Context: Substructures - dark lanes and tails - of umbral dots (UDs) were predicted by numerical simulations of magnetoconvection and have been detected later in some observations. Aims: To provide constraints for realistic theoretical models of sunspot umbrae, we describe the observed properties and evolutionary characteristics of UDs (including their substructure) and of other umbral structures. Methods: We analyse a 6 h 23 min time series of broadband images of a large umbra in the active region NOAA 10634, acquired with the 1-m Swedish Solar Telescope, in the wavelength band around 602 nm. A 43 min part of this series was reconstructed with the MFBD method, reaching a spatial resolution of 0.14 arcsec. With the help of image segmentation, feature tracking, and local correlation tracking, we measured brightness, size, lifetime, and horizontal velocities of various umbral structures. Results: Large structures in the umbra - strong and faint light bridges (LBs) and an extended penumbral filament - evolve on time scales of hours. Most (90%) of UDs and bright point-like features in faint LBs split and merge, and their median lifetimes are 3.5 or 5.7 min, depending on whether the split or merge event is considered as the end of their life. Both UDs and features in faint LBs that do not split or merge are clearly smaller (0.15 arcsec) than the average size (0.17 arcsec) of all features. Horizontal motions of umbral bright small-scale features are directed either into the umbra or along faint LBs with mean horizontal velocities of 0.34 km s-1. Features faster than 0.4 km s-1 appear mostly at the periphery of the umbra. The motion of peripheral UDs (PUDs) seems to be the continuation of the motion of penumbral grains (PGs). The intensity of dark lanes, measured in four bright central UDs (CUDs), is by a factor 0.8 lower than the peak intensity of CUDs. The width of dark lanes is probably less than the resolution limit 0.14 arcsec. The characteristic time of substructure changes of UDs is ~4 min. We observe narrow (0.14 arcsec) bright and dark filaments connected with PUDs. The bright filaments are 0.06 I_ph brighter than the dark ones. Usually one dark and two bright filaments form a 0.4 arcsec wide tail attached to one PUD, resembling a short dark-cored penumbral filament. Conclusions: Our results indicate the similarity between PUDs and PGs located at the tips of bright penumbral filaments. The features seen in numerical MHD simulations are consistent with our observations of dark lanes in CUDs and tails attached to PUDs.