I have no idea about the numbering, but I know of at least

• Ferromagnetism (like a fridge magnet)
• Antiferromagnetism (opposite of ferromagnetism at an atomic level)
• Diamagnetism (makes superconductors float)
• Paramagnetism (like that spinny frog)

These all indicate how a material reacts to a magnetic field. This article discusses "altermagnetism", which is somewhere between ferromagnetism and antiferromagnetism.