Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 114 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×Dic3×D15 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 5. #10623811 | C2 | semidirect |
| 11. C3×D60 | C4 | semidirect |
| 25. C4×C5×Dic3 | D3 | semidirect |
| 30. C2×C3×D15 | C2×C4 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 34. C3×C5×Dic3 | D4 | semidirect |
| 39. C3×C4×Dic3 | D5 | semidirect |
| 51. D60 | Dic3 | direct (N × H) |
| 80. C2×D15 | C2×Dic3 | semidirect |
| 87. C3×C4×C5 | C4×D3 | semidirect |
| 88. C3×C4×C5 | C2×Dic3 | semidirect |
| 93. C5×Dic3 | D12 | semidirect |
| 104. C4×Dic3 | D15 | semidirect |
| 105. C32×C5 | C4×D4 | semidirect |
| 117. C32×C4 | C4×D5 | semidirect |
| 120. C3×Dic3 | D20 | semidirect |
| 155. C4×C5 | D3×Dic3 | semidirect |
| 167. C3×C5 | C4×D12 | semidirect |
| 168. C3×C5 | D4×Dic3 | semidirect |
| 181. C3×C4 | D5×Dic3 | semidirect |
| 182. C3×C4 | C4×D15 | semidirect |
| 187. Dic3 | D60 | direct (N × H) |
| 192. C32 | C4×D20 | semidirect |
| 211. C5 | Dic3×D12 | semidirect |
| 219. C4 | Dic3×D15 | semidirect |
| 221. C3 | Dic3×D20 | semidirect |
| 222. C3 | C4×D60 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×Dic3×D15 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C3×C4×C5×Dic3 | 2 |
| #10623811 | 2 |
| C4×D60 | 3 |
| Dic3×D20 | 3 |
| Dic3×D12 | 5 |