We consider relatively prime integer numbers m and n such that each solvable group of order mn has a normal subgroup of order m. We prove that each brace of size mn is a semidirect product of a brace of size m and a brace of size n. We further give a method to classify braces of size mn from the classification of braces of sizes m and n. We apply this result to determine all braces of size p²q², for p and q odd primes satisfying some conditions which hold in particular for p a Germain prime and q=2p+1.

This work was supported by grant PID2019-107297GB-I00, Ministerio de Ciencia, Innovacion y Universidades.