Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 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×Q8 | C2 | semidirect |
| 3. C5×#3755 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C5×#3717 | C2 | semidirect |
| 6. C5×#3715 | C2 | semidirect |
| 7. C5×D3×C3⋊C8 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 17. C3×C5×Dic6 | C22 | semidirect |
| 19. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 21. D3×#215 | C5 | direct (N × H) |
| 23. C5×D3×Q8 | D3 | semidirect |
| 32. C5×#215 | D3 | direct (N × H) |
| 46. C3×D3×Q8 | C2×C5 | semidirect |
| 48. #3755 | C2×C5 | semidirect |
| 49. C3×#215 | C2×C5 | semidirect |
| 50. #3717 | C2×C5 | semidirect |
| 51. #3715 | C2×C5 | semidirect |
| 52. D3×C3⋊C8 | C2×C5 | semidirect |
| 58. C3×C5×Q8 | C2×D3 | semidirect |
| 59. C3×C5×Q8 | C2×D3 | semidirect |
| 72. C5×Dic6 | C2×D3 | semidirect |
| 77. C5×C3⋊C8 | C2×D3 | semidirect |
| 83. C3×C5×D3 | SD16 | semidirect |
| 92. C32×Q8 | C22×C5 | semidirect |
| 98. C3×Dic6 | C22×C5 | semidirect |
| 100. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 101. C3×C3⋊C8 | C22×C5 | semidirect |
| 122. D3×Q8 | C5×D3 | semidirect |
| 131. #215 | C5×D3 | direct (N × H) |
| 136. C32×C5 | C2×SD16 | semidirect |
| 140. C5×Q8 | D32 | semidirect |
| 166. C5×D3 | #215 | direct (N × H) |
| 172. C3×Q8 | C2×C5×D3 | semidirect |
| 173. C3×Q8 | C2×C5×D3 | semidirect |
| 186. Dic6 | C2×C5×D3 | semidirect |
| 191. C3⋊C8 | C2×C5×D3 | semidirect |
| 203. C3×D3 | C5×SD16 | semidirect |
| 212. C3×C5 | D3×SD16 | semidirect |
| 213. C3×C5 | C2×#215 | semidirect |
| 237. C32 | C2×C5×SD16 | semidirect |
| 241. Q8 | C5×D32 | semidirect |
| 258. D3 | C5×#215 | direct (N × H) |
| 259. C5 | D3×#215 | direct (N × H) |
| 269. C3 | C5×D3×SD16 | semidirect |
| 270. C3 | C2×C5×#215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×Q8 | 2 |
| C5×D3×D12 | 2 |
| C5×#3755 | 2 |
| C3×C5×#215 | 2 |
| C5×#3717 | 2 |
| C5×#3715 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C2×C5×#215 | 3 |
| C5×D3×SD16 | 3 |
| D3×#215 | 5 |