Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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. D5⋊(C22⋊C8) | C2 | semidirect |
| 3. #65748 | C2 | semidirect |
| 4. #65702 | C2 | semidirect |
| 7. C2×D5⋊C8 | C22 | semidirect |
| 14. #4003 | C22 | semidirect |
| 15. C4⋊#170 | C22 | semidirect |
| 16. C4×#170 | C22 | semidirect |
| 23. C2×D20 | C8 | semidirect |
| 41. C22×D5 | C2×C8 | semidirect |
| 44. C2×C4×C5 | C2×C8 | semidirect |
| 52. D20 | C2×C8 | semidirect |
| 116. C2×C4 | D5⋊C8 | semidirect |
| 120. C5 | #2972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4039 | 2 |
| D5⋊(C22⋊C8) | 2 |
| #65748 | 2 |
| #65702 | 2 |
| #2972 | 5 |