International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2059 2020 2020 Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia Ashraf Al Al-Quran Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 70300 Negeri Sembilan, Malaysia Zahari Md. Rodzi Curricula and Teaching Methods Department, College of Education, King Faisal University, Al-Ahsa 31982, Saudi Arabia Mona Aladil College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq Rawan A. shlaka Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram, 83125,Indonesia Mamika Ujianita Romdhini Academic Department, Saudi Petroleum Services Polytechnic,Dammam, Saudi Arabia Mohammad K. Tahat Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia,Bangi 43600, Selangor, Malaysia Obadah Said Solaiman Groups and subgroups are rich algebraic structures, and both of them depend on binary operations in their work. The discussion of this paper is organized into two parts. In the first part, we define the notion of Qcomplex neutrosophic soft sets (Q-CNSSs) by amalgamating two previous models of Q-complex neutrosophic set (Q-CNS) and soft set (SS) to address the issues of two-dimensionality (two variables) in a universal set under a parametric environment. Subsequently, the relation between Q-CNSSs and Q- neutrosophic soft sets (Q-NSSs) is verified. A basic set theory for this hybrid model is developed. In particular, null Q-CNSS and absolute Q-CNSS are defined. The basic operators of the complement, subset, equality, union and intersection are advanced and their properties are examined. Further, the notions of the homogeneous and completely homogeneous Q-CNSSs are proposed along with some illustrated examples. In part two, we move to study some algebraic structures of this model when we define the notions of Q-complex neutrosophic soft groups (QCNSG) and Q-complex neutrosophic soft subgroups (Q-CNSSG). Then, the relation between Q-CNSG and Q-neutrosophic soft group (Q-NSG) is scrutinized. Moreover, the algebraic properties of the Q-CNSG and Q-CNSSG are discussed and verified. Finally, some theories that show the relationship between the Q-CNSG and the soft group are proposed. 2023 2023 60 76 10.54216/IJNS.220105 https://www.americaspg.com/articleinfo/21/show/2059