Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #10617197 | C2 | semidirect |
| 3. #10604597 | C2 | semidirect |
| 4. #10604594 | C2 | semidirect |
| 5. #10604450 | C2 | semidirect |
| 6. #10598591 | C2 | semidirect |
| 7. #10598584 | C2 | semidirect |
| 20. C5×#460 | C4 | semidirect |
| 23. #65361 | C4 | semidirect |
| 24. #65309 | C4 | semidirect |
| 25. #65135 | C4 | semidirect |
| 146. #460 | AGL(1,𝔽5) | semidirect |
| 376. C5 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617197 | 2 |
| #10612094 | 2 |
| #10604597 | 2 |
| #10604594 | 2 |
| #10604450 | 2 |
| #10598591 | 2 |
| #10598584 | 2 |
| #9161 | 5 |