Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 268 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. #10624193 | C2 | semidirect |
| 3. #10623910 | C2 | semidirect |
| 4. C3×#6715 | C2 | semidirect |
| 5. #10623809 | C2 | semidirect |
| 6. #10623801 | C2 | semidirect |
| 7. D3×C3⋊#168 | C2 | semidirect |
| 24. C5×#237 | D3 | semidirect |
| 31. #6715 | D3 | semidirect |
| 45. C3×#237 | D5 | semidirect |
| 120. #237 | D15 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #912 | semidirect |
| 208. C3×C5 | #950 | semidirect |
| 230. C32 | #4096 | semidirect |
| 252. C5 | #63933 | semidirect |
| 261. C3 | #91493 | semidirect |
| 262. 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 |
| #10624193 | 2 |
| #10623910 | 2 |
| C3×#6715 | 2 |
| #10623809 | 2 |
| #10623801 | 2 |
| D3×C3⋊#168 | 2 |
| #91839 | 3 |
| #91493 | 3 |
| #63933 | 5 |