Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 80 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. C5×#3795 | C2 | semidirect |
| 3. C5×#3754 | C2 | semidirect |
| 4. C3×C5×#213 | C2 | semidirect |
| 5. C5×#3719 | C2 | semidirect |
| 6. C5×#3715 | C2 | semidirect |
| 7. C5×D3×C3⋊C8 | C2 | semidirect |
| 21. #63933 | C5 | direct (N × H) |
| 24. C5×#237 | D3 | semidirect |
| 33. C5×#213 | D3 | semidirect |
| 45. C3×#237 | C2×C5 | semidirect |
| 46. #3795 | C2×C5 | semidirect |
| 47. #3754 | C2×C5 | semidirect |
| 48. C3×#213 | C2×C5 | semidirect |
| 49. #3719 | C2×C5 | semidirect |
| 50. #3715 | C2×C5 | semidirect |
| 51. D3×C3⋊C8 | C2×C5 | semidirect |
| 120. #237 | C5×D3 | semidirect |
| 129. #213 | C5×D3 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #912 | semidirect |
| 208. C3×C5 | #950 | semidirect |
| 230. C32 | C5×#135 | semidirect |
| 252. C5 | #63933 | direct (N × H) |
| 261. C3 | C5×#912 | semidirect |
| 262. C3 | C5×#950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#237 | 2 |
| C5×#3795 | 2 |
| C5×#3754 | 2 |
| C3×C5×#213 | 2 |
| C5×#3719 | 2 |
| C5×#3715 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C5×#950 | 3 |
| C5×#912 | 3 |
| #63933 | 5 |