A subgroup of a group G, which is transformed into itself by every isomorphism of G, is called a characteristic subgroup.
Moreover, the isomorphism is simple unless for one or more operations, other than identity, the sets all remain unaltered.
In this case H would contain a self-conjugate subgroup, and the isomorphism is multiple.
The following table shows where isomorphism may be generally expected.
In the first case the isomorphism is spoken of as simple, in the second as multiple.
from German Isomorphismus, 1828, coined by German chemist Eilhard Mitscherlich (1794-1863) from isomorph; see isomorphic. Related: Isomorph.
isomorphism i·so·mor·phism (ī'sə-môr'fĭz'əm)
n.
A similarity in form, as in organisms of different ancestry.
A close similarity in the crystalline structure of two or more substances of similar chemical composition.