Science has revealed that alleles exist in all populations all over the world in some frequency. This trend is defined as a cline. Therefore, while some characteristics are more frequent in some populations than others, it is impossible to define a population by one particular set of alleles. For this reason, it is biologically impossible to define a race. The classification system would be subjective.
Race is a social concept disguised in the eugenics movement as a biological one.
It is important to note that eugenics and Nazism evolved along different trajectories and they are not synonymous. Eugenics was associated more with an elitist effort to breed superior individuals. While it was most definitely a stark form of racism, the extent to which it was taken was not as inhumane and violent as the Nazi's disastrous concentration on negative eugenics. The synthesis between Nazism and eugenics was a process of adaptation on both sides. The Nazi takeover marks a fundamental change in course of eugenics.