Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
322 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C5×M16 | C8 | semidirect |
| 21. C22×C5×C8 | C8 | semidirect |
| 104. C2×M16 | #168 | semidirect |
| 110. C22×C8 | #168 | semidirect |
| 204. C5 | #7190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1729 | 2 |
| #10602364 | 2 |
| #7190 | 5 |