Deep learning is a growing field of research and and so is the application of deep learning to the analysis of medical images. Convolutional neural networks are used to diagnose diseases, determine risk of disease development, finding the exact area of abnormalities and and so on. Mammography is an imaging technique, which aims at the early detection of breast cancer. Invasive Lobular Carcinoma (ILC) is a type of breast cancer with properties that make it less visible on mammography. This study compares six models which apply convolutional neural networks to detect breast cancer, on its ability to detect ILC. Furthermore, transfer learning with ILC and healthy images is applied to one of these models to improve the performance on ILC data. For the evaluated breast cancer detection models, the performance on ILC data is worse than for a dataset which includes all breast cancer types and more healthy images. The model that transfer learning is applied to performs better on ILC data after transfer learning than before, with an increase of 0.09 for the AUC value. Additional analyses of the results show that women with high breast density have a lower chance of getting a correct ILC diagnosis from the model than women with low beast density and this also holds for other types of breast cancer. Lastly, the model outcomes are compared to radiologist reviews, to determine the additional value of models to the routine screening performed by radiologists. Within the images that are labeled as healthy by the radiologists, a model could be applied to detect tumor that have been missed by radiologists. When a specificity of 89% was allowed, 23% of the missed tumors could have been detected by the original GMIC model. In this way, the models used in this study and other deep learning models that are in development now, can contribute to breast cancer detection from mammography, and ILC specifically.