List questions from normal-subgroups

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Proving isomorphic groups have the same number of subgroups.

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Group of order $24$ with no subgroup of order $6$

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Isomorphisms between normal subgroups and their quotients

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If a normal subgroup and its factor group are both abelian, then what can be said about the group?

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A normal subgroup of a matrix such that $G/N$ is isomorphic to $\mathbb{R}^{\times} \times \mathbb{R}^{\times}$

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Group $G$ isomorphic to kernel of a homomorphism $\times$ a subgroup of the center

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A group $G_1$ isomorphic to a subgroup and a quotient group of $G$

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Normal subgroup implies $g^2 \in H$ for any element $g$

Published on 05 Dec 2019 - 3:33

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Show that $N=\{g_1^3 \times \cdots \times {g_r}^3 \mid g_i \in G, r \geq 0\}$ where $g_i \in G$ and $r \ge 0$ is normal subgroup

Published on 08 Dec 2019 - 3:05

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$G = S_7$, $a=(2,5,7)$, $b=(5,7)(4,3,1,6)$, $H = \langle a, b \rangle$, and let $K=\langle b \rangle$. Is K normal in H?

Published on 26 Mar 2026 - 4:53

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Normal subgroup of index a divisor of n!

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Normal subgroups of a group of order $102$

Published on 27 Mar 2026 - 18:09

List Question

Normal subgroup is still normal after isomorphism

Proving isomorphic groups have the same number of subgroups.

Group of order $24$ with no subgroup of order $6$

Isomorphisms between normal subgroups and their quotients

If a normal subgroup and its factor group are both abelian, then what can be said about the group?

A normal subgroup of a matrix such that $G/N$ is isomorphic to $\mathbb{R}^{\times} \times \mathbb{R}^{\times}$

Group $G$ isomorphic to kernel of a homomorphism $\times$ a subgroup of the center

Questions about 2nd isomorphism theorem

A group $G_1$ isomorphic to a subgroup and a quotient group of $G$

Normal subgroup implies $g^2 \in H$ for any element $g$

Normal subgroup of $S_3$?

Show that $N=\{g_1^3 \times \cdots \times {g_r}^3 \mid g_i \in G, r \geq 0\}$ where $g_i \in G$ and $r \ge 0$ is normal subgroup

$G = S_7$, $a=(2,5,7)$, $b=(5,7)(4,3,1,6)$, $H = \langle a, b \rangle$, and let $K=\langle b \rangle$. Is K normal in H?

Normal subgroup of index a divisor of n!

Normal subgroups of a group of order $102$

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