Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. C2×#65208 | C2 | semidirect |
| 2. C2×#64741 | C2 | semidirect |
| 3. C2×D160 | C2 | semidirect |
| 4. #10600120 | C2 | semidirect |
| 5. C5×#1416 | C2 | semidirect |
| 6. #10598085 | C2 | semidirect |
| 7. #10598068 | C2 | semidirect |
| 34. C5×Q32 | D4 | semidirect |
| 43. D80 | D4 | semidirect |
| 52. #1416 | D5 | semidirect |
| 126. Q32 | D20 | semidirect |
| 207. C5 | #13663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65208 | 2 |
| C2×#64741 | 2 |
| C2×D160 | 2 |
| #10600120 | 2 |
| C5×#1416 | 2 |
| #10598085 | 2 |
| #10598068 | 2 |
| #13663 | 5 |