Let G be a finite group with proper subgroups H, J and K. Further, let K ⊂ J ⊂ H. If [G:H] = 5, [H:J] = 3 and [J:K] = 7, what is [G:K]?

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Let G be a finite group with proper subgroups H, J and K. Further, let K ⊂ J ⊂ H. If [G:H] = 5, [H:J] = 3 and [J:K] = 7, what is [G:K]?