Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #10604765 | C2 | semidirect |
| 4. #10598790 | C2 | semidirect |
| 5. C2×#4053 | C4 | semidirect |
| 10. C5×#423 | C4 | semidirect |
| 11. #65418 | C4 | semidirect |
| 13. C2×#3935 | C4 | semidirect |
| 97. #423 | AGL(1,𝔽5) | semidirect |
| 250. C5 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610773 | 2 |
| #10604765 | 2 |
| #10604142 | 2 |
| #10598790 | 2 |
| #12808 | 5 |