Abstract Algebra: Prove that A5 has no proper subgroups with order 15 or greater.
3439
Other proofs that subgroups of $A_5$ have order at most 12
109060
Group containing no subgroup of index 2
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
75012
Additive group of rationals has no minimal generating set
50762
If $S_n$ has cyclic subgroups of these orders or not?
53990
Group with more than one element and with no proper, nontrivial sub groups must have prime order.
61387
Incorrect Solution for Problem 7 of Pinter's Book of Abstract Algebra, Chapter 2?
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
88344
Order of a group and subsequent subgroups
64518
Prove $S_4$ has only 1 subgroup of order 12
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
157853
$Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?