Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
566 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 156 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. #10598794 | C2 | semidirect |
| 248. C5 | #8128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617473 | 2 |
| C2×#65407 | 2 |
| #10598794 | 2 |
| #8128 | 5 |