Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 88 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. C5×#3746 | C2 | semidirect |
| 3. C3×C5×Dic12 | C2 | semidirect |
| 5. C5×#3719 | C2 | semidirect |
| 15. D3×Dic12 | C5 | direct (N × H) |
| 25. C5×Dic12 | D3 | direct (N × H) |
| 34. #3746 | C2×C5 | semidirect |
| 35. C3×Dic12 | C2×C5 | semidirect |
| 37. #3719 | C2×C5 | semidirect |
| 57. C3×C5×D3 | Q16 | semidirect |
| 91. Dic12 | C5×D3 | direct (N × H) |
| 93. C32×C5 | C2×Q16 | semidirect |
| 111. C5×D3 | Dic12 | direct (N × H) |
| 134. C3×D3 | C5×Q16 | semidirect |
| 141. C3×C5 | C2×Dic12 | semidirect |
| 142. C3×C5 | D3×Q16 | semidirect |
| 157. C32 | C2×C5×Q16 | semidirect |
| 169. D3 | C5×Dic12 | direct (N × H) |
| 170. C5 | D3×Dic12 | direct (N × H) |
| 177. C3 | C2×C5×Dic12 | semidirect |
| 178. C3 | C5×D3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Dic6 | 2 |
| C5×#3746 | 2 |
| C3×C5×Dic12 | 2 |
| C3×C5×D3×C8 | 2 |
| C5×#3719 | 2 |
| C5×D3×Q16 | 3 |
| C2×C5×Dic12 | 3 |
| D3×Dic12 | 5 |