International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3698 2020 2020 Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Mae Ka, Mueang, Phayao 56000, Thailand admin admin Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamil Nadu, India C. Sivakumar Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamil Nadu, India Neelamegarajan Rajesh This paper explores the fundamental concepts of sub-level subgroups, element orders, normalizers, and centralizers within the framework of neutrosophic group theory. Additionally, it examines quotient groups and the index of a subgroup, extending classical algebraic structures to a neutrosophic setting. Finally, a generalized formulation of Lagrange’s theorem is presented, demonstrating its applicability in the neutrosophic environment and highlighting its implications for uncertain and indeterminate group structures. 2025 2025 55 66 10.54216/IJNS.260206 https://www.americaspg.com/articleinfo/21/show/3698