The worldwide spread of the novel coronavirus originating from Wuhan, China led to an ongoing pandemic as COVID-19. The disease being a contagion transmitted rapidly in India through the people having travel histories to the affected countries, and their contacts that tested positive. Millions of people across all states and union territories (UT) were affected leading to serious respiratory illness and deaths. In the present study, two unsupervised clustering algorithms namely k-means clustering and hierarchical agglomerative clustering are applied on the COVID-19 dataset in order to group the Indian states/UTs based on the pandemic effect and the vaccination program from the period of March, 2020 to early June, 2021. The aim of the study is to observe the plight of each state and UT of India combating the novel coronavirus infection and to monitor their vaccination status. The research study will be helpful to the government and to the frontline workers coping to restrict the transmission of the virus in India. Also, the results of the study will provide a source of information for future research regarding the COVID-19 pandemic in India.