I have studied a bit on Indian history and I know that there were some great dynasties there Mughal, Chola, Pandiya etc. But is true that they've never tried to occupy any land outside the Indian subcontinent. I recently saw this as a fact somewhere.
As no one has answered this so far, I'll attempt to provide at least a bit of background, as well as why this isn't true:
While it's certainly true that many large Indian Empires did not hold land outside of the immediate subcontinent, there are a number of exceptions to this rule. Empires situated near the edges of the Indian subcontinent (usually near the Hindu Kush or the Coromandel Coast) often held considerable territory outside of the Indian Subcontinent, although some did not hold on to this territory for very long. Quite simply, the area's geography makes it somewhat difficult to expand in certain directions, the Hindu Kush in the west and the Himalayas to the North make expanding outwards very difficult, as the area is difficult to traverse and contains few immediate resources worth taking (in the case of the Himalayas, the existence of powerful Chinese empires such as the Ming and Qing made expansion even less profitable. Further, it is important to remember that India itself comprises a rather large area (the modern state of Pakistan alone is about the size of Germany and Italy combined). This massive area, sometimes coupled with the relative lack of culture homogeneity (in the case of larger empires) made even internal administration quite an undertaking for some Indian empires, and limited outwards expansion.
Despite these geographic barriers, however, a number of Indian Empires did expand outside of the Indian subcontinent. One very notable early example of this expansion was the Maurya Empire, which controlled most of modern-day Afghanistan, as well as parts of Iran during the reign of Emperor Ashoka. It is my understanding that much of this territory was rather autonomous from direct Maurya rule, however, the Maurya did control the area nonetheless. Regarding the Mughals, Babur's empire encompassed parts of Afghanistan, and the empire later exerted control over a very small part of modern Iran during its height. Continuing this trend of Northwest-oriented empires, the Sikh Empire under Maharaja Ranjit Singh controlled parts of modern Afghanistan, as well as a very small part of modern Tibet. You'll notice that most of this imperial expansion outside of the subcontinent was limited in scope, and the reasons for this are frankly quite diverse, however, the sheer geographic challenges of administering a region bisected by mountain ranges cannot be understated.
Finally, your own example of the Chola Empire is a great demonstrator of Indian expansion outside of the subcontinent. The Cholas commanded an extremely impressive navy and sourced a great deal of their income from Southeast Asian trade, a situation that naturally allowed for significant military expansion. Unfortunately, I'm not all that familiar with the details of Chola expansion, however, the empire did control territory in the Maldives and in parts of Southeast Asia during the reign of Rajendra Chola I, who conducted campaigns in modern Malaysia.
u/PeddaKondappa2 has also elaborated on Mughal expansion into Central Asia here: