In large-scale panel data models with latent factors the number of factors and their loadings may change over time. This paper proposes an adaptive group-LASSO estimator that consistently determines the numbers of pre- and post-break factors and the stability of factor loadings. The data-dependent LASSO penalty is customized to account for unobserved factors and an unknown break date. A novel feature of our estimator is its robustness to unknown break dates. Existing procedures either overestimate the number of factors by neglecting the breaks or require known break dates for a subsample analysis. In an empirical application, we study the change in factor loadings and the emergence of new factors during the Great Recession. (Coauthors: Z.Liao, F. Schorfheide.)