Question

the number of normal subgroups of Q8​

Answer 1

Answer:

(c) Since |Q8| = 8, by the Lagrange's Theorem, any proper subgroup of Q8 has to be of order 2 or 4. Furthermore, any subgroup of order 4 has index 2 in Q8, and hence has to be normal. So it suffices to show that every subgroup of order 2 is normal in Q8.