Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #10623832 | C2 | semidirect |
| 5. #10623831 | C2 | semidirect |
| 6. #10623831 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #879 | semidirect |
| 200. C3×C5 | #879 | semidirect |
| 231. C32 | #4025 | semidirect |
| 251. C5 | #63956 | semidirect |
| 263. C3 | #91530 | semidirect |
| 264. C3 | #91531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3757 | 2 |
| C3×#6719 | 2 |
| #10623832 | 2 |
| #10623831 | 2 |
| #10623828 | 2 |
| #91531 | 3 |
| #91530 | 3 |
| #63956 | 5 |