Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
436 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 181 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×C4×C5×C8 | C2 | semidirect |
| 4. C2×C4×#168 | C2 | semidirect |
| 5. #64770 | C2 | semidirect |
| 16. #3952 | C4 | direct (N × H) |
| 29. C2×C4×D5 | C8 | semidirect |
| 33. C2×C5×C8 | C2×C4 | semidirect |
| 41. C2×#168 | C2×C4 | semidirect |
| 45. C2×C4×C8 | D5 | semidirect |
| 92. C2×D5 | C4×C8 | semidirect |
| 93. C4×C5 | C22⋊C8 | semidirect |
| 115. C2×C8 | C4×D5 | semidirect |
| 151. C5 | C4×C22⋊C8 | semidirect |
| 164. C4 | #3952 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D5 | 2 |
| C2×C4×C5×C8 | 2 |
| C2×#3952 | 2 |
| C2×C4×#168 | 2 |
| #64770 | 2 |
| C4×C22⋊C8 | 5 |