We conducted a deep survey of resolved subsystems among wide binaries with solar-type components within 67 pc of the Sun. Images of 61 stars in the K and H bands were obtained with the Near-Infrared Coronagraphic Imager adaptive-optics instrument on the 8 m Gemini-South telescope. Our maximum detectable magnitude difference is about 5 mag and 7.8 mag at 0.'' 15 and 0.'' 9 separations, respectively. This enables a complete census of subsystems with stellar companions in the projected separation range from 5 to 100 AU. Out of seven such companions found in our sample, only one was previously known. We determine that the fraction of subsystems with projected separations above 5 AU is 0.12 +/- 0.04 and that the distribution of their mass ratio is flat, with a power-law index of 0.2 +/- 0.5. Comparing this with the properties of closer spectroscopic subsystems (separations below 1 AU), it appears that the mass-ratio distribution does not depend on the separation. The frequency of subsystems in the separation ranges below 1 AU and between 5 and 100 AU is similar, about 0.15. Unbiased statistics of multiplicity higher than 2, advanced by this work, provide constraints on star formation theory.