Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
782 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 320 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. C2×#64849 | C2 | direct (N × H) |
| 8. C22×C5×C16 | C4 | semidirect |
| 9. C22×#672 | C4 | semidirect |
| 10. C2×D5×C16 | C4 | semidirect |
| 12. #64849 | C22 | direct (N × H) |
| 26. C2×C5×C16 | C2×C4 | semidirect |
| 27. C2×#672 | C2×C4 | semidirect |
| 28. D5×C16 | C2×C4 | semidirect |
| 53. C5×C16 | C22×C4 | semidirect |
| 54. #672 | C22×C4 | semidirect |
| 60. C22×C16 | AGL(1,𝔽5) | semidirect |
| 97. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 100. C22×C5 | #366 | semidirect |
| 102. C2×D5 | #366 | semidirect |
| 133. C16 | C22×AGL(1,𝔽5) | semidirect |
| 134. C2×C5 | C2×#366 | semidirect |
| 136. D5 | C2×#366 | semidirect |
| 159. C5 | C22×#366 | semidirect |
| 165. C22 | #64849 | direct (N × H) |
| 175. C2 | C2×#64849 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3994 | 2 |
| C22×D5×C16 | 2 |
| C2×#64849 | 2 |
| C22×#366 | 5 |