  In this paper, we consider the following nonlinear Schr\"odinger system in
$R^3$: \begin{align*}
  -\Delta u_j +P_j(x) u=\mu_j u_j^3+\sum\limits_{i=1,i\neq
j}^N\beta_{ij}u_i^2u_j, \end{align*} where $N\geq3$, $P_j$ are nonnegative
radial potentials, $\mu_j>0$ and $\beta_{ij}=\beta_{ji}$ are coupling
constants. This type of systems have been widely studied in the last decade,
many purely synchronized or segregated solutions are constructed, but few
considerations for simultaneous synchronized and segregated positive solutions
exist. Using Lyapunov-Schmidt reduction method, we construct new type of
solutions with simultaneous synchronization and segregation. Comparing to known
results in the literature, the novelties are threefold. We prove the existence
of infinitely many non-radial positive and also sign-changing vector solutions,
where some components are synchronized but segregated with other components;
the energy level can be arbitrarily large; and our approach works for any $N
\geq 3$.
