Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 5. C2×C5×C4⋊Q8 | C4 | semidirect |
| 10. C5×#391 | C4 | semidirect |
| 13. C4×C5×C4⋊C4 | C4 | semidirect |
| 101. C2×C4⋊Q8 | Dic5 | semidirect |
| 108. #391 | Dic5 | semidirect |
| 112. C4×C4⋊C4 | Dic5 | semidirect |
| 216. C4×C5 | #354 | semidirect |
| 313. C5 | #13224 | semidirect |
| 340. C4 | #64761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2547 | 2 |
| C2×#64761 | 2 |
| #10602412 | 2 |
| C4×#3966 | 2 |
| #13224 | 5 |