GATE Computer Science (CS) 2021 Shift 1 Solved Paper

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Question : 44 of 65

Marks: +1, -0

Let G be a group order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

G is always cyclic, but H may not be cyclic.
G may not be cyclic, but H is always cyclic.
Both G and H are always cyclic.
Both G and H may not be cyclic.

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