Editing Index of a subgroup (section)

==Infinite index==
If ''H'' has an infinite number of cosets in ''G'', then the index of ''H'' in ''G'' is said to be infinite.  In this case, the index <math>|G:H|</math> is actually a [[cardinal number]].  For example, the index of ''H'' in ''G'' may be [[countable set|countable]] or [[Uncountable set|uncountable]], depending on whether ''H'' has a countable number of cosets in ''G''. Note that the index of ''H'' is at most the order of ''G,'' which is realized for the trivial subgroup, or in fact any subgroup ''H'' of infinite cardinality less than that of ''G.''