Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
702 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 21. C5×#498 | C4 | semidirect |
| 22. #65367 | C4 | semidirect |
| 24. #65147 | C4 | semidirect |
| 26. #64969 | C4 | semidirect |
| 54. C8×AGL(1,𝔽5) | Q8 | semidirect |
| 102. #498 | AGL(1,𝔽5) | semidirect |
| 234. C5 | #21732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617374 | 2 |
| #10613622 | 2 |
| #10604665 | 2 |
| #10604057 | 2 |
| #10604053 | 2 |
| #10603858 | 2 |
| C4×C8×AGL(1,𝔽5) | 2 |
| #21732 | 5 |