Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
318 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 318 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. #64852 | C4 | semidirect |
| 14. C16×AGL(1,𝔽5) | C4 | semidirect |
| 15. C5×#367 | C4 | semidirect |
| 16. #64725 | C4 | semidirect |
| 17. #64709 | C4 | semidirect |
| 77. #367 | AGL(1,𝔽5) | semidirect |
| 177. C5 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64852 | 2 |
| C2×C16×AGL(1,𝔽5) | 2 |
| #10604077 | 2 |
| #10600138 | 2 |
| #10598620 | 2 |
| #12670 | 5 |