Modes of low-frequency variability in the 500 hPa heights in the Northern Hemisphere are investigated separately by means of rotated principal component analysis for low, moderate, and high solar activity. The study is based on monthly values from 54 extended winter seasons (December to March, 1950--2003). The modes identified correspond well with the patterns described in the comprehensive studies of the low-frequency circulation variability. All the modes exhibit variations in their spatial extent, position of action centers, and intensity in response to the solar activity. Two of the modes disappear under a particular phase of the solar cycle: The East Pacific pattern is absent under solar minima, whereas the tropical/North American pattern disappears under solar maxima. Under the high solar activity the North Atlantic Oscillation (NAO) tends to split into two modes, one of which resembles the original NAO shifted to the west, while the other consists of a wave train centered over the Mediterranean and reaching to central Asia. Under a high solar activity, zonal modes tend to be more intensive, whereas the meridionally oriented modes tend to be less active. A general tendency is that under solar maxima the modes are more zonal, their teleconnections span longer distances, and their action centers occupy larger areas. The one-point correlation maps for the action centers of the modes indicate that the changes in the appearance of the modes can be attributed to two major mechanisms: (1) autocorrelation structures change between different phases of the solar cycle and (2) the weight (intensity) of the autocorrelation structures with which they operate is changing, which results in geographical shifts of the modes.