The phase diagram of underdoped cuprates in a magnetic field ($H$) is the key ingredient in understanding the anomalous normal state of these high-temperature superconductors. However, the upper critical field ($H_{c2}$) or the extent of superconducting phase with vortices, a type of topological excitations, and the role of charge orders that are present at high $H$, remain under debate. We address these questions by studying stripe-ordered La-214, i.e. cuprates in which charge orders are most pronounced and zero-field transition temperatures $T_{c}^{0}$ are lowest; the latter opens a much larger energy scale window to explore the vortex phases compared to previous studies. By combining linear and nonlinear transport techniques sensitive to vortex matter, we determine the $T$-$H$ phase diagram, directly detect $H_{c2}$, and reveal novel properties of the high-field ground state. Our results demonstrate that, while the vortex phase diagram of underdoped cuprates is not very sensitive to the details of the charge orders, quantum fluctuations and disorder play a key role as $Trightarrow 0$. The presence of stripes, on the other hand, seems to alter the nature of the anomalous normal state, such that the high-field ground state is a metal, as opposed to an insulator.
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