Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________ .

**Note –** This question was Numerical Type.

**(A)** 1

**(B)** 5

**(C)** 7

**(D)** 35

**Answer:** **(C)** **Explanation:** According to the Lagrange’s Theorem:

“If H is a subgroup of finite group G then the order of subgroup H divides the order of group G.”

Order of subgroup must be factor of Order of group.

Since order of a group is number of elements present in that group, therefore order of given group will be 35.

Factor of 35 are: 1, 5, 7, 35.

So, largest possible size of a subgroup of G other than G itself is **7**.

Size of group = Ο(G) = 35 Let H be subgroup of G ∴ Ο(H)⏐Ο(G) Possible orders of H are 1, 5, 7, 35 Size of largest possible proper subgroup = 7.

Option (C) is correct.

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