Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 100 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. C5×C82 | C4 | semidirect |
| 14. #64674 | C4 | semidirect |
| 15. C8×#168 | C4 | semidirect |
| 71. C82 | AGL(1,𝔽5) | semidirect |
| 165. C5 | #8790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603860 | 2 |
| #10603849 | 2 |
| #10598840 | 2 |
| #10598527 | 2 |
| #8790 | 5 |