Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 9. C22⋊#674 | C4 | semidirect |
| 13. C5×C22⋊C16 | C4 | semidirect |
| 14. C22⋊#672 | C4 | semidirect |
| 91. C22⋊C16 | AGL(1,𝔽5) | semidirect |
| 249. C5 | #7185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604717 | 2 |
| #10604706 | 2 |
| #10599899 | 2 |
| #7185 | 5 |