Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
554 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 108 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. C22×C5×D32 | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C2×C5×#625 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 6. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 13. C22×C3×C5×D3 | C22 | semidirect |
| 17. C2×C32×C4×C5 | C22 | semidirect |
| 18. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 19. C2×C3×C5×Dic3 | C22 | semidirect |
| 23. #63922 | C5 | direct (N × H) |
| 31. C2×C5×D12 | D3 | semidirect |
| 38. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 42. C2×C5×C3⋊D3 | D4 | semidirect |
| 50. C2×C3×C5×D3 | D4 | semidirect |
| 51. C2×C3×C5×D3 | D4 | semidirect |
| 57. C22×D32 | C2×C5 | semidirect |
| 58. C2×C3×D12 | C2×C5 | semidirect |
| 59. C2×#626 | C2×C5 | semidirect |
| 60. C2×#625 | C2×C5 | semidirect |
| 61. #3752 | C2×C5 | semidirect |
| 62. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 63. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 78. C22×C5×D3 | C2×D3 | semidirect |
| 82. C2×C3×C4×C5 | C2×D3 | semidirect |
| 83. C2×C3×C4×C5 | C2×D3 | semidirect |
| 90. C2×C5×Dic3 | C2×D3 | semidirect |
| 112. C22×C3×D3 | C22×C5 | semidirect |
| 116. C2×C32×C4 | C22×C5 | semidirect |
| 117. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 118. C2×C3×Dic3 | C22×C5 | semidirect |
| 152. C2×C5×D3 | D12 | semidirect |
| 153. C2×C5×D3 | #67 | semidirect |
| 169. C2×D12 | C5×D3 | semidirect |
| 176. (C2×D3)⋊C4 | C5×D3 | semidirect |
| 177. C32×C5 | #120 | semidirect |
| 190. C2×C4×C5 | D32 | semidirect |
| 194. C2×C3⋊D3 | C5×D4 | semidirect |
| 202. C2×C3×D3 | C5×D4 | semidirect |
| 203. C2×C3×D3 | C5×D4 | semidirect |
| 241. C22×D3 | C2×C5×D3 | semidirect |
| 245. C2×C3×C4 | C2×C5×D3 | semidirect |
| 246. C2×C3×C4 | C2×C5×D3 | semidirect |
| 253. C2×Dic3 | C2×C5×D3 | semidirect |
| 288. C3×C5 | #882 | semidirect |
| 289. C3×C5 | #937 | semidirect |
| 320. C2×D3 | C5×D12 | semidirect |
| 321. C2×D3 | C5×#67 | semidirect |
| 337. C32 | C5×#120 | semidirect |
| 350. C2×C4 | C5×D32 | semidirect |
| 369. C5 | #63922 | direct (N × H) |
| 388. C3 | C5×#882 | semidirect |
| 389. C3 | C5×#937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D32 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C5×#626 | 2 |
| C2×C5×#625 | 2 |
| C5×#3752 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#937 | 3 |
| C5×#882 | 3 |
| #63922 | 5 |