List questions from simple-groups

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Proper subgroup of simple groups

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Prove that there are no simple groups of order 224.

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simplicity of G

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Maximal subgroups of almost simple groups with socle $PSL(2, q)$

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Soluble subgroups of finite classical simple groups

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Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple

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Every simple group of odd order is isomorphic to $\mathbb{Z}_{p} $ iff every group of odd order is solvable

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Is there a counterexample to this weakened converse of Hall's theorem?

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Is there a simple and a non-simple group with same numbers of elements of each order.

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List Question

The extension of $PSL_2(q)$ by its outer automorphism group

Proper subgroup of simple groups

Prove that there are no simple groups of order 224.

simplicity of G

Maximal subgroups of almost simple groups with socle $PSL(2, q)$

Soluble subgroups of finite classical simple groups

Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple

Maximal soluble subgroups in a parabolic subgroup of finite classical simple group

Every simple group of odd order is isomorphic to $\mathbb{Z}_{p} $ iff every group of odd order is solvable

Is there a counterexample to this weakened converse of Hall's theorem?

Non-Abelian simple group of order $120$

The "architecture" of a finite group

Is there a simple and a non-simple group with same numbers of elements of each order.

On Group of order $30$ and $60$.

Simple groups of order 168

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