Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10604660 | C2 | semidirect |
| 4. D5⋊#333 | C2 | semidirect |
| 6. #10598596 | C2 | semidirect |
| 7. #10598593 | C2 | semidirect |
| 378. C5 | #9170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617189 | 2 |
| #10612743 | 2 |
| #10604660 | 2 |
| D5⋊#333 | 2 |
| #10604437 | 2 |
| #10598596 | 2 |
| #10598593 | 2 |
| #9170 | 5 |