Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
716 conjugacy classes of subgroups; only the 380 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 380 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. #10604369 | C2 | semidirect |
| 4. C2×#64860 | C2 | semidirect |
| 8. #65791 | C4 | semidirect |
| 28. #3998 | C2×C4 | semidirect |
| 30. C2×#674 | C2×C4 | semidirect |
| 149. C5 | #33329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617530 | 2 |
| #10614242 | 2 |
| #10604369 | 2 |
| C2×#64860 | 2 |
| #33329 | 5 |