# Subgroup of finite cyclic group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on theambient group: finite cyclic group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Definition

A subgroup of a group is termed a **subgroup of finite cyclic group** if the whole group is a finite cyclic group.

## Relation with other properties

### Weaker properties

- Variety-containing subgroup of finite group
- Quotient-variety-containing subgroup of finite group
- Prehomomorph-contained subgroup of finite group
- Isomorph-free subgroup of finite group
- Fully invariant subgroup of finite group
- Characteristic subgroup of finite group
- Normal subgroup of finite group
- Subgroup of finite abelian group