 
 <prompt> Wetin dey make subgroup necessary? Based on di previous question, write one context wey get di answer. E fit be 1 - 20 sentences. Context: <response>: ```In di example wey dey above, di identity and di rotations na subgroup R = {id, r1, r2, r3}, wey dey highlighted for red for di group table above: any two rotations wey dey composed still dey rotation, and a rotation fit undo by (i.e. na inverse to) di complementary rotations 270° for 90°, 180° for 180°, and 90° for 270° (note say rotation for di opposite direction no dey defined). Di subgroup test na necessary and sufficient condition for a subset H of a group G to be a subgroup: e dey sufficient to check say g−1h ∈ H for all elements g, h ∈ H. Knowing di subgroups dey important to understand di group as a whole.d[›]``` 