Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
140 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 34 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×Q32 | C4 | semidirect |
| 10. #64725 | C4 | semidirect |
| 44. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 118. C5 | #7423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602298 | 2 |
| #10598666 | 2 |
| #10598657 | 2 |
| #7423 | 5 |