Within the framework of the Interacting Boson Model (IBM-1), we try to examine the ability to characterize the nuclear structure of molybdenum isotopes in the range of 96–108 Mo. The goal of this study is to use the three basic dynamic symmetries incorporated into the model to investigate the nuclear structure of specific atomic nuclei. There is a significant agreement between the calculated energy levels and the experimental measurements for molybdenum isotopes. We also calculated and compared the probability for reduced electromagnetic transitions, specifically B(E2), with the model's theoretical results. Our research has shown that molybdenum isotopes have a wide range of characteristics. We found that there are different kinds of molybdenum isotopes with atomic numbers 96 to 108. Some of them have U(5) vibrational symmetry, while others have features that are somewhere between U(5) and SU(3) symmetries. These nuclei, commonly referred to as X(5) nuclei, are located in the transition region and exhibit shape coexistence.