Subgroups — C₂₁₁⋊#3874 #44539554

Order 31650.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₅₅	—	3	1	no	maximal, Hall
3	C₅²×C₂₁₁	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₀₅₅	—	3	1	no	—
5	C₅×D₂₁₁	—	15	1	no	—
6	D₆₃₃	—	25	1	no	maximal, Hall
7	C₅×C₂₁₁	—	3	1	no	—
8	C₅×C₂₁₁	—	3	1	no	—
9	C₃×C₂₁₁	—	25	1	no	Hall
10	D₂₁₁	—	15	1	no	Hall
11	C₂₁₁	#3874	1	1	yes	characteristic, complemented, Sylow
12	#3874	—	211	1	no	maximal, Hall
13	C₅²⋊C₃	D₂₁₁	1	1	yes	characteristic, complemented, Hall
14	C₅×D₅	—	633	1	no	Hall
15	C₅²	D₆₃₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅	—	3165	1	no	—
17	D₅	—	633	1	no	—
18	D₃	—	5275	1	no	Hall
19	C₅	—	3	1	no	—
20	C₅	—	3	1	no	—
21	C₃	—	25	1	no	Sylow
22	C₂	—	3165	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅²⋊C₃×C₂₁₁	C₂
Fitting, socle	C₅²×C₂₁₁	D₃
LCS	G ▷ C₅²⋊C₃×C₂₁₁
UCS	C₁

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.