Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #66161 | C2 | semidirect |
| 3. C5×#408 | C2 | semidirect |
| 4. #65422 | C2 | semidirect |
| 5. #65410 | C2 | semidirect |
| 6. #65402 | C2 | semidirect |
| 7. C2×#3949 | C2 | semidirect |
| 8. #65026 | C2 | semidirect |
| 9. #65024 | C2 | semidirect |
| 10. #65012 | C2 | semidirect |
| 11. #65010 | C2 | semidirect |
| 88. #408 | D5 | semidirect |
| 241. C5 | #3099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66167 | 2 |
| #66161 | 2 |
| C5×#408 | 2 |
| #65422 | 2 |
| #65410 | 2 |
| #65402 | 2 |
| C2×#3949 | 2 |
| #65026 | 2 |
| #65024 | 2 |
| #65012 | 2 |
| #65010 | 2 |
| #3099 | 5 |