Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10611048 | C2 | semidirect |
| 4. #10600359 | C2 | semidirect |
| 6. C5×#1288 | C2 | semidirect |
| 7. #10598161 | C2 | semidirect |
| 20. #64983 | C4 | semidirect |
| 21. #64982 | C4 | semidirect |
| 22. #64971 | C4 | semidirect |
| 23. #64970 | C4 | semidirect |
| 74. #1288 | D5 | semidirect |
| 288. C5 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611048 | 2 |
| #10610264 | 2 |
| #10601604 | 2 |
| #10600359 | 2 |
| #10600357 | 2 |
| C5×#1288 | 2 |
| #10598161 | 2 |
| #9418 | 5 |