Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
274 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 111. #168 | Q32 | semidirect |
| 190. C5 | #12528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2247 | 2 |
| #10602105 | 2 |
| #10602103 | 2 |
| #10602091 | 2 |
| #10602089 | 2 |
| #10599858 | 2 |
| #10597990 | 2 |
| #12528 | 5 |