To create unit tests, it may be necessary to refactor the production code, e.g. by widening access to specific methods or by decomposing classes into smaller units that are easier to test independently. We report on an extensive study to understand such composite refactoring procedures for the purpose of improving testability. We collected and studied 346,841 java pull requests from 621 GitHub projects. First, we compared the atomic refactorings in two populations: pull requests with changed test-pairs (i.e. with co-changes in production and test code and thus potentially including testability refactoring) and pull requests without test-pairs. We found significantly more atomic refactorings in test-pairs pull requests, such as Change Variable Type Operation or Change Parameter Type. Second, we manually analyzed the code changes of 200 pull requests, where developers explicitly mention the terms "testability" or "refactor + test". We identified ten composite refactoring procedures for the purpose of testability, which we call testability refactoring patterns. Third, we manually analyzed additional 524 test-pairs pull requests: both randomly selected and where we assumed to find testability refactorings, e.g. in pull requests about dependency or concurrency issues. About 25% of all analyzed pull requests actually included testability refactoring patterns. The most frequent were extract a method for override or for invocation, widen access to a method for invocation, and extract a class for invocation. We also report on frequent atomic refactorings which co-occur with the patterns and discuss the implications of our findings for research, practice, and education