Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#4130 | C2 | semidirect |
| 3. #65785 | C2 | direct (N × H) |
| 4. C2×#3999 | C2 | semidirect |
| 5. C22×C5×Q8 | C4 | semidirect |
| 9. C2×#713 | C4 | semidirect |
| 11. C22×D20 | C4 | semidirect |
| 13. C22×C4×D5 | C4 | semidirect |
| 17. #4130 | C22 | semidirect |
| 20. #3999 | C22 | semidirect |
| 27. C2×C5×Q8 | C2×C4 | semidirect |
| 40. C2×D20 | C2×C4 | semidirect |
| 46. C2×C4×D5 | C2×C4 | semidirect |
| 96. C22×Q8 | AGL(1,𝔽5) | semidirect |
| 134. C2×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 161. C2×C5 | #410 | semidirect |
| 198. C5 | C2×#410 | semidirect |
| 223. C2 | #65785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#713 | 2 |
| C2×#4130 | 2 |
| #65785 | 2 |
| C2×#3999 | 2 |
| C2×#410 | 5 |