Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10611047 | C2 | semidirect |
| 3. #10601629 | C2 | semidirect |
| 6. C5×#1287 | C2 | semidirect |
| 7. #10598228 | C2 | semidirect |
| 21. #64988 | C4 | semidirect |
| 22. #64983 | C4 | semidirect |
| 23. #64982 | C4 | semidirect |
| 24. #64970 | C4 | semidirect |
| 77. #1287 | D5 | semidirect |
| 311. C5 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611047 | 2 |
| #10611037 | 2 |
| #10601629 | 2 |
| #10601625 | 2 |
| #10601594 | 2 |
| C5×#1287 | 2 |
| #10598228 | 2 |
| #9282 | 5 |