In this paper, we study the complex-type Padovan-p sequence modulo m and then we give some results concerning the periods and ranks of this sequence for any p and m. Furthermore, we produce the cyclic groups using the multiplicative orders of the generating matrix of the complex-type Padovan-p sequence when read modulo m. Finally, we give the relationships between the periods of the complex-type Padovan-p sequence modulo m and the orders of the cyclic groups produced.