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 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 \pm 1.8 days . The multiplets also allow us to identify the pulsations to an unprecedented extent for this class of pulsator . We also detect l \geq 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 these regions are complicated by several factors . Two are combination frequencies that originate in the superNyquist region and were found to be reflected below the Nyquist frequency . The Fourier peaks are clear in the superNyquist region , but the orbital motion of Kepler smears the Nyquist frequency in the barycentric reference frame and this effect is passed on to the subNyquist reflections . Others are likely multiplets but unstable in amplitudes and/or frequencies . The density of periodicities also make KIC 10139564 challenging to explain using published models . This menagerie of properties should provide tight constraints on structural models , making this subdwarf B 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 S/N average spectrum to improve the atmospheric parameters of the sdB star , deriving T _ { eff } = 31,859 K and \log g = 5.673 dex .