Hindu society could be seen as a collection of institutions. Collectivities evolve at each stage of human life. Traditionally woman is always a part of a jati. Man however, does not always belong to the same collectivity. In the four ashramas there are different collectivities he belongs to. During brahmacarya there is no established group he belongs to, except his gurukula. Gurukula is the vyavastha for brahmacaris. In grhastha ashrama he belongs to the varna he pursues and the jati he is born in. In vanaprastha there is no collectivity. During sanyasa he is very much alone, but there is a system/framework within which his activities are facilitated.
Family is the basic unit of the society. Marriage is the arrangement that enables this. Jati is the cultural unit that binds families. Varna is an abstraction that diversifies and arranges jatis in the society.
Guru-sishya parampara is really the corner stone of the society, which enables keeping religious/philosophical pursuits of a person separate from the remaining social system. Absence of this is the reason why religions in the west have penetrated into socio-economic-political system and have not really remained religions.
Broadly, these are the institutions that form the foundation of Hindu society:
- kutumba (family)
- jati (cultural unit)
- Vivaha (marriage - very much covered in the above two)
- Varna (an abstraction over jati)
- Gurukula Vyavastha (schooling and education system)
- Guru-Sishya parampara (teacher - disciple lineages)
- Sanyasi Vyavastha (monk hood and monastery system)
- Public administration
- Judiciary (8-12 are necessarily interrelated and not separate systems)