Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 4. #10601629 | C2 | semidirect |
| 5. #10600655 | C2 | semidirect |
| 6. #10598245 | C2 | semidirect |
| 7. #10598156 | C2 | semidirect |
| 19. #65320 | C4 | semidirect |
| 21. #65310 | C4 | semidirect |
| 22. #65308 | C4 | semidirect |
| 24. #65297 | C4 | semidirect |
| 363. C5 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2970 | 2 |
| #10614266 | 2 |
| #10602436 | 2 |
| #10601629 | 2 |
| #10600655 | 2 |
| #10598245 | 2 |
| #10598156 | 2 |
| #9159 | 5 |