Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
430 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 148 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×#335 | C4 | semidirect |
| 18. #64699 | C4 | semidirect |
| 19. #64678 | C4 | semidirect |
| 34. #3993 | C8 | semidirect |
| 86. #335 | AGL(1,𝔽5) | semidirect |
| 108. C5×C8 | C4×C8 | semidirect |
| 111. #168 | C4×C8 | semidirect |
| 200. C8 | C8×AGL(1,𝔽5) | semidirect |
| 201. C5 | #8285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604033 | 2 |
| C4×#3993 | 2 |
| #10603807 | 2 |
| D5×#335 | 2 |
| #10598589 | 2 |
| #8285 | 5 |