The number of subgroups of the group (Z_{5}, | vedclass

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(D) The group $(Z_{5}, +_{5})$ is a cyclic group of prime order $p = 5$. By Lagrange's Theorem,the order of any subgroup must divide the order of the

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$2$

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(D) The group $(Z_{5}, +_{5})$ is a cyclic group of prime order $p = 5$. By Lagrange's Theorem,the order of any subgroup must divide the order of the group. Since $5$ is a prime number,its only divisors are $1$ and $5$. Therefore,the only subgroups are the trivial subgroup ${0}$ of order $1$ and the group itself $Z_{5}$ of order $5$. Thus,the total number of subgroups is $2$.

The number of subgroups of the group $(Z_{5}, +_{5})$ is

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