Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#64740 | C2 | semidirect |
| 3. C2×#64669 | C2 | semidirect |
| 4. #10600111 | C2 | semidirect |
| 5. C5×#1415 | C2 | semidirect |
| 6. #10598081 | C2 | semidirect |
| 7. #10598068 | C2 | semidirect |
| 37. Dic40 | D4 | semidirect |
| 48. #1415 | D5 | semidirect |
| 133. Dic5 | SD64 | semidirect |
| 178. C5 | #13686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602257 | 2 |
| C2×#64740 | 2 |
| C2×#64669 | 2 |
| #10600111 | 2 |
| C5×#1415 | 2 |
| #10598081 | 2 |
| #10598068 | 2 |
| #13686 | 5 |