MEXICO CITY, July 28 (Reuters) - Mexican metals miner and railroad operator Grupo Mexico said on Monday its second-quarter profit rose 74 percent compared with the same period last year, as the company's mining, transport and infrastructure divisions all showed solid gains.

Grupo Mexico reported a profit of $509 million in the three months to end-June, the company said in a filing with the Mexican stock exchange.

Revenue during the quarter rose 5.5 percent to $2.36 billion.

Grupo Mexico runs copper mines in Mexico, Peru and the United States as well as cargo train lines across Mexico.

Grupo Mexico said copper output rose 6 percent while gold production was up 20 percent compared to the same period last year, even as average prices for the metals fell 4.7 percent and 8.9 percent respectively during the quarter.

Profits from the company's mining sector rose 5.4 percent during the quarter to $307.6 million.

The company recorded its first sales of copper from its new ESDE III plant at its flagship Buenavista mine in northern Mexico during the second quarter. The expansion at the mine, which has the world's largest copper reserves, is set to reach maximum annual capacity of 120,000 tonnes during the third quarter, the company said in its filing.

The company's infrastructure division posted record sales of $123 million, up 83 percent compared to the same period in 2013, in part due to new energy projects that came online during the quarter.

Meanwhile, Grupo Mexico's transport division reported profits of $121.8 million, up nearly 180 percent compared to the year-earlier period.

(Reporting by David Alire Garcia; Editing by Stephen Coates)