The Lieb-Schultz-Mattis theorem is a powerful principle for quantum many-body systems. In this talk, I will discuss 1d LSM theorem in the presence of an exotic antiunitary translation or inversion symmetry involving time reversal. This explains the gaplessness of a class of chiral spin models not indicated by the Lieb-Schultz-Mattis (LSM) theorem and its known extensions. Moreover, I will present symmetry classes with minimal sets of magnetic space group generators that give nontrivial LSM-type constraints. These extended LSM theorems apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and triple-product interactions.