Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
490 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10617199 | C2 | semidirect |
| 5. #10604452 | C2 | semidirect |
| 6. #10598596 | C2 | semidirect |
| 7. #10598595 | C2 | semidirect |
| 21. C5×#460 | C4 | semidirect |
| 23. #65364 | C4 | semidirect |
| 24. #65320 | C4 | semidirect |
| 25. #65138 | C4 | semidirect |
| 158. #460 | AGL(1,𝔽5) | semidirect |
| 406. C5 | #9306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617199 | 2 |
| #10612114 | 2 |
| #10604604 | 2 |
| #10604596 | 2 |
| #10604452 | 2 |
| #10598596 | 2 |
| #10598595 | 2 |
| #9306 | 5 |