Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
256 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 256 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×#3995 | C2 | semidirect |
| 3. C2×#3990 | C2 | semidirect |
| 4. #64906 | C2 | direct (N × H) |
| 17. #3995 | C22 | semidirect |
| 19. #3990 | C22 | semidirect |
| 128. C2×C5 | #361 | semidirect |
| 156. C5 | C2×#361 | semidirect |
| 175. C2 | #64906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D8 | 2 |
| C2×#3995 | 2 |
| C2×#3990 | 2 |
| #64906 | 2 |
| C2×#361 | 5 |