Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
490 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10617375 | C2 | semidirect |
| 3. #10604631 | C2 | semidirect |
| 6. #10598529 | C2 | semidirect |
| 7. #10598527 | C2 | semidirect |
| 20. C5×#486 | C4 | semidirect |
| 21. #65377 | C4 | semidirect |
| 22. #65365 | C4 | semidirect |
| 25. #64982 | C4 | semidirect |
| 114. D5⋊C8 | SD16 | semidirect |
| 136. #486 | AGL(1,𝔽5) | semidirect |
| 365. C5 | #9294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617375 | 2 |
| #10613299 | 2 |
| #10604631 | 2 |
| #10604617 | 2 |
| #10604609 | 2 |
| #10598529 | 2 |
| #10598527 | 2 |
| #9294 | 5 |