Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
364 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 108 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. #10598727 | C2 | semidirect |
| 193. C5 | #11458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613935 | 2 |
| C2×#64912 | 2 |
| #10598727 | 2 |
| #11458 | 5 |