This paper describes the system Clustering on Manifolds of Contextualized Embeddings (CMCE) submitted to the SemEval-2020 Task 1 on Unsupervised Lexical Semantic Change Detection. Subtask 1 asks to identify whether or not a word gained/lost a sense across two time periods. Subtask 2 is about computing a ranking of words according to the amount of change their senses underwent. Our system uses contextualized word embeddings from MBERT, whose dimensionality we reduce with an autoencoder and the UMAP algorithm, to be able to use a wider array of clustering algorithms that can automatically determine the number of clusters. We use Hierarchical Density Based Clustering (HDBSCAN) and compare it to Gaussian MixtureModels (GMMs) and other clustering algorithms. Remarkably, with only 10 dimensional MBERT embeddings (reduced from the original size of 768), our submitted model performs best on subtask 1 for English and ranks third in subtask 2 for English. In addition to describing our system, we discuss our hyperparameter configurations and examine why our system lags behind for the other languages involved in the shared task (German, Swedish, Latin). Our code is available at https://github.com/DavidRother/semeval2020-task1