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	Uses	Fact about
No common composition factor with quotient group is quotient-transitive		Normal subgroup having no common composition factor with its quotient group (1) Quotient-transitive subgroup property (2)
No common composition factor with quotient group is transitive	No common composition factor with quotient group implies characteristic Characteristic of normal implies normal Third isomorphism theorem	Normal subgroup having no common composition factor with its quotient group (1) Transitive subgroup property (2)

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