Looks like Yellow Nut Sedge, Crab Grass, and something else similar to Johnson or Quack grass. A clue as to where in the United States you are would be helpful.
All are difficult to control in any lawn since what might kill them will also kill the desirable grass.
Sedges evolved in wetlands, although many have adapted to growing in dryer soils now. Still, where I see sedges growing most are in irrigated lawns, lawns watered daily while I seldom see them in lawns watered once a week.
Crab Grass is an annual and the best control is a pre emergent properly applied. Some control can be had by proper mowing and making sure the soil the desirable grasses grow in supports them, proper pH and nutrient supply.
Be sure the soil pH is optimal for good grass growth
(6.2 to 6.8) and the soil the desirable grass is growing in is good and healthy so it can support a strong and healthy turf. A good reliable soil test helps and adequate levels of organic matter in the soil will as well.