  We present a reconstructions of galaxy-cluster-scale mass distributions from
simulated gravitational lensing data sets including strong lensing, weak
lensing shear, and measurements of quadratic image distortions -- flexion. The
lensing data is constructed to make a direct comparison between mass
reconstructions with and without flexion. We show that in the absence of
flexion measurements, significant galaxy-group scale substructure can remain
undetected in the reconstructed mass profiles, and that the resulting profiles
underestimate the aperture mass in the substructure regions by $\sim25-40\%$.
When flexion is included, subhaloes down to a mass of $\sim3\times10^{12}$
M$_\odot$ can be detected at an angular resolution smaller than 10\arcsec.
Aperture masses from profiles reconstructed with flexion match the input
distribution values to within an error of $\sim13\%$, including both
statistical error and scatter. This demonstrates the important constraint that
flexion measurements place on substructure in galaxy clusters and its utility
for producing high-fidelity mass reconstructions.
