Subgroups — D₆₄₁⋊C₂₅ #44545324

Order 32050.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₄₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₄₁	C₅	1	1	yes	maximal, characteristic
3	C₅×C₆₄₁	C₂×C₅	1	1	yes	characteristic
4	D₆₄₁	C₂₅	1	1	yes	characteristic, complemented, Hall
5	C₆₄₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₂₅	—	641	1	no	maximal, Hall
7	C₂₅	—	641	1	no	Sylow
8	C₂×C₅	—	641	1	no	—
9	C₅	D₆₄₁⋊C₅	1	1	yes	characteristic
10	C₂	—	641	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	D₆₄₁⋊C₅
commutator, hypocenter	C₆₄₁	C₂×C₂₅
Fitting, socle, cosocle	C₅×C₆₄₁	C₂×C₅
prime radical	C₅×D₆₄₁	C₅
LCS	G ▷ C₆₄₁
UCS	C₁ ◁ C₅

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.