Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
214 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #10600110 | C2 | semidirect |
| 3. C5×#1423 | C2 | semidirect |
| 4. Dic5×C32 | C2 | semidirect |
| 5. #10598068 | C2 | semidirect |
| 13. D160 | C4 | semidirect |
| 23. D80 | C2×C4 | semidirect |
| 24. C5×C32 | C2×C4 | semidirect |
| 28. #1423 | D5 | semidirect |
| 72. C32 | C4×D5 | semidirect |
| 81. Dic5 | D32 | semidirect |
| 109. C5 | C4×D32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D160 | 2 |
| #10600110 | 2 |
| C5×#1423 | 2 |
| Dic5×C32 | 2 |
| #10598068 | 2 |
| C4×D32 | 5 |