Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 266 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. #10624221 | C2 | semidirect |
| 2. C5×#3746 | C2 | semidirect |
| 3. C3×D120 | C2 | semidirect |
| 4. C3×C8×D15 | C2 | semidirect |
| 5. #10623823 | C2 | semidirect |
| 18. D120 | D3 | semidirect |
| 19. C8×D15 | D3 | semidirect |
| 34. #3746 | D5 | semidirect |
| 94. C32×C5 | #135 | semidirect |
| 145. C3×C5 | #904 | semidirect |
| 146. C3×C5 | #912 | semidirect |
| 162. C32 | #4065 | semidirect |
| 177. C5 | #63807 | semidirect |
| 184. C3 | #91271 | semidirect |
| 185. C3 | #91277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624221 | 2 |
| C5×#3746 | 2 |
| C3×D120 | 2 |
| C3×C8×D15 | 2 |
| #10623823 | 2 |
| #91277 | 3 |
| #91271 | 3 |
| #63807 | 5 |