Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
440 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 1. C22×C5×D8 | C2 | semidirect |
| 2. C22×D40 | C2 | semidirect |
| 3. C2×#3958 | C2 | direct (N × H) |
| 4. C22×#672 | C2 | semidirect |
| 8. C2×C5×D8 | C22 | semidirect |
| 11. C2×D40 | C22 | semidirect |
| 12. #3958 | C22 | direct (N × H) |
| 13. C2×#672 | C22 | semidirect |
| 23. C5×D8 | C23 | semidirect |
| 27. D40 | C23 | semidirect |
| 28. #672 | C23 | semidirect |
| 30. C22×D8 | D5 | semidirect |
| 51. C2×D8 | C2×D5 | semidirect |
| 57. C22×C5 | D16 | semidirect |
| 73. D8 | C22×D5 | semidirect |
| 78. C2×C5 | C2×D16 | semidirect |
| 94. C5 | C22×D16 | semidirect |
| 99. C22 | #3958 | direct (N × H) |
| 105. C2 | C2×#3958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D8 | 2 |
| C22×D40 | 2 |
| C2×#3958 | 2 |
| C22×#672 | 2 |
| C22×D16 | 5 |