Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10598845 | C2 | semidirect |
| 3. C5×C8×C16 | C2 | semidirect |
| 4. #10597995 | C2 | semidirect |
| 5. #10597991 | C2 | semidirect |
| 35. C8×C16 | D5 | semidirect |
| 52. C5×C16 | M16 | semidirect |
| 75. C5×C8 | D16 | semidirect |
| 119. C16 | #676 | semidirect |
| 137. C8 | D80 | semidirect |
| 140. C5 | #12081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D80 | 2 |
| #10598845 | 2 |
| C5×C8×C16 | 2 |
| #10597995 | 2 |
| #10597991 | 2 |
| #12081 | 5 |