Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #10607917 | C2 | semidirect |
| 5. #10598129 | C2 | semidirect |
| 6. #10597971 | C2 | semidirect |
| 7. #10597969 | C2 | semidirect |
| 384. C5 | #7743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10607917 | 2 |
| C5×#2041 | 2 |
| #10602561 | 2 |
| #10602555 | 2 |
| #10598129 | 2 |
| #10597971 | 2 |
| #10597969 | 2 |
| #7743 | 5 |