Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
310 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 13. #64850 | C4 | semidirect |
| 14. #64849 | C4 | semidirect |
| 15. #64844 | C4 | semidirect |
| 16. #64844 | C4 | semidirect |
| 17. C5×#368 | C4 | semidirect |
| 18. #64726 | C4 | semidirect |
| 19. #64713 | C4 | semidirect |
| 82. #368 | AGL(1,𝔽5) | semidirect |
| 184. C5 | #12671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604107 | 2 |
| C2×#64844 | 2 |
| #10604089 | 2 |
| D5×#368 | 2 |
| #10598626 | 2 |
| #12671 | 5 |