Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1294 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1294 conjugacy classes of subgroups — too many to draw. Only its 220 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 |
|---|---|---|
| 3. C2×#64897 | C2 | semidirect |
| 185. C22×C5 | #338 | semidirect |
| 292. C5 | C22⋊#338 | semidirect |
| 304. C22 | #64897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#676 | 2 |
| D5⋊#407 | 2 |
| C2×#64897 | 2 |
| C22⋊#338 | 5 |