Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
992 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 269 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×C5×M16 | C2 | semidirect |
| 3. C22×#681 | C2 | semidirect |
| 4. C2×#3955 | C2 | direct (N × H) |
| 14. C2×C5×M16 | C22 | semidirect |
| 17. C2×#681 | C22 | semidirect |
| 19. #3955 | C22 | direct (N × H) |
| 42. C5×M16 | C23 | semidirect |
| 45. #681 | C23 | semidirect |
| 49. C22×M16 | D5 | semidirect |
| 87. C2×M16 | C2×D5 | semidirect |
| 93. C22×C5 | #100 | semidirect |
| 128. M16 | C22×D5 | semidirect |
| 133. C2×C5 | C2×#100 | semidirect |
| 161. C5 | C22×#100 | semidirect |
| 168. C22 | #3955 | direct (N × H) |
| 179. C2 | C2×#3955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D20 | 2 |
| C22×C5×M16 | 2 |
| C22×#681 | 2 |
| C2×#3955 | 2 |
| C22×#100 | 5 |