The set of elements produced by a genetic code is examined. The set is calculated for unusual ways of record of the genetic information named as overlapped genes, when the same site of DNA can code two protein sequences. The concept of elementary overlapping is entered which corresponds to overlapping for single amino acids. Five sets of elementary overlappings are constructed, each of which corresponds to one of five ways of the genetic overlappings which have been found out experimentally. The structure of sets of elementary overlappings and their properties is analyzed. The detailed and compressed representation of sets of elementary overlappings is given. The questions of application of sets are examined.