Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 3. C22×Dic40 | C2 | semidirect |
| 4. #10610900 | C2 | semidirect |
| 6. #10602194 | C2 | semidirect |
| 7. #10601447 | C2 | semidirect |
| 8. #10600029 | C2 | semidirect |
| 9. #10599998 | C2 | semidirect |
| 325. C5 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615638 | 2 |
| C2×#65484 | 2 |
| C22×Dic40 | 2 |
| #10610900 | 2 |
| C5×#2138 | 2 |
| #10602194 | 2 |
| #10601447 | 2 |
| #10600029 | 2 |
| #10599998 | 2 |
| #33588 | 5 |