Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 103 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. #10615062 | C2 | semidirect |
| 3. #10602629 | C2 | semidirect |
| 6. #10598238 | C2 | semidirect |
| 7. #10598228 | C2 | semidirect |
| 10. C5×#494 | C4 | semidirect |
| 11. C5×#492 | C4 | semidirect |
| 12. C5×#487 | C4 | semidirect |
| 13. C5×#486 | C4 | semidirect |
| 120. #494 | Dic5 | semidirect |
| 121. #492 | Dic5 | semidirect |
| 122. #487 | Dic5 | semidirect |
| 123. #486 | Dic5 | semidirect |
| 311. C5 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3210 | 2 |
| #10615062 | 2 |
| #10602629 | 2 |
| #10602605 | 2 |
| #10602596 | 2 |
| #10598238 | 2 |
| #10598228 | 2 |
| #9282 | 5 |