In the WHO glioma classification guidelines grade (glioblastoma versus lower-grade glioma), IDH mutation and 1p/19q co-deletion status play a central role as they are important markers for prognosis and optimal therapy planning. Currently, diagnosis requires invasive surgical procedures. Therefore, we propose an automatic segmentation and classification pipeline based on routinely acquired pre-operative MRI (T1, T1 postcontrast, T2 and/or FLAIR). A 3D U-Net was designed for segmentation and trained on the BraTS 2019 training dataset. After segmentation, the 3D tumor region of interest is extracted from the MRI and fed into a CNN to simultaneously predict grade, IDH mutation and 1p19q co-deletion. Multi-task learning allowed to handle missing labels and train one network on a large dataset of 628 patients, collected from The Cancer Imaging Archive and BraTS databases. Additionally, the network was validated on an independent dataset of 110 patients retrospectively acquired at the Ghent University Hospital (GUH). Segmentation performance calculated on the BraTS validation set shows an average whole tumor dice score of 90% and increased robustness to missing image modalities by randomly excluding input MRI during training. Classification area under the curve scores are 93%, 94% and 82% on the TCIA test data and 94%, 86% and 87% on the GUH data for grade, IDH and 1p19q status respectively. We developed a fast, automatic pipeline to segment glioma and accurately predict important (molecular) markers based on pre-therapy MRI.