Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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×#3994 | C2 | semidirect |
| 3. D5⋊M32 | C2 | semidirect |
| 4. #64908 | C2 | semidirect |
| 5. #64904 | C2 | semidirect |
| 8. C5×#135 | C4 | semidirect |
| 10. #4065 | C4 | semidirect |
| 14. #4058 | C4 | semidirect |
| 16. #4050 | C4 | semidirect |
| 38. C5×Q16 | C2×C4 | semidirect |
| 40. C5×D8 | C2×C4 | semidirect |
| 47. Dic20 | C2×C4 | semidirect |
| 48. D40 | C2×C4 | semidirect |
| 95. #135 | AGL(1,𝔽5) | semidirect |
| 136. Q16 | C2×AGL(1,𝔽5) | semidirect |
| 143. D8 | C2×AGL(1,𝔽5) | semidirect |
| 189. C5 | #2139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#135 | 2 |
| C2×#3994 | 2 |
| D5⋊M32 | 2 |
| #64908 | 2 |
| #64904 | 2 |
| #2139 | 5 |