The paper provides a methodology for identifying and analyzing group-theoretical symmetry in socio-economic applications. Symmetry is disclosed in the tasks of estimating contingent claims, the main hypotheses of financial markets, time
series of stock indexes, including pre-crisis periods, the distribution of urban population, and the duration of historical periods. The connection of solutions based on symmetry is displayed, in particular, with the management of pension savings and migration flows, as well as with the "digital" transformation of people's life attitudes.