In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (i) $p$-values from a previous study and (ii) omics annotation. The inclusion of this information in the analysis may enhance classification performance and feature selection but is not straightforward. We propose a group-regularized (logistic) elastic net regression method, where each penalty parameter corresponds to a group of features based on the external information. The method, termed gren, makes use of the Bayesian formulation of logistic elastic net regression to estimate both the model and penalty parameters in an approximate empirical-variational Bayes framework. Simulations and applications to three cancer genomics studies and one Alzheimer metabolomics study show that, if the partitioning of the features is informative, classification performance, and feature selection are indeed enhanced.