3⋊Dic15 | 2 |
| C3×C4⋊Dic15 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| D4×Dic15 | 3 |
| #91435 | 3 |
| #63898 | 5 |