Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C2×#4065 | C2 | semidirect |
| 2. C2×C5×Q32 | C2 | semidirect |
| 3. C2×#3960 | C2 | semidirect |
| 4. #65208 | C2 | direct (N × H) |
| 5. C2×D80 | C2 | semidirect |
| 6. C2×D5×C16 | C2 | semidirect |
| 11. #4065 | C22 | semidirect |
| 14. C5×Q32 | C22 | semidirect |
| 16. #3960 | C22 | semidirect |
| 18. D80 | C22 | semidirect |
| 19. D5×C16 | C22 | semidirect |
| 41. C2×Q32 | D5 | semidirect |
| 68. Q32 | C2×D5 | semidirect |
| 101. C2×C5 | #508 | semidirect |
| 121. C5 | C2×#508 | semidirect |
| 133. C2 | #65208 | 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×C5×Q32 | 2 |
| C2×#3960 | 2 |
| #65208 | 2 |
| C2×D80 | 2 |
| C2×D5×C16 | 2 |
| C2×#508 | 5 |