Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10604802 | C2 | semidirect |
| 3. C2×#64904 | C2 | semidirect |
| 4. C2×#64849 | C2 | semidirect |
| 5. C2×C16×AGL(1,𝔽5) | C2 | semidirect |
| 12. C2×C5×D16 | C4 | semidirect |
| 13. C2×#3958 | C4 | semidirect |
| 16. C2×D80 | C4 | semidirect |
| 87. C5×C16 | C22⋊C4 | semidirect |
| 88. #672 | C22⋊C4 | semidirect |
| 94. C2×D16 | AGL(1,𝔽5) | semidirect |
| 115. C2×AGL(1,𝔽5) | D16 | semidirect |
| 212. C16 | C22⋊AGL(1,𝔽5) | semidirect |
| 249. C5 | #13235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D16 | 2 |
| #10604802 | 2 |
| C2×#64904 | 2 |
| C2×#64849 | 2 |
| C2×C16×AGL(1,𝔽5) | 2 |
| #13235 | 5 |