Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10602613 | C2 | semidirect |
| 3. #10602612 | C2 | semidirect |
| 4. #10598288 | C2 | semidirect |
| 8. C2×C5×#127 | C4 | semidirect |
| 9. C5×#496 | C4 | semidirect |
| 13. C4×C5×M16 | C4 | semidirect |
| 18. #64762 | C22 | semidirect |
| 19. #64761 | C22 | semidirect |
| 103. C2×#127 | Dic5 | semidirect |
| 104. #496 | Dic5 | semidirect |
| 110. C4×M16 | Dic5 | semidirect |
| 287. C5 | #13579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3151 | 2 |
| #10602613 | 2 |
| #10602612 | 2 |
| #10598288 | 2 |
| #13579 | 5 |