Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10611017 | C2 | semidirect |
| 3. #10601551 | C2 | semidirect |
| 4. #10600349 | C2 | semidirect |
| 5. #10600338 | C2 | semidirect |
| 6. C5×#1286 | C2 | semidirect |
| 7. #10598205 | C2 | semidirect |
| 19. #65132 | C4 | semidirect |
| 20. #65130 | C4 | semidirect |
| 75. #1286 | D5 | semidirect |
| 357. C5 | #9305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611017 | 2 |
| #10610786 | 2 |
| #10601551 | 2 |
| #10600349 | 2 |
| #10600338 | 2 |
| C5×#1286 | 2 |
| #10598205 | 2 |
| #9305 | 5 |