Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1214 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 280 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×#3993 | C2 | semidirect |
| 3. C22×#3990 | C2 | semidirect |
| 4. C2×#64907 | C2 | direct (N × H) |
| 7. C22×C5×Q16 | C4 | semidirect |
| 11. C2×#4065 | C4 | semidirect |
| 13. C22×D40 | C4 | semidirect |
| 17. C2×#3993 | C22 | semidirect |
| 19. C2×#3990 | C22 | semidirect |
| 20. #64907 | C22 | direct (N × H) |
| 35. C2×C5×Q16 | C2×C4 | semidirect |
| 43. #4065 | C2×C4 | semidirect |
| 46. C2×D40 | C2×C4 | semidirect |
| 53. #3993 | C23 | semidirect |
| 55. #3990 | C23 | semidirect |
| 87. C5×Q16 | C22×C4 | semidirect |
| 95. D40 | C22×C4 | semidirect |
| 107. C22×Q16 | AGL(1,𝔽5) | semidirect |
| 164. C2×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 182. C22×C5 | #360 | semidirect |
| 221. Q16 | C22×AGL(1,𝔽5) | semidirect |
| 238. C2×C5 | C2×#360 | semidirect |
| 273. C5 | C22×#360 | semidirect |
| 280. C22 | #64907 | direct (N × H) |
| 291. C2 | C2×#64907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4065 | 2 |
| C22×#3993 | 2 |
| C22×#3990 | 2 |
| C2×#64907 | 2 |
| C22×#360 | 5 |