Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
522 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 522 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. #10602412 | C2 | semidirect |
| 3. #10602394 | C2 | semidirect |
| 4. #10598140 | C2 | semidirect |
| 5. #10598136 | C2 | semidirect |
| 7. C2×C5×#121 | C4 | semidirect |
| 9. C5×#398 | C4 | semidirect |
| 11. C5×#394 | C4 | semidirect |
| 16. C2×C5×#95 | C4 | semidirect |
| 118. C2×#121 | Dic5 | semidirect |
| 122. #398 | Dic5 | semidirect |
| 124. #394 | Dic5 | semidirect |
| 130. C2×#95 | Dic5 | semidirect |
| 375. C5 | #11876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2543 | 2 |
| #10602412 | 2 |
| #10602394 | 2 |
| #10598140 | 2 |
| #10598136 | 2 |
| #11876 | 5 |