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Mitotic activity is key for the assessment of malignancy in many tumors. Moreover, it has been demonstrated that the proportion of abnormal mitosis to normal mitosis is of prognostic significance. Atypical mitotic figures (MF) can be identified morphologically as having segregation abnormalities of the chromatids. In this work, we perform, for the first time, automatic subtyping of mitotic figures into normal and atypical categories according to characteristic morphological appearances of the different phases of mitosis. Using the publicly available MIDOG21 and TUPAC16 breast cancer mitosis datasets, two experts blindly subtyped mitotic figures into five morphological categories. Further, we set up a state-of-the-art object detection pipeline extending the anchor-free FCOS approach with a gated hierarchical subclassification branch. Our labeling experiment indicated that subtyping of mitotic figures is a challenging task and prone to inter-rater disagreement, which we found in 24.89% of MF. Using the more diverse MIDOG21 dataset for training and TUPAC16 for testing, we reached a mean overall average precision score of 0.552, a ROC AUC score of 0.833 for atypical/normal MF and a mean class-averaged ROC-AUC score of 0.977 for discriminating the different phases of cells undergoing mitosis.