Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction, and isomorphism of factorial designs have been extensively investigated. Much of the work has been on a case-by-case basis—addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper, we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct and check the isomorphism of multistage factorial designs with randomization restrictions. The examples presented in this paper particularly focus on split-lot designs.