Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #10602222 | C2 | semidirect |
| 5. Dic5×#108 | C2 | semidirect |
| 6. #10598301 | C2 | semidirect |
| 7. #10598225 | C2 | semidirect |
| 18. C5×#362 | C4 | semidirect |
| 19. C5×#361 | C4 | semidirect |
| 114. #362 | Dic5 | semidirect |
| 115. #361 | Dic5 | semidirect |
| 264. C5 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2148 | 2 |
| #10602877 | 2 |
| #10602873 | 2 |
| #10602222 | 2 |
| Dic5×#108 | 2 |
| #10598301 | 2 |
| #10598225 | 2 |
| #13137 | 5 |