ABSTRACT. Classical mathematical methods are insufficient for resolving certain issues in real-life human problems due to the uncertainty of the data. Researchers from around the world have created innovative mathematical models, like soft and fuzzy set theories, to model the uncertainties that arise in different areas. Jun recently developed a hybrid structure that combined fuzzy and soft set concepts. The hybrid structure principle is applied to groupoids in this paper, and the properties of hybrid ideals and hybrid subgroupoids in groupoids are also described. Furthermore, the notions of hybrid subgroups, hybrid normal subgroups, and hybrid cosets in a group, as well as their key properties, are discussed. In addition, we show that any member of the collection of hybrid cut sets of a hybrid normal subgroup of a group G is a normal subgroup of G in the traditional sense. Finally, we obtain a finite-group hybrid version of Lagrange’s theorem.