Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 2. C2×C5×#634 | C2 | semidirect |
| 3. C32×C5×M16 | C2 | semidirect |
| 4. C5×#3746 | C2 | semidirect |
| 5. C5×#3744 | C2 | semidirect |
| 16. #64118 | C5 | direct (N × H) |
| 19. C3×C5×M16 | D3 | semidirect |
| 30. C2×#634 | C2×C5 | semidirect |
| 31. C32×M16 | C2×C5 | semidirect |
| 32. #3746 | C2×C5 | semidirect |
| 33. #3744 | C2×C5 | semidirect |
| 51. C5×M16 | C3⋊D3 | semidirect |
| 69. C3×M16 | C5×D3 | semidirect |
| 72. C32×C5 | #137 | semidirect |
| 114. M16 | C5×C3⋊D3 | semidirect |
| 115. C3×C5 | #909 | semidirect |
| 125. C32 | C5×#137 | semidirect |
| 138. C5 | #64118 | direct (N × H) |
| 145. C3 | C5×#909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C2×C5×#634 | 2 |
| C32×C5×M16 | 2 |
| C5×#3746 | 2 |
| C5×#3744 | 2 |
| C5×#909 | 3 |
| #64118 | 5 |