Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. #10624198 | C2 | semidirect |
| 3. #10623899 | C2 | semidirect |
| 4. C3×Dic60 | C2 | semidirect |
| 5. C3×C5×#204 | C2 | semidirect |
| 6. #10623807 | C2 | semidirect |
| 7. #10623802 | C2 | semidirect |
| 29. Dic60 | D3 | semidirect |
| 33. C5×#204 | D3 | semidirect |
| 49. C3×#204 | D5 | semidirect |
| 128. #204 | D15 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #915 | semidirect |
| 204. C3×C5 | #918 | semidirect |
| 225. C32 | #4061 | semidirect |
| 245. C5 | #63811 | semidirect |
| 254. C3 | #91280 | semidirect |
| 255. C3 | #91804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624198 | 2 |
| #10624196 | 2 |
| #10623899 | 2 |
| C3×Dic60 | 2 |
| C3×C5×#204 | 2 |
| #10623807 | 2 |
| #10623802 | 2 |
| #91804 | 3 |
| #91280 | 3 |
| #63811 | 5 |