Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#4055 | C2 | semidirect |
| 3. C2×#4015 | C2 | semidirect |
| 4. C4×C5×M16 | C2 | semidirect |
| 5. #65004 | C2 | semidirect |
| 6. #64988 | C2 | semidirect |
| 7. #64982 | C2 | semidirect |
| 39. C5×M16 | D4 | semidirect |
| 56. C4×M16 | D5 | semidirect |
| 101. C4×C5 | #137 | semidirect |
| 119. M16 | D20 | semidirect |
| 151. C5 | #3152 | semidirect |
| 161. C4 | #4055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4055 | 2 |
| #65811 | 2 |
| C2×#4015 | 2 |
| C4×C5×M16 | 2 |
| #65004 | 2 |
| #64988 | 2 |
| #64982 | 2 |
| #3152 | 5 |