Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 4. #10598140 | C2 | semidirect |
| 5. C2×C5×C4⋊Q8 | C4 | semidirect |
| 8. C5×#397 | C4 | semidirect |
| 13. C4×C5×C4⋊C4 | C4 | semidirect |
| 96. C2×C4⋊Q8 | Dic5 | semidirect |
| 101. #397 | Dic5 | semidirect |
| 107. C4×C4⋊C4 | Dic5 | semidirect |
| 298. C5 | #11878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2547 | 2 |
| #10602412 | 2 |
| #10602393 | 2 |
| #10598140 | 2 |
| #11878 | 5 |