Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×C5×#131 | C2 | semidirect |
| 3. #66159 | C2 | semidirect |
| 4. C2×#4055 | C2 | semidirect |
| 5. #65426 | C2 | semidirect |
| 6. #65423 | C2 | semidirect |
| 7. #65410 | C2 | semidirect |
| 8. #65405 | C2 | semidirect |
| 9. #65403 | C2 | semidirect |
| 10. #65402 | C2 | semidirect |
| 11. C2×#3948 | C2 | semidirect |
| 65. C5×M16 | D4 | semidirect |
| 87. C2×#131 | D5 | semidirect |
| 203. M16 | C22⋊D5 | semidirect |
| 261. C5 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#131 | 2 |
| #66167 | 2 |
| #66159 | 2 |
| C2×#4055 | 2 |
| #65426 | 2 |
| #65423 | 2 |
| #65410 | 2 |
| #65405 | 2 |
| #65403 | 2 |
| #65402 | 2 |
| C2×#3948 | 2 |
| #3063 | 5 |