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Lagrange's Theorem :

The order of a finite group is a multiple of the order of its every subgroup


Here Order of group is 11 which is Prime no. So only 2 subgroups are possible.
a. Group itself (i.e. Order 11)
b. Group with order 1

but both of above are Trivial Sub Group i.e. no Proper Sub Group possible from Prime Order Group.

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Order/cardinality of the group = 11.

Lagrange's theorem states that the order of every subgroup H of a group G, divides the order of G.

So what divides 11? 1 and 11.

Of order 1, there's only one subgroup, ie, {e} (identity element). This is the trivial subgroup. Every group has it.

Of order 11, the same group itself.

 

So, essentially there are no subgroups.

Option A

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