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. C5×#3795 | C2 | semidirect |
| 2. C5×#3746 | C2 | semidirect |
| 3. C3×C5×D24 | C2 | semidirect |
| 4. C3×C5×D3×C8 | C2 | semidirect |
| 5. C5×#3716 | C2 | semidirect |
| 15. #63807 | C5 | direct (N × H) |
| 24. C5×D24 | D3 | semidirect |
| 26. C5×D3×C8 | D3 | semidirect |
| 33. #3795 | C2×C5 | semidirect |
| 34. #3746 | C2×C5 | semidirect |
| 35. C3×D24 | C2×C5 | semidirect |
| 36. C3×D3×C8 | C2×C5 | semidirect |
| 37. #3716 | C2×C5 | semidirect |
| 91. D24 | C5×D3 | semidirect |
| 93. D3×C8 | C5×D3 | semidirect |
| 94. C32×C5 | #135 | semidirect |
| 145. C3×C5 | #904 | semidirect |
| 146. C3×C5 | #912 | semidirect |
| 162. C32 | C5×#135 | semidirect |
| 177. C5 | #63807 | direct (N × H) |
| 184. C3 | C5×#904 | semidirect |
| 185. C3 | C5×#912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3795 | 2 |
| C5×#3746 | 2 |
| C3×C5×D24 | 2 |
| C3×C5×D3×C8 | 2 |
| C5×#3716 | 2 |
| C5×#912 | 3 |
| C5×#904 | 3 |
| #63807 | 5 |