Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10598525 | C2 | semidirect |
| 5. #10598524 | C2 | semidirect |
| 6. #10598523 | C2 | semidirect |
| 7. #10598522 | C2 | semidirect |
| 71. #676 | C16 | semidirect |
| 110. C5×C8 | C2×C16 | semidirect |
| 114. #168 | C2×C16 | semidirect |
| 203. C8 | D5⋊C16 | semidirect |
| 204. C5 | #12015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603829 | 2 |
| D5⋊(C4⋊C16) | 2 |
| #10598860 | 2 |
| #10598525 | 2 |
| #10598524 | 2 |
| #10598523 | 2 |
| #10598522 | 2 |
| #12015 | 5 |