A finite abelian group is isomorphic to the product group Cd1×Cd2×…×Cdk for unique integers d1, d2,… dk⩾2 such that d1|d2|…|dk. Thus, there are five abelian groups of order 240 = 24·3·5, namely C240, C2×C120, C4×C60, C2×C2×C60, C2×C2×C2×C30.
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