Iconography in art is the discipline that studies the visual content of artworks to determine their motifs and themes andto characterize the way these are represented. It is a subject of active research for a variety of purposes, including the interpretation of meaning, the investigation of the origin and diffusion in time and space of representations, and the study of influences across artists and art works. With the proliferation of digital archives of art images, the possibility arises of applying Computer Vision techniques to the analysis of art images at an unprecedented scale, which may support iconography research and education. In this paper we introduce a novel paintings data set for iconography classification and present the quantitativeand qualitative results of applying a Convolutional Neural Network (CNN) classifier to the recognition of the iconography of artworks. The proposed classifier achieves good performances (71.17% Precision, 70.89% Recall, 70.25% F1-Score and 72.73% Average Precision) in the task of identifying saints in Christian religious paintings, a task made difficult by the presence of classes with very similar visual features. Qualitative analysis of the results shows that the CNN focuses on the traditional iconic motifs that characterize the representation of each saint and exploits such hints to attain correct identification. The ultimate goal of our work is to enable the automatic extraction, decomposition, and comparison of iconography elements to support iconographic studies and automatic art work annotation.