Sort a list of lists by increasing order of elements

If the sublists have equal lengths,

list[[Ordering[list]]]

{{1, 1, 2, 8}, {1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 4, 5}, {1, 3, 5, 6}}

With possibly unequal lengths:

list[[Ordering[PadRight @ list]]] 

{{1, 1, 2, 8}, {1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 4, 5}, {1, 3, 5, 6}}

With equal lengths, the simplest answer, as andre314 says in the comment above, is simply Sort:

Sort[list]

{{1, 1, 2, 8}, {1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 4, 5}, {1, 3, 5, 6}}

With unequal lengths, kglr's Ordering + PadRight approach is probably optimal.