Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #10604738 | C2 | semidirect |
| 4. M16×#170 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 55. C5×#100 | C8 | semidirect |
| 189. #100 | #170 | semidirect |
| 308. C5 | #9550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604922 | 2 |
| C2×D4⋊#170 | 2 |
| #10604738 | 2 |
| M16×#170 | 2 |
| Dic5×#100 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #9550 | 5 |