Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×C5×D3×D4 | C2 | semidirect |
| 2. C5×D3×D12 | C2 | semidirect |
| 3. C5×#3753 | C2 | semidirect |
| 4. C3×C5×#213 | C2 | semidirect |
| 5. C5×#3714 | C2 | semidirect |
| 6. C5×#3713 | C2 | semidirect |
| 7. C5×D3×C3⋊C8 | C2 | semidirect |
| 12. C32×C5×D4 | C22 | semidirect |
| 13. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C3×C5×D12 | C22 | semidirect |
| 16. C3×C5×D12 | C22 | semidirect |
| 19. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 21. D3×#213 | C5 | direct (N × H) |
| 24. C5×D3×D4 | D3 | semidirect |
| 33. C5×#213 | D3 | direct (N × H) |
| 47. C3×D3×D4 | C2×C5 | semidirect |
| 48. D3×D12 | C2×C5 | semidirect |
| 49. #3753 | C2×C5 | semidirect |
| 50. C3×#213 | C2×C5 | semidirect |
| 51. #3714 | C2×C5 | semidirect |
| 52. #3713 | C2×C5 | semidirect |
| 53. D3×C3⋊C8 | C2×C5 | semidirect |
| 62. C3×C5×D4 | C2×D3 | semidirect |
| 63. C3×C5×D4 | C2×D3 | semidirect |
| 71. C5×D12 | C2×D3 | semidirect |
| 72. C5×D12 | C2×D3 | semidirect |
| 78. C5×C3⋊C8 | C2×D3 | semidirect |
| 86. C3×C5×D3 | D8 | semidirect |
| 96. C32×D4 | C22×C5 | semidirect |
| 97. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 99. C3×D12 | C22×C5 | semidirect |
| 100. C3×D12 | C22×C5 | semidirect |
| 103. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 104. C3×C3⋊C8 | C22×C5 | semidirect |
| 128. D3×D4 | C5×D3 | semidirect |
| 137. #213 | C5×D3 | direct (N × H) |
| 141. C32×C5 | C2×D8 | semidirect |
| 149. C5×D4 | D32 | semidirect |
| 177. C5×D3 | #213 | direct (N × H) |
| 186. C3×D4 | C2×C5×D3 | semidirect |
| 187. C3×D4 | C2×C5×D3 | semidirect |
| 195. D12 | C2×C5×D3 | semidirect |
| 196. D12 | C2×C5×D3 | semidirect |
| 202. C3⋊C8 | C2×C5×D3 | semidirect |
| 217. C3×D3 | C5×D8 | semidirect |
| 226. C3×C5 | D3×D8 | semidirect |
| 227. C3×C5 | C2×#213 | semidirect |
| 255. C32 | C2×C5×D8 | semidirect |
| 263. D4 | C5×D32 | semidirect |
| 281. D3 | C5×#213 | direct (N × H) |
| 282. C5 | D3×#213 | direct (N × H) |
| 293. C3 | C5×D3×D8 | semidirect |
| 294. C3 | C2×C5×#213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×D4 | 2 |
| C5×D3×D12 | 2 |
| C5×#3753 | 2 |
| C3×C5×#213 | 2 |
| C5×#3714 | 2 |
| C5×#3713 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C2×C5×#213 | 3 |
| C5×D3×D8 | 3 |
| D3×#213 | 5 |