Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 326 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×#3802 | C2 | semidirect |
| 2. C5×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×D24 | C2 | semidirect |
| 4. C5×#3713 | C2 | semidirect |
| 8. C3×C5×D12 | C22 | semidirect |
| 10. C32×C5×C8 | C22 | semidirect |
| 11. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 12. #63797 | C5 | direct (N × H) |
| 16. C5×D24 | D3 | semidirect |
| 25. #3802 | C2×C5 | semidirect |
| 26. C8×C3⋊D3 | C2×C5 | semidirect |
| 27. C3×D24 | C2×C5 | semidirect |
| 28. #3713 | C2×C5 | semidirect |
| 32. C5×D12 | C2×D3 | semidirect |
| 36. C3×C5×C8 | C2×D3 | semidirect |
| 41. C5×C3⋊D3 | D8 | semidirect |
| 49. C3×D12 | C22×C5 | semidirect |
| 51. C32×C8 | C22×C5 | semidirect |
| 52. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 65. D24 | C5×D3 | semidirect |
| 68. C32×C5 | C2×D8 | semidirect |
| 74. C5×C8 | D32 | semidirect |
| 90. D12 | C2×C5×D3 | semidirect |
| 94. C3×C8 | C2×C5×D3 | semidirect |
| 103. C3⋊D3 | C5×D8 | semidirect |
| 110. C3×C5 | D3×D8 | semidirect |
| 123. C32 | C2×C5×D8 | semidirect |
| 129. C8 | C5×D32 | semidirect |
| 136. C5 | #63797 | direct (N × H) |
| 143. C3 | C5×D3×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3802 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×D24 | 2 |
| C5×#3713 | 2 |
| C5×D3×D8 | 3 |
| #63797 | 5 |