Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
296 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 112 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. #64889 | C4 | semidirect |
| 15. #64861 | C4 | semidirect |
| 18. C5×#346 | C4 | semidirect |
| 19. C16×Dic5 | C4 | semidirect |
| 20. C16×Dic5 | C4 | semidirect |
| 21. #64681 | C4 | semidirect |
| 94. #346 | AGL(1,𝔽5) | semidirect |
| 207. C5 | #12667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604101 | 2 |
| #10603851 | 2 |
| D5⋊#364 | 2 |
| #10599864 | 2 |
| #10598661 | 2 |
| #12667 | 5 |