Which type of company does not issue shares and typically has a limited number of members?

A private company is characterized by its structure, which does not allow for the issuance of shares to the general public. Typically, its membership is limited to a specified number of individuals, often requiring personal relationships or strategic partnerships among the members. This structure is designed to provide more control and privacy compared to public companies, which are required to disclose financial information and may have thousands of shareholders.

Private companies are often seen in contexts where there is a desire to keep operations and financing more intimate and less publicly scrutinized. They can enjoy a certain degree of flexibility in management and decision-making that larger public companies do not, as they do not have the same requirement for transparency and accountability to public investors. This makes private companies particularly appealing for small businesses or startups that seek to maintain a close-knit operational structure.

In contrast, public companies issue shares that are traded on a stock exchange and are required to meet rigorous reporting standards, which is not a feature of private companies. Limited companies can refer to different types, including private and public, thus making it a less precise option. Sole traders represent individuals running a business without a separate legal entity, differing fundamentally from the concept of a company. Thus, a private company most accurately fits the description in the question.