Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #10613750 | C2 | semidirect |
| 2. C2×C5×D32 | C2 | semidirect |
| 3. #10602265 | C2 | semidirect |
| 4. #10602251 | C2 | semidirect |
| 5. #10598316 | C2 | semidirect |
| 6. #10598089 | C2 | semidirect |
| 7. #10598086 | C2 | semidirect |
| 10. C2×C5×D16 | C22 | semidirect |
| 19. C2×C5×C32 | C22 | semidirect |
| 23. #64726 | C22 | semidirect |
| 24. #64719 | C22 | semidirect |
| 55. C2×D32 | D5 | semidirect |
| 95. C2×D16 | C2×D5 | semidirect |
| 102. C2×C32 | C2×D5 | semidirect |
| 224. C5 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613750 | 2 |
| C2×C5×D32 | 2 |
| #10602265 | 2 |
| #10602251 | 2 |
| #10598316 | 2 |
| #10598089 | 2 |
| #10598086 | 2 |
| #13669 | 5 |