Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
706 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 3. #10598695 | C2 | semidirect |
| 11. #65754 | C4 | semidirect |
| 12. C4×#704 | C4 | semidirect |
| 42. C4×#170 | C2×C4 | semidirect |
| 72. C42×C5 | M16 | semidirect |
| 82. C4×Dic5 | M16 | semidirect |
| 212. C42 | #704 | semidirect |
| 249. C5 | #7855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617473 | 2 |
| C2×#65221 | 2 |
| #10598695 | 2 |
| #7855 | 5 |