Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10624222 | C2 | semidirect |
| 3. C5×#3743 | C2 | semidirect |
| 4. C3×Dic60 | C2 | semidirect |
| 5. C3×#6706 | C2 | semidirect |
| 6. #10623827 | C2 | semidirect |
| 7. #10623825 | C2 | semidirect |
| 26. Dic60 | D3 | semidirect |
| 27. #6706 | D3 | semidirect |
| 47. #3743 | D5 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #915 | semidirect |
| 204. C3×C5 | #918 | semidirect |
| 225. C32 | #4055 | semidirect |
| 245. C5 | #63811 | semidirect |
| 254. C3 | #91263 | semidirect |
| 255. C3 | #91274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624222 | 2 |
| #10624220 | 2 |
| C5×#3743 | 2 |
| C3×Dic60 | 2 |
| C3×#6706 | 2 |
| #10623827 | 2 |
| #10623825 | 2 |
| #91274 | 3 |
| #91263 | 3 |
| #63811 | 5 |