The secret to getting more than a few wearings out of expensive and delicate socks like the cashmere and silk argyles in the photo (they were courtesy of Kabbaz Kelly - profligate though I might be $80 socks are too dear for my wardrobe) is cold water, and plenty of it. For heat is the killer of expensive hose, whether wool, cashmere, silk or cotton.
Even after a man has been playing in the mud, socks come perfectly clean washed in cold water on the delicates cycle. That is still more true if they are washed in Persil Universal Powder, a laundry detergent that is optimized for cold water (find it at Amazon).
Once the washer has finished its job, do not use the dryer. Always hang socks to dry. A rack located directly under the laundry room fan is ideal as the moving air under the fan dries them quickly and without the stiffness that occurs for some reason when they are hung in still air (the fan should be turned on if that was not obvious).
And that is the best way to wash socks.