Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 77 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. #10598849 | C2 | semidirect |
| 5. #10597963 | C2 | semidirect |
| 6. #10597960 | C2 | semidirect |
| 7. #10597928 | C2 | semidirect |
| 75. #672 | M16 | semidirect |
| 194. C5 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1589 | 2 |
| C4×#3959 | 2 |
| #10598849 | 2 |
| #10598254 | 2 |
| #10597963 | 2 |
| #10597960 | 2 |
| #10597928 | 2 |
| #12084 | 5 |