Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
998 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 175 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×(C3⋊D3)⋊D5 | C2 | semidirect |
| 2. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×C3×D60 | C2 | semidirect |
| 4. C2×C3×C4×D15 | C2 | semidirect |
| 5. C2×#67156 | C2 | semidirect |
| 6. #10624226 | C2 | direct (N × H) |
| 9. C22×C5×C3⋊D3 | C22 | semidirect |
| 11. C22×C3×D15 | C22 | semidirect |
| 13. C2×(C3⋊D3)⋊D5 | C22 | semidirect |
| 14. C2×C32×C4×C5 | C22 | semidirect |
| 15. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 16. C2×C3×Dic15 | C22 | semidirect |
| 17. C3×D60 | C22 | semidirect |
| 18. C3×C4×D15 | C22 | semidirect |
| 19. #67156 | C22 | semidirect |
| 23. C2×D60 | D3 | semidirect |
| 24. C2×C4×D15 | D3 | semidirect |
| 36. C2×C5×C3⋊D3 | C23 | semidirect |
| 38. C2×C3×D15 | D4 | semidirect |
| 40. C2×C3×D15 | C23 | semidirect |
| 42. C32×C4×C5 | C23 | semidirect |
| 43. C3×Dic15 | C23 | semidirect |
| 46. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 52. C22×D15 | C2×D3 | semidirect |
| 63. C2×C3×C4×C5 | C2×D3 | semidirect |
| 64. C2×C3×C4×C5 | C2×D3 | semidirect |
| 65. C2×Dic15 | C2×D3 | semidirect |
| 66. D60 | C2×D3 | semidirect |
| 67. C4×D15 | C2×D3 | semidirect |
| 78. C2×C32×C5 | C2×D4 | semidirect |
| 82. C3×D15 | C2×D4 | semidirect |
| 89. C22×C3⋊D3 | C2×D5 | semidirect |
| 94. C2×C32×C4 | C2×D5 | semidirect |
| 95. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 104. C2×D15 | D12 | semidirect |
| 106. C2×D15 | C22×D3 | semidirect |
| 120. C3×C4×C5 | C22×D3 | semidirect |
| 121. C3×C4×C5 | C22×D3 | semidirect |
| 122. Dic15 | C22×D3 | semidirect |
| 137. C32×C5 | C22×D4 | semidirect |
| 144. C2×C4×C5 | D32 | semidirect |
| 151. C2×C3⋊D3 | C22×D5 | semidirect |
| 157. C32×C4 | C22×D5 | semidirect |
| 162. C2×C3×C5 | C2×D12 | semidirect |
| 163. C2×C3×C5 | D3×D4 | semidirect |
| 167. D15 | C2×D12 | semidirect |
| 188. C2×C3×C4 | D3×D5 | semidirect |
| 189. C2×C3×C4 | D3×D5 | semidirect |
| 206. C4×C5 | C2×D32 | semidirect |
| 208. C2×C32 | D4×D5 | semidirect |
| 220. C3×C5 | C22×D12 | semidirect |
| 221. C3×C5 | C2×D3×D4 | semidirect |
| 243. C3×C4 | C2×D3×D5 | semidirect |
| 244. C3×C4 | C2×D3×D5 | semidirect |
| 247. C2×C5 | D3×D12 | semidirect |
| 251. C32 | C2×D4×D5 | semidirect |
| 262. C2×C4 | (C3⋊D3)⋊D5 | semidirect |
| 267. C2×C3 | D5×D12 | semidirect |
| 268. C2×C3 | #6777 | semidirect |
| 276. C5 | C2×D3×D12 | semidirect |
| 286. C4 | C2×(C3⋊D3)⋊D5 | semidirect |
| 288. C3 | C2×D5×D12 | semidirect |
| 289. C3 | C2×#6777 | semidirect |
| 293. C2 | #10624226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊D5 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C3×D60 | 2 |
| C2×C3×C4×D15 | 2 |
| C2×#67156 | 2 |
| #10624226 | 2 |
| C2×#6777 | 3 |
| C2×D5×D12 | 3 |
| C2×D3×D12 | 5 |