Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. #10598621 | C2 | semidirect |
| 5. #10598621 | C2 | semidirect |
| 11. C5×#427 | C4 | semidirect |
| 12. #65395 | C4 | semidirect |
| 16. D5×#107 | C4 | semidirect |
| 17. D5×#107 | C4 | semidirect |
| 111. #427 | AGL(1,𝔽5) | semidirect |
| 285. C5 | #12870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#427 | 2 |
| #10604722 | 2 |
| #10604706 | 2 |
| #10598621 | 2 |
| #12870 | 5 |