Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10602566 | C2 | semidirect |
| 5. C2×#64767 | C2 | semidirect |
| 6. #10600668 | C2 | semidirect |
| 7. #10598159 | C2 | semidirect |
| 343. C5 | #10550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3152 | 2 |
| #10602599 | 2 |
| #10602593 | 2 |
| #10602566 | 2 |
| C2×#64767 | 2 |
| #10600668 | 2 |
| #10598159 | 2 |
| #10550 | 5 |