Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 266 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×#239 | C2 | semidirect |
| 2. C5×#3795 | C2 | semidirect |
| 3. C5×#3756 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C5×#3716 | C2 | semidirect |
| 6. C5×#3713 | C2 | semidirect |
| 7. C5×D3×C3⋊C8 | C2 | semidirect |
| 21. #63947 | C5 | direct (N × H) |
| 23. C5×#239 | D3 | semidirect |
| 30. C5×#215 | D3 | semidirect |
| 45. C3×#239 | C2×C5 | semidirect |
| 46. #3795 | C2×C5 | semidirect |
| 47. #3756 | C2×C5 | semidirect |
| 48. C3×#215 | C2×C5 | semidirect |
| 49. #3716 | C2×C5 | semidirect |
| 50. #3713 | C2×C5 | semidirect |
| 51. D3×C3⋊C8 | C2×C5 | semidirect |
| 119. #239 | C5×D3 | semidirect |
| 126. #215 | C5×D3 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 206. C3×C5 | #916 | semidirect |
| 207. C3×C5 | #950 | semidirect |
| 229. C32 | C5×#135 | semidirect |
| 250. C5 | #63947 | direct (N × H) |
| 259. C3 | C5×#916 | semidirect |
| 260. 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×#239 | 2 |
| C5×#3795 | 2 |
| C5×#3756 | 2 |
| C3×C5×#215 | 2 |
| C5×#3716 | 2 |
| C5×#3713 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C5×#950 | 3 |
| C5×#916 | 3 |
| #63947 | 5 |