Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10598142 | C2 | semidirect |
| 5. #10598140 | C2 | semidirect |
| 7. C2×C5×#117 | C4 | semidirect |
| 8. C5×#400 | C4 | semidirect |
| 10. C5×#398 | C4 | semidirect |
| 16. C4×C5×C22⋊C4 | C4 | semidirect |
| 105. C2×#117 | Dic5 | semidirect |
| 108. #400 | Dic5 | semidirect |
| 110. #398 | Dic5 | semidirect |
| 117. C4×C22⋊C4 | Dic5 | semidirect |
| 317. C5 | #11727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2395 | 2 |
| C4×#3966 | 2 |
| #10602394 | 2 |
| #10598142 | 2 |
| #10598140 | 2 |
| #11727 | 5 |