Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10617122 | C2 | semidirect |
| 3. #10604359 | C2 | semidirect |
| 4. #10604328 | C2 | semidirect |
| 5. #10604270 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 108. C2×D20 | M16 | semidirect |
| 127. C5×M16 | M16 | semidirect |
| 335. M16 | #700 | semidirect |
| 421. C5 | #8956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617122 | 2 |
| #10610930 | 2 |
| #10604359 | 2 |
| #10604328 | 2 |
| #10604270 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #8956 | 5 |