Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
866 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 312 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 |
|---|---|---|
| 4. #10603781 | C2 | semidirect |
| 12. #65683 | C4 | semidirect |
| 193. C5 | #20539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65683 | 2 |
| #10605879 | 2 |
| #10604313 | 2 |
| #10603781 | 2 |
| #20539 | 5 |