Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. #10599837 | C2 | semidirect |
| 4. #10598055 | C2 | semidirect |
| 5. #10597991 | C2 | semidirect |
| 55. C5×C16 | SD16 | semidirect |
| 127. C16 | #687 | semidirect |
| 149. C5 | #12451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C16 | 2 |
| #10601645 | 2 |
| #10599837 | 2 |
| #10598055 | 2 |
| #10597991 | 2 |
| #12451 | 5 |