Subgroups — C₃⋊(C₇₁⋊#3874) #44544074

Order 31950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₆₅	—	3	1	no	maximal
3	C₇₁⋊#3874	—	3	3	no	maximal
4	C₇₁×C₅²⋊C₃	D₃	1	3	yes	complemented
5	C₃×C₅²×C₇₁	D₃	1	1	yes	characteristic, complemented
6	C₅×D₃₅₅	—	9	1	no	Hall
7	D₁₀₆₅	—	3	1	no	—
8	C₅×D₂₁₃	—	15	1	no	—
9	C₅²×C₇₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₂₁₃	—	25	1	no	maximal, Hall
11	C₃×C₅×C₇₁	—	3	1	no	—
12	C₃×C₅×C₇₁	—	3	1	no	—
13	D₃₅₅	—	9	1	no	—
14	C₅×D₇₁	—	45	1	no	—
15	C₃²×C₇₁	—	25	1	no	Hall
16	C₃⋊#3874	—	71	1	no	maximal, Hall
17	D₂₁₃	—	15	1	no	—
18	D₂₁₃	—	75	3	no	—
19	C₅×C₇₁	—	3	1	no	—
20	C₅×C₇₁	—	3	1	no	—
21	C₃×C₅²⋊C₃	D₇₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇₁	—	25	3	no	—
23	C₃×C₇₁	#3874	1	1	yes	characteristic, complemented
24	C₅×D₁₅	—	213	1	no	—
25	#3874	—	213	3	no	—
26	D₇₁	—	45	1	no	Hall
27	C₃×C₅²	D₂₁₃	1	1	yes	characteristic, complemented
28	C₅²⋊C₃	D₂₁₃	1	3	yes	complemented
29	C₇₁	C₃⋊#3874	1	1	yes	characteristic, complemented, Sylow
30	C₅×D₅	—	639	1	no	Hall
31	D₁₅	—	213	1	no	—
32	C₅×D₃	—	1065	1	no	—
33	C₅²	C₃⋊D₂₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₃⋊D₃	—	1775	1	no	Hall
35	C₃×C₅	—	3	1	no	—
36	C₃×C₅	—	3	1	no	—
37	C₂×C₅	—	3195	1	no	—
38	D₅	—	639	1	no	—
39	C₃²	—	25	1	no	Sylow
40	D₃	—	1065	1	no	—
41	D₃	—	5325	3	no	—
42	C₅	—	3	1	no	—
43	C₅	—	3	1	no	—
44	C₃	—	25	3	no	—
45	C₃	C₇₁⋊#3874	1	1	yes	characteristic, complemented
46	C₂	—	3195	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₇₁×C₅²⋊C₃	C₂
Fitting, socle	C₃×C₅²×C₇₁	D₃
LCS	G ▷ C₃×C₇₁×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₁×C₅²⋊C₃	C₂	semidirect
4. C₇₁×C₅²⋊C₃	D₃	semidirect
5. C₃×C₅²×C₇₁	D₃	semidirect
9. C₅²×C₇₁	C₃⋊D₃	semidirect
21. C₃×C₅²⋊C₃	D₇₁	semidirect
23. C₃×C₇₁	#3874	semidirect
27. C₃×C₅²	D₂₁₃	semidirect
28. C₅²⋊C₃	D₂₁₃	semidirect
29. C₇₁	C₃⋊#3874	semidirect
33. C₅²	C₃⋊D₂₁₃	semidirect
45. C₃	C₇₁⋊#3874	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇₁×C₅²⋊C₃	2
C₅×D₁₀₆₅	3
C₇₁⋊#3874	3
C₃⋊D₂₁₃	25
C₃⋊#3874	71

Subgroups — C3⋊(C71⋊#3874) #44544074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇₁⋊#3874) #44544074