Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10624227 | C2 | semidirect |
| 2. C5×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×D120 | C2 | semidirect |
| 4. #10623822 | C2 | semidirect |
| 8. C3×D60 | C22 | semidirect |
| 10. C32×C5×C8 | C22 | semidirect |
| 11. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 14. D120 | D3 | semidirect |
| 26. C8×C3⋊D3 | D5 | semidirect |
| 30. D60 | C2×D3 | semidirect |
| 36. C3×C5×C8 | C2×D3 | semidirect |
| 41. C5×C3⋊D3 | D8 | semidirect |
| 51. C32×C8 | C2×D5 | semidirect |
| 52. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 68. C32×C5 | C2×D8 | semidirect |
| 74. C5×C8 | D32 | semidirect |
| 94. C3×C8 | D3×D5 | semidirect |
| 103. C3⋊D3 | D40 | semidirect |
| 110. C3×C5 | D3×D8 | semidirect |
| 123. C32 | C2×D40 | semidirect |
| 129. C8 | (C3⋊D3)⋊D5 | semidirect |
| 136. C5 | #63797 | semidirect |
| 143. C3 | D3×D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624227 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×D120 | 2 |
| #10623822 | 2 |
| D3×D40 | 3 |
| #63797 | 5 |