Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. C5×#537 | C2 | semidirect |
| 2. #66167 | C2 | semidirect |
| 3. C2×#4096 | C2 | semidirect |
| 4. C2×#4094 | C2 | semidirect |
| 5. #65521 | C2 | semidirect |
| 6. #65341 | C2 | semidirect |
| 7. #65337 | C2 | semidirect |
| 8. #65330 | C2 | semidirect |
| 9. #65328 | C2 | semidirect |
| 10. #65255 | C2 | semidirect |
| 11. C2×#3940 | C2 | semidirect |
| 84. C2×#168 | D4 | semidirect |
| 91. #537 | D5 | semidirect |
| 276. C5 | #3060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#537 | 2 |
| #66167 | 2 |
| C2×#4096 | 2 |
| C2×#4094 | 2 |
| #65521 | 2 |
| #65341 | 2 |
| #65337 | 2 |
| #65330 | 2 |
| #65328 | 2 |
| #65255 | 2 |
| C2×#3940 | 2 |
| #3060 | 5 |