(a) A subagent's certificate of authority shall not cover any kind of insurance for which the agent is not then licensed.

(b) A subagent shall not have power to bind an insurer.

(c) All business transacted by a subagent under such subagent's license shall be in the name of the agent by whom the subagent is employed; and the agent shall be responsible for all the acts or omissions of the subagent within the scope of his or her employment.

(d) A record of each transaction on a form prescribed by the Commissioner shall be maintained by both the agent and the subagent.