Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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×C4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C22×#700 | C2 | semidirect |
| 4. C2×#4010 | C2 | direct (N × H) |
| 6. C22×C5×Q8 | C4 | semidirect |
| 9. C2×#713 | C4 | semidirect |
| 12. C22×D20 | C4 | semidirect |
| 17. C2×C4×AGL(1,𝔽5) | C22 | semidirect |
| 19. C2×#700 | C22 | semidirect |
| 20. #4010 | C22 | direct (N × H) |
| 27. C2×C5×Q8 | C2×C4 | semidirect |
| 34. #713 | C2×C4 | semidirect |
| 39. C2×D20 | C2×C4 | semidirect |
| 48. C4×AGL(1,𝔽5) | C23 | semidirect |
| 50. #700 | C23 | semidirect |
| 64. C5×Q8 | C22×C4 | semidirect |
| 73. D20 | C22×C4 | semidirect |
| 86. C22×Q8 | AGL(1,𝔽5) | semidirect |
| 98. C22×C5 | #104 | semidirect |
| 120. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 141. C2×C5 | C2×#104 | semidirect |
| 153. Q8 | C22×AGL(1,𝔽5) | semidirect |
| 173. C5 | C22×#104 | semidirect |
| 180. C22 | #4010 | direct (N × H) |
| 191. C2 | C2×#4010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#713 | 2 |
| C22×C4×AGL(1,𝔽5) | 2 |
| C22×#700 | 2 |
| C2×#4010 | 2 |
| C22×#104 | 5 |