Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10617549 | C2 | semidirect |
| 3. #10605000 | C2 | semidirect |
| 4. #10604948 | C2 | semidirect |
| 5. #10604922 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 105. C2×C5×D4 | M16 | semidirect |
| 129. C5×M16 | M16 | semidirect |
| 316. C2×D4 | #704 | semidirect |
| 335. M16 | #704 | semidirect |
| 421. C5 | #8956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617549 | 2 |
| Dic5×AGL(1,ℤ/8) | 2 |
| #10605000 | 2 |
| #10604948 | 2 |
| #10604922 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #8956 | 5 |