Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
626 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 15. #64897 | C4 | semidirect |
| 240. C5 | #10815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64997 | 2 |
| #10604730 | 2 |
| C2×#64897 | 2 |
| #10604192 | 2 |
| #10815 | 5 |