[en] We present our analyses of 15 months of Kepler data on KIC 10139564. We detected 57 periodicities with a variety of properties not previously observed all together in one pulsating subdwarf B (sdB) star. Ten of the periodicities were found in the low-frequency region, and we associate them with nonradial g modes. The other periodicities were found in the high-frequency region, which are likely p modes. We discovered that most of the periodicities are components of multiplets with a common spacing. Assuming that multiplets are caused by rotation, we derive a rotation period of 25.6 ± 1.8 d. The multiplets also allow us to identify the pulsations to an unprecedented extent for this class of pulsator. We also detect l ≥ 2 multiplets, which are sensitive to the pulsation inclination and can constrain limb darkening via geometric cancellation factors. While most periodicities are stable, we detected several regions that show complex patterns. Detailed analyses showed that these regions are complicated by several factors. Two are combination frequencies that originate in the super-Nyquist region and were found to be reflected below the Nyquist frequency. The Fourier peaks are clear in the super-Nyquist region, but the orbital motion of Kepler smears the Nyquist frequency in the barycentric reference frame and this effect is passed on to the sub-Nyquist reflections. Others are likely multiplets but unstable in amplitudes and/or frequencies. The density of periodicities also makes KIC 10139564 challenging to explain using published models. This menagerie of properties should provide tight constraints on structural models, making this sdB star the most promising for applying asteroseismology. To support our photometric analysis, we have obtained spectroscopic radial-velocity measurements of KIC 10139564 using low-resolution spectra in the Balmer-line region. We did not find any radial-velocity variation. We used our high signal-to-noise average spectrum to improve the atmospheric parameters of the sdB star, deriving Teff = 31 859 K and log g = 5.673 dex. Based also on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.