Rapid and strong changes in the Blazhko modulation of RR Lyrae stars, as have recently been detected in high-precision satellite data, have become a crucial topic in finding an explanation of the long-standing mystery of the Blazhko effect. We present here an analysis of the most extreme case detected so far, the RRab star V445 Lyr (KIC 6186029) which was observed with the Kepler space mission. V445 Lyr shows very strong cycle-to-cycle changes in its Blazhko modulation, which are caused by both a secondary long-term modulation period and irregular variations. In addition to the complex Blazhko modulation, V445 Lyr also shows a rich spectrum of additional peaks in the frequency range between the fundamental pulsation and the first harmonic. Among those peaks, the second radial overtone could be identified, which, combined with a metallicity estimate of [Fe/H] =-2.0 dex from spectroscopy, allowed us to constrain the mass (0.55-0.65 M⊙) and luminosity (40-50 L⊙) of V445 Lyr through theoretical Petersen diagrams. A non-radial mode and possibly the first overtone are also excited. Furthermore, V445 Lyr shows signs of the period-doubling phenomenon and a long-term period change. A detailed Fourier analysis along with a study of the O - C variation of V445 Lyr is presented, and the origin of the additional peaks and possible causes of the changes in the Blazhko modulation are discussed. The results are then put into context with those of the only other star with a variable Blazhko effect for which a long enough set of high-precision continuous satellite data has been published so far, the CoRoT star 105288363.