Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 1. C3×C5×#237 | C2 | semidirect |
| 2. #10624197 | C2 | semidirect |
| 3. #10623909 | C2 | semidirect |
| 4. C3×#6716 | C2 | semidirect |
| 5. #10623807 | C2 | semidirect |
| 6. #10623806 | C2 | semidirect |
| 7. D3×C3⋊#168 | C2 | semidirect |
| 24. C5×#237 | D3 | semidirect |
| 28. #6716 | D3 | semidirect |
| 45. C3×#237 | D5 | semidirect |
| 120. #237 | D15 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 208. C3×C5 | #916 | semidirect |
| 209. C3×C5 | #950 | semidirect |
| 231. C32 | #4096 | semidirect |
| 254. C5 | #63935 | semidirect |
| 263. C3 | #91495 | semidirect |
| 264. C3 | #91839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#237 | 2 |
| #10624197 | 2 |
| #10623909 | 2 |
| C3×#6716 | 2 |
| #10623807 | 2 |
| #10623806 | 2 |
| D3×C3⋊#168 | 2 |
| #91839 | 3 |
| #91495 | 3 |
| #63935 | 5 |