Hello, the DNA is made up of protein structure and it is used to classify the genome set of organisms. The basic classification would be RNA organisms and DNA organisms. For example corona is a RNA virus while smallpox virus is a DNA virus. The nucleus consists of hereditary material called chromosomes>chromatins>DNA strands.There has been many attempts to classify based on protein particles viz-localization, function etc.. but all are under research process and not yet in application stage.

Hope this helps.