Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×Dic40 | C2 | semidirect |
| 5. #10598069 | C2 | semidirect |
| 6. #10598067 | C2 | semidirect |
| 7. C4×#3926 | C2 | semidirect |
| 15. #64740 | C4 | direct (N × H) |
| 35. Dic40 | C2×C4 | semidirect |
| 37. #3926 | C2×C4 | semidirect |
| 113. C4×C5 | SD64 | semidirect |
| 155. C5 | C4×SD64 | semidirect |
| 164. C4 | #64740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D16 | 2 |
| C2×#64740 | 2 |
| C4×Dic40 | 2 |
| #10598315 | 2 |
| #10598069 | 2 |
| #10598067 | 2 |
| C4×#3926 | 2 |
| C4×SD64 | 5 |