Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×D5×Q16 | C2 | semidirect |
| 4. C5×#462 | C2 | semidirect |
| 5. #65475 | C2 | semidirect |
| 6. #65381 | C2 | semidirect |
| 7. C4×#689 | C2 | semidirect |
| 8. #65138 | C2 | semidirect |
| 10. #65102 | C2 | semidirect |
| 11. #65097 | C2 | semidirect |
| 67. #689 | D4 | semidirect |
| 89. #462 | D5 | semidirect |
| 109. D20 | Q16 | semidirect |
| 156. C2×D5 | C2×Q16 | semidirect |
| 161. C4×C5 | C2×Q16 | semidirect |
| 241. C5 | D4×Q16 | semidirect |
| 254. C4 | D5×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q16 | 2 |
| #66061 | 2 |
| Q8×D20 | 2 |
| C5×#462 | 2 |
| #65475 | 2 |
| #65381 | 2 |
| C4×#689 | 2 |
| #65138 | 2 |
| #65123 | 2 |
| #65102 | 2 |
| #65097 | 2 |
| D4×Q16 | 5 |