= 2-modular defect groups of A5
{c}
In characteristic $2$, a <Sylow subgroup> $P$ of $A_5$ is a <Klein four-group>, and its <normalizer> is $A_4$. Since $kA_4$ has one block, <Brauer first main theorem> gives a unique block of $kA_5$ with defect $P$. No order-two subgroup $D$ can be a <defect group of a block>: both $C_{A_5}(D)$ and $C_{A_5}(P)$ equal $P$, so the <Brauer morphisms> of a central block idempotent at $D$ and at $P$ are equal. A nonzero image is $1$, since a <group algebra of a p-group in characteristic p is local>, and consequently $D$ is not maximal among subgroups with nonzero Brauer image.
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