Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. #10617425 | C2 | semidirect |
| 3. #10604847 | C2 | semidirect |
| 4. #10604834 | C2 | semidirect |
| 5. #10604784 | C2 | semidirect |
| 6. #10598665 | C2 | semidirect |
| 7. #10598662 | C2 | semidirect |
| 20. C2×C5×SD32 | C4 | semidirect |
| 21. C2×#3961 | C4 | semidirect |
| 22. C2×#3958 | C4 | semidirect |
| 25. C2×#3932 | C4 | semidirect |
| 140. C2×SD32 | AGL(1,𝔽5) | semidirect |
| 342. C5 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617425 | 2 |
| C2×#65205 | 2 |
| #10604847 | 2 |
| #10604834 | 2 |
| #10604784 | 2 |
| #10598665 | 2 |
| #10598662 | 2 |
| #13016 | 5 |