Why Germany could not hold Iceland

What would have happened if Germany had invaded Iceland?

Germany lacked the lift and support to hold it; a small force delivered by major warships would face a larger British counter-invasion and expose its supporting ships.

A German surface force might carry a limited number of troops to Iceland, but remaining nearby to support them would tie valuable cruisers to a fixed position. Britain could bring more troops and heavier naval forces, including battleships able to overmatch the German ships. The scenario illustrates that taking an island and sustaining it under hostile sea control are different problems.