Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
718 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 216 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. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C3×C5×#235 | C2 | semidirect |
| 3. C5×#3811 | C2 | semidirect |
| 4. C5×D3×D12 | C2 | semidirect |
| 5. C5×#3799 | C2 | semidirect |
| 7. C22×C5×C3⋊D3 | C22 | semidirect |
| 8. C2×C5×D32 | C22 | semidirect |
| 9. C2×C32×C4×C5 | C22 | semidirect |
| 10. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 11. C3×C5×#67 | C22 | semidirect |
| 12. C3×C5×D12 | C22 | semidirect |
| 13. C3×C4×C5×D3 | C22 | semidirect |
| 14. C3×C5×Dic6 | C22 | semidirect |
| 15. C5×#626 | C22 | semidirect |
| 16. C5×#624 | C22 | semidirect |
| 17. #64308 | C5 | direct (N × H) |
| 23. C5×#235 | D3 | semidirect |
| 35. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 36. C3×#235 | C2×C5 | semidirect |
| 37. #3811 | C2×C5 | semidirect |
| 38. D3×D12 | C2×C5 | semidirect |
| 39. #3799 | C2×C5 | semidirect |
| 48. C2×C3×C4×C5 | C2×D3 | semidirect |
| 50. C5×#67 | C2×D3 | semidirect |
| 55. C5×D12 | C2×D3 | semidirect |
| 57. C4×C5×D3 | C2×D3 | semidirect |
| 58. C5×Dic6 | C2×D3 | semidirect |
| 69. C22×C3⋊D3 | C22×C5 | semidirect |
| 70. C2×D32 | C22×C5 | semidirect |
| 71. C2×C32×C4 | C22×C5 | semidirect |
| 72. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 73. C3×#67 | C22×C5 | semidirect |
| 74. C3×D12 | C22×C5 | semidirect |
| 75. C3×C4×D3 | C22×C5 | semidirect |
| 76. C3×Dic6 | C22×C5 | semidirect |
| 77. #626 | C22×C5 | semidirect |
| 78. #624 | C22×C5 | semidirect |
| 98. #235 | C5×D3 | semidirect |
| 102. C32×C5 | H(5,𝔽2) | semidirect |
| 112. C2×C4×C5 | D32 | semidirect |
| 137. C2×C3×C4 | C2×C5×D3 | semidirect |
| 139. #67 | C2×C5×D3 | semidirect |
| 144. D12 | C2×C5×D3 | semidirect |
| 146. C4×D3 | C2×C5×D3 | semidirect |
| 147. Dic6 | C2×C5×D3 | semidirect |
| 165. C3×C5 | #1009 | semidirect |
| 184. C32 | C5×H(5,𝔽2) | semidirect |
| 194. C2×C4 | C5×D32 | semidirect |
| 203. C5 | #64308 | direct (N × H) |
| 212. C3 | C5×#1009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C3×C5×#235 | 2 |
| C5×#3811 | 2 |
| C5×D3×D12 | 2 |
| C5×#3799 | 2 |
| C5×#1009 | 3 |
| #64308 | 5 |