When referring to might and power accomplished by the Mexica people, the Mexica has everything to owe to the militaristic and political culture of the Tecpaneca. Without the Tecpaneca, the Mexica would have never existed as we know them today.
Atzcapotzalco was the nation of the Tecpaneca people, today´s Atzcapotzalco delegation in Mexico City. The Mexica arrived from their long pilgrimage from Aztlan when Atzcapotzalco was the most powerful nation in the Anahuac. Eventhough a Triple Alliance existed since Toltec times, established in part by Ce Acatl Quetzalcoatl himself, the ruling family in Atzcapotzalco decided to destroy it, by eliminating the other two nations. But Atzcapotzalco itself could have never done it, if it wasn't to the aid of troops provided by the Mexica.
Under Tecpaneca rule, the Mexica were considered to be a parallel army to the national army. The Mexica had military tactics never before seen in the lakes area. But such a war monster was never useful without proper coordination. An example is the Battle of Chapultepec, where the ferocious Mexica lost bitterly to a more organized international alliance. Such brave warriors needed guidance, which they recieved from Atzcapotzalco. In exchange to their services, they recieved the right to live in a tiny and undesired island. Remember the Mexica were running from Colhuacan.
Such protection under Tezozomoc, tlahtoani of Atzcapotzalco, benefited more the Mexica in the long run. Because their war tactics were directed and narrowed to specific missions, battles or wars. Such is the case when Atzcapotzalco shattered its Triple Alliance with Xaltocan and Colhuacan. The Tecpaneca provided with tools, weapons, and military guidance to the Mexica, so they could be sent to attack Xaltocan island, the last powerful Hñahñu nation. The result, the combined forces destroyed the island.
As the Mexica grew in numbers and prestige, they started benefeting from political protection from Atzcapotzalco. The Mexica intermarried with Tecpaneca. The most famous person of such mixed blood was Chimalpopoca, described by historians as a "cute child". This cute child was the key for the Mexico to enter into big-time politics and decision-making. Remember Mexico-Tenochtitlan was not independent, and was just another city of Atzcapotzalco. But this was about to change, because Mexica introduction into politics was a big factor for Mexico. Mexico was learning the trades of politics, lobbying, intrigue, government, planning, among many other things from Atzcapotzalco, specially from Tezozomoc, their high-ruler. Tezozomoc, described by historians of his time as a "clever old man" expanded Atzcapotzalco into all directions, using advanced use of logistics, war plans, and trickery. Thanks to politics, Tezozomoc conquered Colhuacan without fighting a battle. He sent orders to kill the tlahtoani of Colhuacan during a party. Consequently, his Colhua followers named him high-ruler. Again, the Mexica learned a big deal from these tactics of overlordship and controlling different territories.
After the conquest of the Mazahuacan, the land of the Mazahuas, and Tetzcoco, the land of Netzahualcoyotl, Tezozomoc became the most powerful man in our world. He controled not only territories, but politics, tax, laws, and military logistics. To this point, the Mexica, especially Chimalpopoca, Tezozomoc's grandson, were up in the highest spheres of power in Atzcapotzalco. Not Mexico-Tenochtitlan, because remember Tenochtitlan was still not independent, something severely forgotten.
Time passed, and a rebellion made by an exiled prince, Netzahualcoyotl, turned into an all-out world war. Tlaxcaltecas, Huexotzincas, Cholultecas, Acolhuaque, Hñahñu, Tecpaneca-rebels, and Mexica rose against Atzcapotzalco. The pretext was the coup d'etat made in Atzcapotzalco by Maxtla, by killing the legal tlahtoani, his brother Quetzalayatzin, dubbed Tayatzin. Mexico-Tenochtitlan gained independence, and Itzcoatl became the first legal tlahtoani of Mexico, Tlacaelel the architect of the Mexicayotl, and Netzahualcoyotl its godfather. This is how the tlahtocayotl of the Mexica began. Applying all that was learned under Atzcapotzalco's rule, they managed to expand and grow strong... at some extent. The student surpassed the teacher.