Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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. #10600307 | C2 | semidirect |
| 5. #10600250 | C2 | semidirect |
| 6. #10600242 | C2 | semidirect |
| 7. #10598116 | C2 | semidirect |
| 129. C5×C22⋊C4 | SD16 | semidirect |
| 384. C22⋊C4 | #687 | semidirect |
| 456. C5 | #10565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614361 | 2 |
| C5×#1964 | 2 |
| #10602474 | 2 |
| #10600307 | 2 |
| #10600250 | 2 |
| #10600242 | 2 |
| #10598116 | 2 |
| #10565 | 5 |