Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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×#688 | C2 | semidirect |
| 3. C5×#391 | C2 | semidirect |
| 4. C2×#3941 | C2 | semidirect |
| 5. #64744 | C2 | semidirect |
| 23. C2×C5×Q8 | D4 | semidirect |
| 42. C2×#168 | D4 | semidirect |
| 46. #391 | D5 | semidirect |
| 63. C2×C4×C5 | SD16 | semidirect |
| 105. C2×Q8 | D20 | semidirect |
| 151. C2×C4 | #688 | semidirect |
| 157. C5 | #2014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#688 | 2 |
| C2×#4020 | 2 |
| C5×#391 | 2 |
| C2×#3941 | 2 |
| #64744 | 2 |
| #2014 | 5 |