Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#4047 | C2 | semidirect |
| 3. C5×#408 | C2 | semidirect |
| 4. C2×#3969 | C2 | semidirect |
| 5. C2×#3957 | C2 | semidirect |
| 6. #64778 | C2 | semidirect |
| 7. #64770 | C2 | semidirect |
| 14. C2×#689 | C4 | semidirect |
| 15. C2×#688 | C4 | semidirect |
| 16. C2×#687 | C4 | semidirect |
| 17. C2×#686 | C4 | semidirect |
| 74. #408 | D5 | semidirect |
| 235. C5 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4096 | 2 |
| C2×#4047 | 2 |
| C5×#408 | 2 |
| C2×#3969 | 2 |
| C2×#3957 | 2 |
| #64778 | 2 |
| #64770 | 2 |
| #1876 | 5 |