Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4038 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 4038 conjugacy classes of subgroups — too many to draw. Only its 827 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×#687 | C2 | semidirect |
| 3. C23×#686 | C2 | semidirect |
| 4. C22×#4021 | C2 | semidirect |
| 5. C2×#65363 | C2 | direct (N × H) |
| 6. C22×#3935 | C2 | semidirect |
| 12. C2×C5×#127 | C22 | semidirect |
| 15. C22×#687 | C22 | semidirect |
| 17. C22×#686 | C22 | semidirect |
| 21. C2×#4021 | C22 | semidirect |
| 22. #65363 | C22 | direct (N × H) |
| 23. C2×#3935 | C22 | semidirect |
| 43. C5×#127 | C23 | semidirect |
| 47. C2×#687 | C23 | semidirect |
| 49. C2×#686 | C23 | semidirect |
| 51. C22×#168 | D4 | semidirect |
| 54. #4021 | C23 | semidirect |
| 55. #3935 | C23 | semidirect |
| 58. C22×#127 | D5 | semidirect |
| 96. C2×#168 | C2×D4 | semidirect |
| 108. C2×#127 | C2×D5 | semidirect |
| 142. #168 | C22×D4 | semidirect |
| 167. #127 | C22×D5 | semidirect |
| 177. C22×C5 | #496 | semidirect |
| 225. C2×C5 | C2×#496 | semidirect |
| 257. C5 | C22×#496 | semidirect |
| 264. C22 | #65363 | direct (N × H) |
| 274. C2 | C2×#65363 | 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×#687 | 2 |
| C23×#686 | 2 |
| C22×#4021 | 2 |
| C2×#65363 | 2 |
| C22×#3935 | 2 |
| C22×#496 | 5 |