Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10604299 | C2 | semidirect |
| 5. C2×#64870 | C2 | semidirect |
| 6. #10598557 | C2 | semidirect |
| 7. #10598556 | C2 | semidirect |
| 361. C5 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617267 | 2 |
| #10613193 | 2 |
| #10604507 | 2 |
| #10604299 | 2 |
| C2×#64870 | 2 |
| #10598557 | 2 |
| #10598556 | 2 |
| #9266 | 5 |