SEOUL, South Korea — This is a partial list of the businesses of Samsung, the South Korean business empire: smartphones, microchips, insurance, gas ovens, hospitals, dishwashers, cargo ships, stocks, microwave ovens, apartment buildings, vacuum cleaners, credit cards, pharmaceuticals, air-conditioners and bidets.

Samsung is South Korea’s No. 1 brand and, when all its products are added together, its single biggest export. It dominates South Korean business and social life in a way that can be difficult for outsiders to comprehend.

That dominance may make it difficult to keep its top executive in prison.

A South Korean court on Friday shocked the country by sentencing Lee Jae-yong, the third-generation de facto leader of one of the world’s largest business empires, to five years in prison after his conviction of bribery, embezzlement and other charges. Mr. Lee’s attorneys have said they will appeal, and experts predict a fierce legal battle.

Mr. Lee is not the first big business figure in South Korea to be convicted, but if he stays in prison it would represent something of a milestone. His father, Samsung’s longtime chief, was twice convicted of crimes and twice pardoned by a South Korean president. Other top business South Korean leaders have avoided conviction, negotiated light sentences or been allowed to run their corporate empires from prison.