Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3999 | C2 | semidirect |
| 3. #64922 | C2 | direct (N × H) |
| 4. C22×C5×D4 | C4 | semidirect |
| 9. #4086 | C4 | semidirect |
| 11. C2×C4×Dic5 | C4 | semidirect |
| 13. #3999 | C22 | semidirect |
| 21. C2×C5×D4 | C2×C4 | semidirect |
| 35. C4×Dic5 | C2×C4 | semidirect |
| 66. C22×D4 | AGL(1,𝔽5) | semidirect |
| 105. C2×D4 | C2×AGL(1,𝔽5) | semidirect |
| 116. C2×C5 | #353 | semidirect |
| 145. C5 | C2×#353 | semidirect |
| 169. C2 | #64922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4086 | 2 |
| C2×#3999 | 2 |
| #64922 | 2 |
| C2×#353 | 5 |