I think you meant Greenland, Iceland is its own country since 930 A.D.
Oops, pretty big error here as I found out on a visit there several years back. Started off as a Viking settlement at a time when there was no real worry about national sovereignty. Mostly looked to Norway for support because most of its landed settlers from 874's initial settlement were of that ancestry. This affiliation became a legal tie in the 1200s but 'control' largely switched to the more populous Denmark when the two countries had a shared monarchy and Norway suffered a near 50% death rate from its first attack of the Black Plague in 1347-50.
Iceland remained a largely ignored & self governing stepchild till the Protestant Reformation when Denmark forced conversion to Lutheranism, the state church of Denmark (1550). This caused the expected upset and resistance against the imported and heavy-handed Danish clergy and their armed protectors. The last Roman Catholic Bishop of Iceland was beheaded in 1550 along with his 2 sons (wry grin!)
Over the next 200 years Denmark exercised a much stronger control but provided little support when slavers raided with near impunity and when a smallpox epidemic in the 1700s killed near 1-in-3 residents. A further disaster from a massive eruption of the Laki Volcano in 1783 caused a famine with a near 25% death toll (percentage deaths greater than the Irish Potato Famine!)
Iceland strived for its own independence from Denmark from the end of the Napoleonic Wars (1814) to making a 25 year negotiated break with self-governance while Denmark retained foreign affairs in 1918. Final recognized independence was achieved at the end of that period in 1944 with Iceland establishing a parliamentarian government.