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If (A, B) and (A′, B′) are co-t-structures of a triangulated category, then (A′, B′) is called intermediate if A⊆ A′⊆ Σ A. Our main results show that intermediate co-t-structures are in bijection with two-term silting subcategories, and also with support τ-tilting subcategories under some assumptions. We also show that support τ-tilting subcategories are in bijection with certain finitely generated torsion classes. These results generalise work by Adachi, Iyama, and Reiten.