Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
322 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 28. C2×#681 | C8 | semidirect |
| 34. C22×#168 | C8 | semidirect |
| 253. C5 | #7188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1458 | 2 |
| #10602372 | 2 |
| #10602364 | 2 |
| #7188 | 5 |