Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4008 | C2 | semidirect |
| 3. C42×AGL(1,𝔽5) | C2 | semidirect |
| 4. #65681 | C2 | semidirect |
| 9. C5×#127 | C4 | semidirect |
| 11. #4082 | C4 | semidirect |
| 14. #4015 | C4 | semidirect |
| 31. C4×AGL(1,𝔽5) | D4 | semidirect |
| 64. #127 | AGL(1,𝔽5) | semidirect |
| 79. C4×C5 | #104 | semidirect |
| 128. C5 | #1962 | semidirect |
| 139. C4 | #4008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66050 | 2 |
| C2×#4008 | 2 |
| C42×AGL(1,𝔽5) | 2 |
| #65681 | 2 |
| #1962 | 5 |