1 They are respectively the fourth-, sixth-, first-, and third-largest natural satellites in the Solar System, containing approximately 99.997% of the total mass in orbit around Jupiter. 2  Jupiter is almost 5,000 times more massive than the Galilean moons. 3  The inner moons are in a 1:2:4 orbital resonance.
https://en.wikipedia.org/wiki/Moons_of_Jupiter
Ganymede: Next up is Ganymede. At 5262.4 kilometers in diameter, Ganymede is the largest moon in the Solar System. While it is larger than the planet Mercury, the fact that it is an icy world means that it has only half of Mercury’s mass.
http://www.universetoday.com/44796/galilean-moons/
Like the Earth, Jupiter was a planet with moons orbiting it. Galileo took the Jupiter system to be like a miniature solar system. These four satellites are called the Galilean satellites in honor of their discoverer. In order of increasing distance from Jupiter they are Io, Europa, Ganymede and Callisto. The largest of the Galilean satellites (and the largest moon in the solar system) is Ganymede. At 5262 km across, Ganymede is larger than Mercury but because Ganymede orbits a planet, it is classified as a moon. Ganymede orbits Jupiter in 7.15 days.
http://www.astronomynotes.com/solarsys/s14.htm
The Galilean satellites (Jupiter's four largest moons) to the same scale. Our Moon is also shown for reference. Cutaway views of the possible internal structures of the Galilean satellites. Clockwise from top left: Io, Europa, Callisto, Ganymede.
http://www.astronomynotes.com/solarsys/s14.htm
The second largest of the Galilean satellites (4821 km across) and the farthest from Jupiter is the heavily-cratered moon called Callisto. Callisto orbits Jupiter in 16.7 days. It has a density of 1.83 X water, so it has proportionally more frozen water surrounding a smaller rocky core than Ganymede.
http://www.astronomynotes.com/solarsys/s14.htm
The Galilean moons of Jupiter (Io, Europa, Ganymede and Callisto) were named by Simon Marius soon after their discovery in 1610.
https://en.wikipedia.org/wiki/Moons_of_Jupiter
The moons' physical and orbital characteristics vary widely. The four Galileans are all over 3,100 kilometres (1,900 mi) in diameter; the largest Galilean, Ganymede, is the ninth largest object in the Solar System, after the Sun and seven of the planets, Ganymede being larger than Mercury.
https://en.wikipedia.org/wiki/Moons_of_Jupiter
Jupiter’s largest moons are known as the Galileans, all of which were discovered by Galileo Galilei and named in his honor. They include Io, Europa, Ganymede, and Callisto, and are the Solar System’s fourth, sixth, first and third largest satellites, respectively.
http://www.universetoday.com/44796/galilean-moons/
However, the first certain observations of Jupiter's satellites were those of Galileo Galilei in 1609. By January 1610, he had sighted the four massive Galilean moons with his 30x magnification telescope, and published his results in March 1610.
https://en.wikipedia.org/wiki/Moons_of_Jupiter
Callisto: Callisto is the fourth and farthest Galilean moon. At 4820.6 kilometers in diameter, it is also the second largest of the Galileans and third largest moon in the Solar System. Callisto is named after the daughter of the Arkadian King, Lykaon, and a hunting companion of the goddess Artemis.
http://www.universetoday.com/44796/galilean-moons/
largest of the galilean moons
The Ganymede is the largest of the Galilean moons.