Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #10599851 | C2 | semidirect |
| 3. #10599837 | C2 | semidirect |
| 4. #10598851 | C2 | semidirect |
| 5. C5×C8×C16 | C2 | semidirect |
| 35. C8×C16 | D5 | semidirect |
| 51. C5×C16 | SD16 | semidirect |
| 73. C5×C8 | D16 | semidirect |
| 114. C16 | #677 | semidirect |
| 130. C8 | D80 | semidirect |
| 133. C5 | #12503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599853 | 2 |
| #10599851 | 2 |
| #10599837 | 2 |
| #10598851 | 2 |
| C5×C8×C16 | 2 |
| #12503 | 5 |