Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
536 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 88 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. C4×#4131 | C2 | semidirect |
| 3. #10604650 | C2 | semidirect |
| 4. #10604633 | C2 | semidirect |
| 5. #10604406 | C2 | semidirect |
| 6. #10598592 | C2 | semidirect |
| 7. #10598588 | C2 | semidirect |
| 395. C5 | #9211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4131 | 2 |
| #10612776 | 2 |
| #10604650 | 2 |
| #10604633 | 2 |
| #10604406 | 2 |
| #10598592 | 2 |
| #10598588 | 2 |
| #9211 | 5 |