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. C5×#3799 | C2 | semidirect |
| 2. C5×#3795 | C2 | semidirect |
| 3. C5×#3744 | C2 | semidirect |
| 4. C3×C5×#204 | C2 | semidirect |
| 5. C3×C5×D3×C8 | C2 | semidirect |
| 6. C5×#3719 | C2 | semidirect |
| 7. C5×#3714 | C2 | semidirect |
| 21. #63806 | C5 | direct (N × H) |
| 35. C5×#204 | D3 | semidirect |
| 36. C5×D3×C8 | D3 | semidirect |
| 45. #3799 | C2×C5 | semidirect |
| 46. #3795 | C2×C5 | semidirect |
| 47. #3744 | C2×C5 | semidirect |
| 48. C3×#204 | C2×C5 | semidirect |
| 49. C3×D3×C8 | C2×C5 | semidirect |
| 50. #3719 | C2×C5 | semidirect |
| 51. #3714 | C2×C5 | semidirect |
| 131. #204 | C5×D3 | semidirect |
| 132. D3×C8 | C5×D3 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #904 | semidirect |
| 208. C3×C5 | #916 | semidirect |
| 230. C32 | C5×#135 | semidirect |
| 252. C5 | #63806 | direct (N × H) |
| 261. C3 | C5×#904 | semidirect |
| 262. C3 | C5×#916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3799 | 2 |
| C5×#3795 | 2 |
| C5×#3744 | 2 |
| C3×C5×#204 | 2 |
| C3×C5×D3×C8 | 2 |
| C5×#3719 | 2 |
| C5×#3714 | 2 |
| C5×#916 | 3 |
| C5×#904 | 3 |
| #63806 | 5 |