We explore the halo structure of four gravitational lenses with well-observed , thin Einstein rings .
We find that the gravitational potentials are well described by ellipsoidal density distributions in the sense that the best-fit nonellipsoidal models have parameters consistent with their ellipsoidal counterparts .
We find upper limits on the standard parameters for the deviation from an ellipse of |a _ { 3 } ^ { B } / a _ { 0 } | < 0.023 , 0.019 , 0.037 , and 0.035 , and |a _ { 4 } ^ { B } / a _ { 0 } | < 0.034 , 0.041 , 0.051 , and 0.064 for SDSS J0924+0219 , HE 0435 - 1223 , B 1938+666 , and PG 1115+080 , respectively .
We find that the lens galaxies are at the centers of their dark matter halos , and obtain upper limits for the offset of each center of mass from the center of light of | \Delta \boldsymbol { x } | < 0 \farcs 004 , 0 \farcs 005 , 0 \farcs 009 , and 0 \farcs 005 , corresponding to 22 , 29 , 70 , and 23 pc .
These limits also exclude the possibility of any significant lopsidedness of the dark matter halos and set an upper limit of f _ { sat } \lesssim \sqrt { N } \% on the mass fraction of massive substructures inside the Einstein ring if they are divided over N satellites .
We also explore the properties of galaxies as substructures in groups for the lens PG 1115+080 , finding evidence for dark matter halos associated with the galaxies but no evidence for a clear distinction between satellite and central galaxies .