Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3993 | C2 | semidirect |
| 3. C2×#3990 | C2 | semidirect |
| 4. #64907 | C2 | direct (N × H) |
| 7. C2×C5×Q16 | C4 | semidirect |
| 11. #4065 | C4 | semidirect |
| 13. C2×D40 | C4 | semidirect |
| 17. #3993 | C22 | semidirect |
| 19. #3990 | C22 | semidirect |
| 34. C5×Q16 | C2×C4 | semidirect |
| 40. D40 | C2×C4 | semidirect |
| 78. C2×Q16 | AGL(1,𝔽5) | semidirect |
| 111. Q16 | C2×AGL(1,𝔽5) | semidirect |
| 125. C2×C5 | #360 | semidirect |
| 153. C5 | C2×#360 | semidirect |
| 169. C2 | #64907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4065 | 2 |
| C2×#3993 | 2 |
| C2×#3990 | 2 |
| #64907 | 2 |
| C2×#360 | 5 |