Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4638 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 987 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×C5×#127 | C2 | semidirect |
| 2. C23×#686 | C2 | semidirect |
| 3. C22×#4020 | C2 | semidirect |
| 4. C2×#65362 | C2 | direct (N × H) |
| 5. C22×C4×#168 | C2 | semidirect |
| 11. C2×C5×#127 | C22 | semidirect |
| 14. C22×#686 | C22 | semidirect |
| 17. C2×#4020 | C22 | semidirect |
| 18. #65362 | C22 | direct (N × H) |
| 19. C2×C4×#168 | C22 | semidirect |
| 36. C5×#127 | C23 | semidirect |
| 40. C2×#686 | C23 | semidirect |
| 41. C22×#168 | D4 | semidirect |
| 44. #4020 | C23 | semidirect |
| 45. C4×#168 | C23 | semidirect |
| 48. C22×#127 | D5 | semidirect |
| 64. C22×C4×C5 | D8 | semidirect |
| 78. C2×#168 | C2×D4 | semidirect |
| 90. C2×#127 | C2×D5 | semidirect |
| 109. C2×C4×C5 | C2×D8 | semidirect |
| 117. #168 | C22×D4 | semidirect |
| 139. #127 | C22×D5 | semidirect |
| 146. C22×C5 | #493 | semidirect |
| 154. C4×C5 | C22×D8 | semidirect |
| 175. C22×C4 | #686 | semidirect |
| 186. C2×C5 | C2×#493 | semidirect |
| 207. C2×C4 | C2×#686 | semidirect |
| 214. C5 | C22×#493 | semidirect |
| 221. C22 | #65362 | direct (N × H) |
| 225. C4 | C22×#686 | semidirect |
| 230. C2 | C2×#65362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#127 | 2 |
| C23×#686 | 2 |
| C22×#4020 | 2 |
| C2×#65362 | 2 |
| C22×C4×#168 | 2 |
| C22×#493 | 5 |