We use the Wide Field Camera 3 onboard the Hubble Space Telescope to obtain deep, highresolution photometry of the young (similar to 100 Myr) star clusterNGC1850 in the Large Magellanic Cloud. We analyse the cluster colour-magnitude diagram (CMD) and find that it hosts an extended main-sequence turn-off (MSTO) and a double main sequence (MS). We demonstrate that these features cannot be due to photometric errors, field star contamination or differential reddening. From a comparison with theoretical models and Monte Carlo simulations, we show that a coeval stellar population featuring a distribution of stellar rotation rates can reproduce the MS split quite well. However, it cannot reproduce the observed MSTO region, which is significantly wider than the simulated ones. Exploiting narrow-band H alpha imaging, we find that the MSTO hosts a population of H alpha-emitting stars that are interpreted as rapidly rotating Be-type stars. We explore the possibility that the discrepancy between the observed MSTO morphology and that of the simulated simple stellar population (SSP) is caused by the fraction of these objects that are highly reddened, but we rule out this hypothesis. We demonstrate that the global CMD morphology is well reproduced by a combination of SSPs that covers an age range of similar to 35 Myr as well as a wide variety of rotation rates. We derive the cluster mass and escape velocity, and use dynamical evolution models to predict their evolution starting at an age of 10 Myr. We discuss these results and their implications in the context of the extended MSTO phenomenon.