  The bright polarized synchrotron emission, away from the Galactic plane,
originates mostly from filamentary structures. We implement a filament finder
algorithm which allows the detection of bright elongated structures in
polarized intensity maps. We analyse the sky at 23 and 30 GHz as observed
respectively by WMAP and Planck. We identify 19 filaments, 13 of which have
been previously observed. For each filament, we study the polarization
fraction, finding values typically larger than for the areas outside the
filaments, excluding the Galactic plane, and a fraction of about 30% is reached
in two filaments. We study the polarization spectral indices of the filaments,
and find a spectral index consistent with the values found in previous analysis
(about -3.1) for more diffuse regions. Decomposing the polarization signals
into the $E$ and $B$ families, we find that most of the filaments are detected
in $P_E$, but not in $P_B$. We then focus on understanding the statistical
properties of the diffuse regions of the synchrotron emission at 23 GHz. Using
Minkowski functionals and tensors, we analyse the non-Gaussianity and
statistical isotropy of the polarized intensity maps. For a sky coverage
corresponding to 80% of the fainter emission, and on scales smaller than 6
degrees ($\ell > 30$), the deviations from Gaussianity and isotropy are
significantly higher than 3$\sigma$. The level of deviation decreases for
smaller scales, however, it remains significantly high for the lowest analised
scale ($\sim 1.5^\circ$). When 60% sky coverage is analysed, we find that the
deviations never exceed 3$\sigma$. Finally, we present a simple data-driven
model to generate non-Gaussian and anisotropic simulations of the synchrotron
polarized emission. The simulations are fitted in order to match the spectral
and statistical properties of the faintest 80% sky coverage of the data maps.
