Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10617377 | C2 | semidirect |
| 3. #10604622 | C2 | semidirect |
| 6. #10598531 | C2 | semidirect |
| 7. #10598530 | C2 | semidirect |
| 21. C5×#486 | C4 | semidirect |
| 22. #65368 | C4 | semidirect |
| 23. #65365 | C4 | semidirect |
| 27. #64970 | C4 | semidirect |
| 112. #700 | SD16 | semidirect |
| 140. #486 | AGL(1,𝔽5) | semidirect |
| 365. C5 | #9054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617377 | 2 |
| #10613287 | 2 |
| #10604622 | 2 |
| #10604620 | 2 |
| #10604604 | 2 |
| #10598531 | 2 |
| #10598530 | 2 |
| #9054 | 5 |