Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1470 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1470 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 |
|---|---|---|
| 2. C22×#3994 | C2 | semidirect |
| 3. C22×D5⋊C16 | C2 | semidirect |
| 4. C2×#64904 | C2 | direct (N × H) |
| 7. C22×C5×D8 | C4 | semidirect |
| 11. C2×D5×D8 | C4 | semidirect |
| 13. C22×D40 | C4 | semidirect |
| 17. C2×#3994 | C22 | semidirect |
| 19. C2×D5⋊C16 | C22 | semidirect |
| 20. #64904 | C22 | direct (N × H) |
| 35. C2×C5×D8 | C2×C4 | semidirect |
| 43. D5×D8 | C2×C4 | semidirect |
| 46. C2×D40 | C2×C4 | semidirect |
| 53. #3994 | C23 | semidirect |
| 55. D5⋊C16 | C23 | semidirect |
| 89. C5×D8 | C22×C4 | semidirect |
| 97. D40 | C22×C4 | semidirect |
| 111. C22×D8 | AGL(1,𝔽5) | semidirect |
| 175. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 191. C22×C5 | #357 | semidirect |
| 198. C2×D5 | #357 | semidirect |
| 239. D8 | C22×AGL(1,𝔽5) | semidirect |
| 253. C2×C5 | C2×#357 | semidirect |
| 256. D5 | C2×#357 | semidirect |
| 294. C5 | C22×#357 | semidirect |
| 307. C22 | #64904 | direct (N × H) |
| 319. C2 | C2×#64904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D8 | 2 |
| C22×#3994 | 2 |
| C22×D5⋊C16 | 2 |
| C2×#64904 | 2 |
| C22×#357 | 5 |