  We present results from a systematic investigation of the X-ray properties of
a sample of moderate redshift (0.3<z<0.6) galaxy groups. These groups were
selected not by traditional X-ray or optical search methods, but rather by an
association, either physical or along the line of sight, with a strong
gravitational lens. We calculate the properties of seven galaxy groups in the
fields of six lens systems. Diffuse X-ray emission from the intragroup medium
is detected in four of the groups. All of the detected groups have X-ray
luminosities greater than 10^{42} h^{-2} erg/s, and lie on the L_X-sigma_v
relations defined by local groups and clusters. The upper limits for the
non-detections are also consistent with the local L_X-sigma_v relationships.
Although the sample size is small and deeper optical and X-ray data are needed,
these results suggest that lens-selected groups are similar to X-ray selected
samples and, thus, are more massive than the typical poor-group environments of
local galaxies.
