Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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×C5×C4⋊C8 | C2 | semidirect |
| 4. C2×#3946 | C2 | semidirect |
| 6. #64770 | C2 | semidirect |
| 7. #64744 | C2 | semidirect |
| 60. C2×C4⋊C8 | D5 | semidirect |
| 78. C2×C4×C5 | M16 | semidirect |
| 93. C2×Dic5 | M16 | semidirect |
| 208. C2×C4 | #676 | semidirect |
| 219. C5 | #1851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#676 | 2 |
| C2×C5×C4⋊C8 | 2 |
| C2×#3952 | 2 |
| C2×#3946 | 2 |
| C4×#685 | 2 |
| #64770 | 2 |
| #64744 | 2 |
| #1851 | 5 |