Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 21. C5×C4⋊Q8 | C8 | semidirect |
| 129. C4⋊Q8 | #168 | semidirect |
| 239. C5 | #11478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C4⋊Q8 | 2 |
| #10602417 | 2 |
| #10598134 | 2 |
| #10598126 | 2 |
| #11478 | 5 |