Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
184 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #10602304 | C2 | semidirect |
| 3. #10598320 | C2 | semidirect |
| 4. #10598084 | C2 | semidirect |
| 5. #10598080 | C2 | semidirect |
| 8. C5×Q64 | C4 | semidirect |
| 9. C5×SD64 | C4 | semidirect |
| 10. C5×D32 | C4 | semidirect |
| 50. Q64 | Dic5 | semidirect |
| 51. SD64 | Dic5 | semidirect |
| 52. D32 | Dic5 | semidirect |
| 113. C5 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2262 | 2 |
| #10602304 | 2 |
| #10598320 | 2 |
| #10598084 | 2 |
| #10598080 | 2 |
| #13656 | 5 |