Subgroups — C₄₁×D₃₆₁ #44444010

Order 29602.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₄₁	—	19	1	no	maximal
3	C₁₉×C₄₁	D₁₉	1	1	yes	characteristic
4	D₃₆₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₆₁	C₂×C₄₁	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₄₁	—	361	1	no	Hall
7	C₄₁	D₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
8	D₁₉	—	19	1	no	—
9	C₁₉	D₁₉×C₄₁	1	1	yes	characteristic
10	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	D₃₆₁
commutator, cosocle, hypocenter	C₃₆₁	C₂×C₄₁
Frattini	C₁₉	D₁₉×C₄₁
Fitting	C₄₁×C₃₆₁	C₂
socle	C₁₉×C₄₁	D₁₉
LCS	G ▷ C₃₆₁
UCS	C₁ ◁ C₄₁

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.