Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 15. #64879 | C4 | semidirect |
| 16. #64879 | C4 | semidirect |
| 17. C5×#334 | C4 | semidirect |
| 18. #64700 | C4 | semidirect |
| 19. #64677 | C4 | semidirect |
| 86. #334 | AGL(1,𝔽5) | semidirect |
| 108. C5×C8 | #97 | semidirect |
| 111. #168 | #97 | semidirect |
| 201. C8 | #3992 | semidirect |
| 202. C5 | #8287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604034 | 2 |
| C4×#3994 | 2 |
| #10603807 | 2 |
| D5×#334 | 2 |
| #10598589 | 2 |
| #8287 | 5 |