We describe a general, symmetry-conditioned way of enumerating isomers of saturated singly substituted one-dimensional nanothreads of the (CH)5E and (CH)5CR type, where E is a heteroatom and R is a substituent. Four nanothreads - so-called tube (3,0), polytwistane, the zipper polymer, and polymer I, are treated in detail. The methodology, combining symmetry arguments and computer-based enumeration, is generally applicable to isomerism problems in polymers.