Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 3. C2×#4003 | C2 | semidirect |
| 4. #64920 | C2 | direct (N × H) |
| 6. C22×C5×D4 | C4 | semidirect |
| 13. #4084 | C4 | semidirect |
| 15. C2×C4⋊Dic5 | C4 | semidirect |
| 17. (C2×AGL(1,𝔽5))⋊C4 | C22 | semidirect |
| 19. #4003 | C22 | semidirect |
| 29. C2×C5×D4 | C2×C4 | semidirect |
| 47. C4⋊Dic5 | C2×C4 | semidirect |
| 86. C22×D4 | AGL(1,𝔽5) | semidirect |
| 131. C2×D4 | C2×AGL(1,𝔽5) | semidirect |
| 151. C2×C5 | #327 | semidirect |
| 191. C5 | C2×#327 | semidirect |
| 219. C2 | #64920 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4084 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| C2×#4003 | 2 |
| #64920 | 2 |
| C2×#327 | 5 |