Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
776 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10602412 | C2 | semidirect |
| 3. #10602394 | C2 | semidirect |
| 4. #10598136 | C2 | semidirect |
| 5. C23×C5×D4 | C4 | semidirect |
| 9. C5×#394 | C4 | semidirect |
| 12. C5×#380 | C4 | semidirect |
| 17. #64746 | C22 | semidirect |
| 19. #64745 | C22 | semidirect |
| 109. C23×D4 | Dic5 | semidirect |
| 115. #394 | Dic5 | semidirect |
| 119. #380 | Dic5 | semidirect |
| 360. C5 | #11873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2408 | 2 |
| #10602412 | 2 |
| #10602394 | 2 |
| #10598136 | 2 |
| #11873 | 5 |