Intuition behind why order of a subgroup divides order of a group.
68422
Understanding Lagrange's Theorem (Group Theory)
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
22995
Let f:G to H be 1-1 homomorphism show that order of f(a) divides the order of G.
12667
How many subgroups of order $n$ does $D_n$ have?
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
104549
When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
40513
A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
122821
Is the following proof valid? About the closure of a subgroup, of a topological group, being again a subgroup
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
41731
Question about the order of the product of two elements in an abelian group
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
157806
Order of a element on a Symmetric Group
54195
Do groups of prime order have one subgroup?
103002
Group equals union of two subgroups
98734
Order of a product of elements in a generic group
21568
Maximal order of an element in a symmetric group