There are several nationalities who fought on the Hungarian side in this conflict. The most important of them is the Polish Legion. 
Polish cavalry, infantry and officers 
From left to the right: Soldier of the German Legion, the Polish Legion and a jaeger of Tyrol
Here are some generals: 
Arthur Görgey the most talented brilliant Hungarian general 
János Damjanich who was never defeated in battle 
Józef Bem the Polish commander of the Hungarian army in Transylvania 
Karl August Graf zu Leiningen-Westerburg general of the Hungarian 3rd. corps 
Ernst Ritter Poelt von Poeltenberg general of the Hungarian 7th. corps a valiant hussar
And finally some hussars
The Habsburg Empire’s army had 14 hussar regiments out of these 10 fought in the war on the Hungarian side. In the rest 2 regiments fought in Italy and the other two was not rallied of Hungarians but Croatians and they fought against Hungary during the conflict. Hungary recruited four more regiment during the war and called them honvéd hussars. I’m going to present these 14 regiments that formed the cavalry of the Hungarian army. 
1st. Kaiser (Császár) Hussar Regiment 
2nd. Hannover Hussar Regiment 
3rd. Ferdinand Hussar Regiment 
4th. Alexander (Sándor) Hussar Regiment 
6th. Württemberg Hussar Regiment 
8th. Coburg Hussar Regiment 
9th Nicholas (Miklós) Hussar Regiment 
10th Wilhelm (Vilmos) Hussar Regiment 
11th Székely Huszár Regiment 
12th Palatinus (Nádor) Hussar Regiment 
13th. Hunyadi Honvéd Hussar Regiment 
14th Lehel Honvéd Hussar Regiment 
15th Mátyás Honvéd Hussar Regiment 
16th Károlyi Honvéd Hussar Regiment 
17th Bocskai Honvéd Hussar Regiment
18th Attila Honvéd Hussar Regiment
