Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
620 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 103 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. #10614905 | C2 | semidirect |
| 3. #10602606 | C2 | semidirect |
| 4. #10602553 | C2 | semidirect |
| 5. #10598157 | C2 | semidirect |
| 10. C5×#493 | C4 | semidirect |
| 11. C5×#492 | C4 | semidirect |
| 29. C5×C4⋊Q8 | C2×C4 | semidirect |
| 32. C5×#127 | C2×C4 | semidirect |
| 41. C4×C5×C8 | C2×C4 | semidirect |
| 90. #493 | Dic5 | semidirect |
| 91. #492 | Dic5 | semidirect |
| 137. C4⋊Q8 | C2×Dic5 | semidirect |
| 140. #127 | C2×Dic5 | semidirect |
| 152. C4×C8 | C2×Dic5 | semidirect |
| 239. C5 | #9428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3151 | 2 |
| #10614905 | 2 |
| #10602606 | 2 |
| #10602553 | 2 |
| #10598157 | 2 |
| #9428 | 5 |