Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2190 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 360 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. C22×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 3. C22×#4003 | C2 | semidirect |
| 4. C2×#64920 | C2 | direct (N × H) |
| 6. C23×C5×D4 | C4 | semidirect |
| 13. C2×#4084 | C4 | semidirect |
| 15. C22×C4⋊Dic5 | C4 | semidirect |
| 17. C2×(C2×AGL(1,𝔽5))⋊C4 | C22 | semidirect |
| 19. C2×#4003 | C22 | semidirect |
| 20. #64920 | C22 | direct (N × H) |
| 30. C22×C5×D4 | C2×C4 | semidirect |
| 50. #4084 | C2×C4 | semidirect |
| 53. C2×C4⋊Dic5 | C2×C4 | semidirect |
| 55. (C2×AGL(1,𝔽5))⋊C4 | C23 | semidirect |
| 57. #4003 | C23 | semidirect |
| 81. C2×C5×D4 | C22×C4 | semidirect |
| 109. C4⋊Dic5 | C22×C4 | semidirect |
| 111. C23×D4 | AGL(1,𝔽5) | semidirect |
| 179. C22×D4 | C2×AGL(1,𝔽5) | semidirect |
| 211. C22×C5 | #327 | semidirect |
| 251. C2×D4 | C22×AGL(1,𝔽5) | semidirect |
| 281. C2×C5 | C2×#327 | semidirect |
| 333. C5 | C22×#327 | semidirect |
| 348. C22 | #64920 | direct (N × H) |
| 363. C2 | C2×#64920 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4084 | 2 |
| C22×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C22×#4003 | 2 |
| C2×#64920 | 2 |
| C22×#327 | 5 |