Non-metallic elements do not follow the properties of metallic elements. Non-metallic elements cannot conduct electricity because they do not have free electrons.
Non-metals that conduct electricity:
Graphite, i.e an allotrope of Carbon, is a non-metal which conducts electricity.
Graphite is also a non-metallic substance with a metallic luster.
As, graphite has a layered structure that contains free electrons, and the free electron is responsible for electrical conduction.
Final Answer: Graphite is the only non-metal that can conduct electricity.