Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
488 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 4. #10604330 | C2 | semidirect |
| 5. #10604271 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 111. C2×Dic10 | M16 | semidirect |
| 122. C5×M16 | M16 | semidirect |
| 318. M16 | #700 | semidirect |
| 400. C5 | #8955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617122 | 2 |
| #10610931 | 2 |
| #10604359 | 2 |
| #10604330 | 2 |
| #10604271 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #8955 | 5 |