Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
472 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #10604849 | C2 | semidirect |
| 4. C2×#64910 | C2 | semidirect |
| 6. #10598663 | C2 | semidirect |
| 7. #10598660 | C2 | semidirect |
| 20. C2×C5×Q32 | C4 | semidirect |
| 21. C2×#3961 | C4 | semidirect |
| 22. C2×#3960 | C4 | semidirect |
| 25. C2×#3932 | C4 | semidirect |
| 140. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 353. C5 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65741 | 2 |
| C2×#65207 | 2 |
| #10604849 | 2 |
| C2×#64910 | 2 |
| C2×#64907 | 2 |
| #10598663 | 2 |
| #10598660 | 2 |
| #13039 | 5 |