Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
226 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 226 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 |
|---|---|---|
| 3. #10600074 | C2 | semidirect |
| 5. #10598045 | C2 | semidirect |
| 6. #10597997 | C2 | semidirect |
| 7. #10597989 | C2 | semidirect |
| 75. #672 | SD16 | semidirect |
| 194. C5 | #12049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#672 | 2 |
| C8×#687 | 2 |
| #10600074 | 2 |
| C5×D4⋊C16 | 2 |
| #10598045 | 2 |
| #10597997 | 2 |
| #10597989 | 2 |
| #12049 | 5 |