  The fractional quantum Hall (FQH) effect is a canonical example of
electron-electron interactions producing new ground states in many-body
systems. Most FQH studies have focused on the lowest Landau level (LL), whose
fractional states are successfully explained by the composite fermion (CF)
model, in which an even number of magnetic flux quanta are attached to an
electron and where states form the sequence of filling factors $\nu = p/(2mp
\pm 1)$, with $m$ and $p$ positive integers. In the widely-studied GaAs-based
system, the CF picture is thought to become unstable for the $N \geq 2$ LL,
where larger residual interactions between CFs are predicted and competing
many-body phases have been observed. Here we report transport measurements of
FQH states in the $N=2$ LL (filling factors $4 < \nu < 8$) in bilayer graphene,
a system with spin and valley degrees of freedom in all LLs, and an additional
orbital degeneracy in the 8-fold degenerate $N=0$/$N=1$ LLs. In contrast with
recent observations of particle-hole asymmetry in the $N=0$/$N=1$ LLs of
bilayer graphene, the FQH states we observe in the $N=2$ LL are consistent with
the CF model: within a LL, they form a complete sequence of particle-hole
symmetric states whose relative strength is dependent on their denominators.
The FQH states in the $N=2$ LL display energy gaps of a few Kelvin, comparable
to and in some cases larger than those of fractional states in the $N=0$/$N=1$
LLs. The FQH states we observe form, to the best of our knowledge, the highest
set of particle-hole symmetric pairs seen in any material system.
