Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
246 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 52. #672 | Q16 | semidirect |
| 128. C5 | #12524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1710 | 2 |
| #10602178 | 2 |
| #10602177 | 2 |
| #10598858 | 2 |
| #10597928 | 2 |
| #12524 | 5 |