Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
244 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #10604414 | C2 | semidirect |
| 2. #10604021 | C2 | semidirect |
| 4. D4⋊#674 | C2 | semidirect |
| 5. #10598579 | C2 | semidirect |
| 6. #10598525 | C2 | semidirect |
| 7. #10598512 | C2 | semidirect |
| 78. #674 | D8 | semidirect |
| 106. D20 | M32 | semidirect |
| 207. C5 | #12038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604414 | 2 |
| #10604021 | 2 |
| #10598941 | 2 |
| D4⋊#674 | 2 |
| #10598579 | 2 |
| #10598525 | 2 |
| #10598512 | 2 |
| #12038 | 5 |