New posts in Normal Subgroups

Classification of surjective group homomorphisms

Isomorphic subgroups such that the quotient is isomorphic.

Existence of a subgroup $H$ of a finite group $G$ with $|H|>\sqrt{|G|}$

Can the group $\mathbb Z \times \mathbb Z$ be written as union of finitely many proper subgroups of it?

Does a group of order $400$ always have a subgroup of order $200$?

Let $G$ and $H$ be groups so that $|G|=21$, $|H|=49$. If $G$ has no normal subgroups of order 3, find all homomorphisms $f \colon G \to H$.

If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$

Does it suffice to check the normal subgroup property for the generators?

Almost normal subgroups: Is there any notion which is weaker than normal subgroup?

Is the normality of a subgroup dependent on which group is its parent?