Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
654 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 112 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. C23×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C3×C5×#217 | C2 | semidirect |
| 5. C5×#3722 | C2 | semidirect |
| 12. C22×C3×C5×D3 | C22 | semidirect |
| 14. C2×C3×C5×Dic3 | C22 | semidirect |
| 15. C2×C3×C5×Dic3 | C22 | semidirect |
| 17. #63981 | C5 | direct (N × H) |
| 23. C2×C5×#67 | D3 | semidirect |
| 26. C5×#217 | D3 | semidirect |
| 30. C22×C32×C5 | D4 | semidirect |
| 35. C2×C5×C3⋊D3 | D4 | semidirect |
| 41. C23×C3⋊D3 | C2×C5 | semidirect |
| 42. C2×C3×#67 | C2×C5 | semidirect |
| 43. C2×#626 | C2×C5 | semidirect |
| 44. C3×#217 | C2×C5 | semidirect |
| 45. #3722 | C2×C5 | semidirect |
| 59. C22×C5×D3 | C2×D3 | semidirect |
| 65. C2×C5×Dic3 | C2×D3 | semidirect |
| 66. C2×C5×Dic3 | C2×D3 | semidirect |
| 84. C22×C3×D3 | C22×C5 | semidirect |
| 86. C2×C3×Dic3 | C22×C5 | semidirect |
| 87. C2×C3×Dic3 | C22×C5 | semidirect |
| 96. C22×C3×C5 | D12 | semidirect |
| 97. C22×C3×C5 | #67 | semidirect |
| 123. C2×#67 | C5×D3 | semidirect |
| 126. #217 | C5×D3 | semidirect |
| 129. C32×C5 | #120 | semidirect |
| 140. C22×C32 | C5×D4 | semidirect |
| 145. C2×C3⋊D3 | C5×D4 | semidirect |
| 178. C22×D3 | C2×C5×D3 | semidirect |
| 184. C2×Dic3 | C2×C5×D3 | semidirect |
| 185. C2×Dic3 | C2×C5×D3 | semidirect |
| 194. C22×C5 | #626 | semidirect |
| 209. C3×C5 | #882 | semidirect |
| 210. C3×C5 | #937 | semidirect |
| 218. C22×C3 | C5×D12 | semidirect |
| 219. C22×C3 | C5×#67 | semidirect |
| 245. C32 | C5×#120 | semidirect |
| 269. C5 | #63981 | direct (N × H) |
| 277. C22 | C5×#626 | semidirect |
| 282. C3 | C5×#882 | semidirect |
| 283. C3 | C5×#937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×C5×#626 | 2 |
| C3×C5×#217 | 2 |
| C5×#3722 | 2 |
| C5×#937 | 3 |
| C5×#882 | 3 |
| #63981 | 5 |