Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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. D3×Dic30 | C2 | semidirect |
| 3. #10623900 | C2 | semidirect |
| 4. C3×Dic60 | C2 | semidirect |
| 5. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 6. #10623808 | C2 | semidirect |
| 7. #10623804 | C2 | semidirect |
| 28. Dic60 | D3 | semidirect |
| 33. C5×ΓL(1,𝔽25) | D3 | semidirect |
| 49. C3×ΓL(1,𝔽25) | D5 | semidirect |
| 131. ΓL(1,𝔽25) | D15 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #909 | semidirect |
| 204. C3×C5 | #918 | semidirect |
| 225. C32 | #4055 | semidirect |
| 245. C5 | #63801 | semidirect |
| 254. C3 | #91263 | semidirect |
| 255. C3 | #91798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624197 | 2 |
| D3×Dic30 | 2 |
| #10623900 | 2 |
| C3×Dic60 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| #10623808 | 2 |
| #10623804 | 2 |
| #91798 | 3 |
| #91263 | 3 |
| #63801 | 5 |