Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
678 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×#67158 | C2 | semidirect |
| 2. C2×#67153 | C2 | semidirect |
| 3. C2×C5×#627 | C2 | semidirect |
| 6. D5×#627 | C2 | direct (N × H) |
| 13. #67158 | C22 | semidirect |
| 14. #67153 | C22 | semidirect |
| 15. C5×#627 | C22 | semidirect |
| 29. C2×C32×D5 | Q8 | semidirect |
| 41. C2×#627 | D5 | direct (N × H) |
| 61. C2×C32×C5 | C2×Q8 | semidirect |
| 63. C32×D5 | C2×Q8 | semidirect |
| 79. #627 | C2×D5 | direct (N × H) |
| 84. C2×C3×D5 | Dic6 | semidirect |
| 103. C32×C5 | C22×Q8 | semidirect |
| 124. C2×C3×C5 | C2×Dic6 | semidirect |
| 127. C3×D5 | C2×Dic6 | semidirect |
| 147. C2×D5 | #627 | direct (N × H) |
| 154. C2×C32 | Q8×D5 | semidirect |
| 163. C3×C5 | C22×Dic6 | semidirect |
| 178. C2×C5 | C2×#627 | semidirect |
| 180. D5 | C2×#627 | direct (N × H) |
| 181. C32 | C2×Q8×D5 | semidirect |
| 196. C2×C3 | D5×Dic6 | semidirect |
| 198. C5 | C22×#627 | semidirect |
| 207. C3 | C2×D5×Dic6 | semidirect |
| 209. C2 | D5×#627 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67158 | 2 |
| C2×#67153 | 2 |
| C2×C5×#627 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C2×C3×D5×Dic3 | 2 |
| D5×#627 | 2 |
| C2×D5×Dic6 | 3 |
| C22×#627 | 5 |