Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
444 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. #10604803 | C2 | semidirect |
| 3. #10604798 | C2 | semidirect |
| 4. C2×#64906 | C2 | semidirect |
| 5. C2×#64903 | C2 | semidirect |
| 6. C2×#64847 | C2 | semidirect |
| 7. C2×#64846 | C2 | semidirect |
| 18. C2×C5×D16 | C4 | semidirect |
| 19. C2×#3959 | C4 | semidirect |
| 20. C2×#3958 | C4 | semidirect |
| 23. C2×#3932 | C4 | semidirect |
| 128. C5×C16 | C22⋊C4 | semidirect |
| 129. #672 | C22⋊C4 | semidirect |
| 137. C2×D16 | AGL(1,𝔽5) | semidirect |
| 302. C16 | C22⋊AGL(1,𝔽5) | semidirect |
| 349. C5 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65200 | 2 |
| #10604803 | 2 |
| #10604798 | 2 |
| C2×#64906 | 2 |
| C2×#64903 | 2 |
| C2×#64847 | 2 |
| C2×#64846 | 2 |
| #13249 | 5 |