We apply a state-of-the-art membership inference attack (MIA) to systematically test the practical privacy vulnerability of fine-tuning large image classification models.We focus on understanding the properties of data sets and samples that make them vulnerable to membership inference. In terms of data set properties, we find a strong power law dependence between the number of examples per class in the data and the MIA vulnerability, as measured by true positive rate of the attack at a low false positive rate. For an individual sample, large gradients at the end of training are strongly correlated with MIA vulnerability.