Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
562 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10598704 | C2 | semidirect |
| 22. C2×C5×C22⋊C4 | C8 | semidirect |
| 63. C5×C22⋊C4 | C2×C8 | semidirect |
| 133. C2×C22⋊C4 | #170 | semidirect |
| 194. C22⋊C4 | C2×#170 | semidirect |
| 239. C5 | #11453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613825 | 2 |
| C2×#64933 | 2 |
| #10598704 | 2 |
| #11453 | 5 |