We have been able to connect the statistics of the observed double image gravitational lenses to the general properties of the internal structure of dark matter haloes .
Our analytical theory for the GNFW lenses with parametrized cusp slope ( \alpha ) gives us a relation connecting the cusp slope of the lensing profile to the observed magnification ratio of the produced images and location of the optical axis .
The relation does not depend on cosmology , total lens mass , concentration or redshifts of the the lens and the lensed object .
Simple geometry of axially symmetric lensing and aforementioned relation enables us to define a threshold value \alpha _ { \mbox { \tiny CSL } } for the cusp slope , independent from location of the optical axis .
The threshold cusp slope value \alpha = \alpha _ { \mbox { \tiny CSL } } is the shallowest slope for the inner part of the GNFW profile that can produce the observed magnification ratio with any lensing configuration .
We use distribution of these threshold values in a statistical study of the double image lenses in order to limit the possible cusp slope values , and identify whether there exists a population of haloes with similar profiles .
Our theoretical fit indicates that within our sample of double image gravitational lenses , most of the haloes have cusp slope \alpha = -1.95 \pm 0.02 .
We have also found an indication of a second population of lenses with a cusp slope value \alpha = -1.49 \pm 0.09 .
We estimate that there is about 99 per cent probability that the observed feature in the threshold value limit distribution is produced by the second population of lenses , with their own characteristic density profile .
The data indicating the exact characteristics of the sub-population is noisy .
Roughly one out of six haloes within the sample belong to this shallower cusp slope group .
We investigate errors in our analysis by constructing mock catalogues with the Monte-Carlo method .