Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 27. C5×#97 | C8 | semidirect |
| 104. #97 | #170 | semidirect |
| 170. C5 | #8786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604190 | 2 |
| #10604185 | 2 |
| Dic5×#97 | 2 |
| #10598771 | 2 |
| #8786 | 5 |