Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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. C5×#2995 | C2 | semidirect |
| 3. #10602547 | C2 | semidirect |
| 4. #10601594 | C2 | semidirect |
| 5. #10601306 | C2 | semidirect |
| 6. #10598239 | C2 | semidirect |
| 7. #10598201 | C2 | semidirect |
| 20. #65356 | C4 | semidirect |
| 21. #65354 | C4 | semidirect |
| 22. #65347 | C4 | semidirect |
| 23. #65344 | C4 | semidirect |
| 92. #2995 | D5 | semidirect |
| 402. C5 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2995 | 2 |
| #10614866 | 2 |
| #10602547 | 2 |
| #10601594 | 2 |
| #10601306 | 2 |
| #10598239 | 2 |
| #10598201 | 2 |
| #8997 | 5 |