Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#687 | C2 | semidirect |
| 3. C22×#676 | C2 | semidirect |
| 4. C2×#4043 | C2 | semidirect |
| 5. C2×C5×#102 | C2 | semidirect |
| 6. C2×#3948 | C2 | semidirect |
| 7. C2×#3939 | C2 | semidirect |
| 8. #65069 | C2 | direct (N × H) |
| 19. C2×#687 | C22 | semidirect |
| 25. C2×#676 | C22 | semidirect |
| 27. #4043 | C22 | semidirect |
| 28. C5×#102 | C22 | semidirect |
| 29. #3948 | C22 | semidirect |
| 30. #3939 | C22 | semidirect |
| 63. C2×#168 | D4 | semidirect |
| 73. C2×#102 | D5 | semidirect |
| 106. #168 | C2×D4 | semidirect |
| 128. #102 | C2×D5 | semidirect |
| 183. C2×C5 | #468 | semidirect |
| 221. C5 | C2×#468 | semidirect |
| 243. C2 | #65069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4084 | 2 |
| C22×#687 | 2 |
| C22×#676 | 2 |
| C2×#4043 | 2 |
| C2×C5×#102 | 2 |
| C2×#3948 | 2 |
| C2×#3939 | 2 |
| #65069 | 2 |
| C2×#468 | 5 |