Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10602605 | C2 | semidirect |
| 3. #10602591 | C2 | semidirect |
| 4. #10600544 | C2 | semidirect |
| 5. #10600525 | C2 | semidirect |
| 7. C5×#500 | C4 | semidirect |
| 8. C5×#493 | C4 | semidirect |
| 9. C5×#486 | C4 | semidirect |
| 94. #500 | Dic5 | semidirect |
| 95. #493 | Dic5 | semidirect |
| 96. #486 | Dic5 | semidirect |
| 253. C5 | #9764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3169 | 2 |
| #10602605 | 2 |
| #10602591 | 2 |
| #10600544 | 2 |
| #10600525 | 2 |
| #9764 | 5 |