A proper subgroup is a proper subset 
of group elements of a group 
that satisfies the four group
requirements. "
is a proper subgroup of 
"
is written 
.
The group order of any subgroup of a group
of group order 
must be a divisor of 
.
Proper Subgroup
See also
Group, SubgroupExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Proper Subgroup." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProperSubgroup.html