Abstract | Many strong gravitational lenses lie in complex environments, such as poor groups of galaxies, that significantly bias conclusions from lens analyses. We are undertaking a photometric survey of all known galaxy-mass strong lenses to characterize their environments and include them in careful lens modeling, as well as to build a large, uniform sample of galaxy groups at intermediate redshifts for evolutionary studies. In this paper we present wide-field photometry of the environments of 12 lens systems with 0.24<=zlens<=0.5. Using a red sequence identifying technique, we find that 8 of the 12 lenses lie in groups and that 10 group-like structures are projected along the line of sight toward 7 of these lenses. Follow-up spectroscopy of a subset of these fields confirms these results. For lenses in groups, the group centroid position is consistent with the direction of the external tidal shear required by lens models. Lens galaxies are not all super-L* elliptical galaxies; the median lens luminosity is <~L*, and the distribution of lens luminosities extends 3 mag below L* (in agreement with theoretical models). Only two of the lenses in groups are the brightest group galaxy, in qualitative agreement with theoretical predictions. As in the local universe, the highest velocity dispersion (σ) groups contain a brightest member spatially coincident with the group centroid, whereas lower σ groups tend to have an offset brightest group galaxy. This suggests that higher σ groups are more dynamically relaxed than lower σ groups and that at least some evolved groups exist by z~0.5. |