Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
244 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 87 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. D4×#672 | C2 | semidirect |
| 3. #10600072 | C2 | semidirect |
| 4. C5×D4⋊C16 | C2 | semidirect |
| 5. #10598046 | C2 | semidirect |
| 6. #10597994 | C2 | semidirect |
| 7. #10597989 | C2 | semidirect |
| 51. D4⋊C16 | D5 | semidirect |
| 78. #672 | D8 | semidirect |
| 97. C5×D4 | M32 | semidirect |
| 189. D4 | #3930 | semidirect |
| 207. C5 | #12038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#672 | 2 |
| C8×#686 | 2 |
| #10600072 | 2 |
| C5×D4⋊C16 | 2 |
| #10598046 | 2 |
| #10597994 | 2 |
| #10597989 | 2 |
| #12038 | 5 |