We explore the halo-to-halo variation of dark matter substructure in galaxy-sized dark matter halos , focusing on its implications for strongly gravitational lensed systems .
We find that the median value for projected substructure mass fractions within projected radii of 3 % of the host halo virial radius is approximately f _ { sub } \approx 0.25 \% , but that the variance is large with a 95-percentile range of 0 \leq f _ { sub } \leq 1 \% .
We quantify possible effects of substructure on quadruply-imaged lens systems using the cusp relation and the simple statistic , R _ { cusp } .
We estimate that the probability of obtaining the large values of the R _ { cusp } which have been observed from substructure effects is roughly \sim 10 ^ { -3 } to \sim 10 ^ { -2 } .
We consider a variety of possible correlations between host halo properties and substructure properties in order to probe possible sample biases .
In particular , low-concentration host dark matter halos have more large substructures and give rise to large values of R _ { cusp } more often .
However , there is no known observational bias that would drive observed quadruply-imaged quasars to be produced by low-concentration lens halos .
Finally , we show that the substructure mass fraction is a relatively reliable predictor of the value of R _ { cusp } .