Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10604726 | C2 | semidirect |
| 5. #10598791 | C2 | semidirect |
| 6. C2×C5×#131 | C4 | semidirect |
| 12. #65523 | C4 | semidirect |
| 15. #65407 | C4 | semidirect |
| 17. C2×C8×Dic5 | C4 | semidirect |
| 18. #64929 | C4 | semidirect |
| 20. #64923 | C4 | semidirect |
| 107. C2×#131 | AGL(1,𝔽5) | semidirect |
| 282. C5 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615517 | 2 |
| #10604998 | 2 |
| #10604996 | 2 |
| #10604726 | 2 |
| #10598791 | 2 |
| #12633 | 5 |