Abstract In this paper, we study topological groups having all closed subgroups (totally) minimal and call such c-(totally) . We show that a locally compact c-minimal connected group is compact. Using well-known theorem of [P. Hall C. R. Kulatilaka, A property finite groups, J. Lond. Math. Soc. 39 1964, 235–239] characterization certain class Lie due to [S. K. Grosser W. N. Herfort, Abelian Tra...