GATE | GATE CS 2021 | Set 1 | Question 44

Let G be a group of order 6, and H be a subgroup of G such that 1

(A) Both G and H are always cyclic
(B) G may not be cyclic, but H is always cyclic
(C) G is always cyclic, but H may not be cyclic
(D) Both G and H may not be cyclic

Answer: (B)
Explanation: We can use Lagrange’ theorem here, which states that “The order of every subgroup of G divides the order of G”.

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