Subgroups — C₇₁×C₃⋊#3874 #44544073

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×D₁₅×C₇₁	—	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×D₅×C₇₁	—	9	1	no	Hall
7	D₁₅×C₇₁	—	3	1	no	—
8	C₅×D₃×C₇₁	—	15	1	no	—
9	C₅²×C₇₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₃×C₇₁	—	25	1	no	maximal, Hall
11	C₃×C₅×C₇₁	—	3	1	no	—
12	C₃×C₅×C₇₁	—	3	1	no	—
13	C₂×C₅×C₇₁	—	45	1	no	—
14	D₅×C₇₁	—	9	1	no	—
15	C₃²×C₇₁	—	25	1	no	Hall
16	C₃⋊#3874	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	D₃×C₇₁	—	15	1	no	—
18	D₃×C₇₁	—	75	3	no	—
19	C₅×C₇₁	—	3	1	no	—
20	C₅×C₇₁	—	3	1	no	—
21	C₃×C₅²⋊C₃	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇₁	—	25	3	no	—
23	C₃×C₇₁	#3874	1	1	yes	characteristic, complemented
24	C₅×D₁₅	—	3	1	no	—
25	#3874	—	3	3	no	—
26	C₂×C₇₁	—	45	1	no	Hall
27	C₃×C₅²	D₃×C₇₁	1	1	yes	characteristic, complemented
28	C₅²⋊C₃	D₃×C₇₁	1	3	yes	complemented
29	C₇₁	C₃⋊#3874	1	1	yes	characteristic, direct product factor, Sylow
30	C₅×D₅	—	9	1	no	Hall
31	D₁₅	—	3	1	no	—
32	C₅×D₃	—	15	1	no	—
33	C₅²	C₃⋊D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
34	C₃⋊D₃	—	25	1	no	Hall
35	C₃×C₅	—	3	1	no	—
36	C₃×C₅	—	3	1	no	—
37	C₂×C₅	—	45	1	no	—
38	D₅	—	9	1	no	—
39	C₃²	—	25	1	no	Sylow
40	D₃	—	15	1	no	—
41	D₃	—	75	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	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	C₃⋊#3874
commutator, cosocle, hypocenter	C₃×C₅²⋊C₃	C₂×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₁	D₃
LCS	G ▷ C₃×C₅²⋊C₃
UCS	C₁ ◁ C₇₁

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
16. C₃⋊#3874	C₇₁	direct (N × H)
21. C₃×C₅²⋊C₃	C₂×C₇₁	semidirect
23. C₃×C₇₁	#3874	semidirect
27. C₃×C₅²	D₃×C₇₁	semidirect
28. C₅²⋊C₃	D₃×C₇₁	semidirect
29. C₇₁	C₃⋊#3874	direct (N × H)
33. C₅²	C₃⋊D₃×C₇₁	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×D₁₅×C₇₁	3
C₇₁×#3874	3
C₃⋊D₃×C₇₁	25
C₃⋊#3874	71

Subgroups — C71×C3⋊#3874 #44544073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×C₃⋊#3874 #44544073