Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
434 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #10604773 | C2 | semidirect |
| 4. #10604765 | C2 | semidirect |
| 5. #10598791 | C2 | semidirect |
| 7. C23×#168 | C4 | semidirect |
| 13. C5×#407 | C4 | semidirect |
| 15. #65411 | C4 | semidirect |
| 16. #65408 | C4 | semidirect |
| 140. #407 | AGL(1,𝔽5) | semidirect |
| 345. C5 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610357 | 2 |
| #10604887 | 2 |
| #10604773 | 2 |
| #10604765 | 2 |
| #10598791 | 2 |
| #12805 | 5 |