Subgroups — C₇₁×C₃⋊((C₅⋊D₅)⋊C₃) #44544075

Order 31950.

52 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	C₇₁×C₃⋊(C₅⋊D₅)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇₁×(C₅⋊D₅)⋊C₃	—	3	1	no	maximal
4	C₇₁×C₅²⋊C₃	—	2	1	no	—
5	C₇₁×C₅²⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊D₅×C₇₁	—	3	1	no	Hall
8	D₁₅×C₇₁	—	15	2	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	2	no	—
12	D₅×C₇₁	—	45	2	no	—
13	C₃²×C₇₁	—	25	1	no	Hall
14	C₃⋊((C₅⋊D₅)⋊C₃)	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×C₇₁	—	75	1	no	—
16	D₃×C₇₁	—	25	1	no	—
17	C₅×C₇₁	—	3	2	no	—
18	C₃×C₅²⋊C₃	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇₁	—	25	1	no	—
20	C₃×C₇₁	—	50	1	no	—
21	C₃×C₇₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
22	C₃⋊(C₅⋊D₅)	C₃×C₇₁	1	1	yes	characteristic, complemented
23	(C₅⋊D₅)⋊C₃	—	3	1	no	—
24	C₂×C₇₁	—	75	1	no	Hall
25	C₃×C₅²	C₂×C₃×C₇₁	1	1	yes	characteristic, complemented
26	C₅²⋊C₃	—	2	1	no	—
27	C₅²⋊C₃	D₃×C₇₁	1	1	yes	characteristic, complemented
28	C₇₁	C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
29	C₅⋊D₅	—	3	1	no	Hall
30	D₁₅	—	15	2	no	—
31	C₅²	C₃×D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₃	—	25	1	no	Hall
33	C₃×C₅	—	3	2	no	—
34	D₅	—	45	2	no	—
35	C₃²	—	25	1	no	Sylow
36	C₂×C₃	—	75	1	no	—
37	D₃	—	25	1	no	—
38	C₅	—	3	2	no	—
39	C₃	—	25	1	no	—
40	C₃	—	50	1	no	—
41	C₃	C₇₁×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
42	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	C₃⋊((C₅⋊D₅)⋊C₃)
commutator, cosocle, hypocenter	C₃×C₅²	C₂×C₃×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₁	C₂×C₃
LCS	G ▷ C₃×C₅²
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
2. C₇₁×C₃⋊(C₅⋊D₅)	C₃	semidirect
5. C₇₁×C₅²⋊C₃	D₃	semidirect
6. C₃×C₅²×C₇₁	C₂×C₃	semidirect
9. C₅²×C₇₁	C₃×D₃	semidirect
14. C₃⋊((C₅⋊D₅)⋊C₃)	C₇₁	direct (N × H)
18. C₃×C₅²⋊C₃	C₂×C₇₁	semidirect
21. C₃×C₇₁	(C₅⋊D₅)⋊C₃	semidirect
22. C₃⋊(C₅⋊D₅)	C₃×C₇₁	semidirect
25. C₃×C₅²	C₂×C₃×C₇₁	semidirect
27. C₅²⋊C₃	D₃×C₇₁	semidirect
28. C₇₁	C₃⋊((C₅⋊D₅)⋊C₃)	direct (N × H)
31. C₅²	C₃×D₃×C₇₁	semidirect
41. C₃	C₇₁×(C₅⋊D₅)⋊C₃	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
C₇₁×C₃⋊(C₅⋊D₅)	3
C₇₁×(C₅⋊D₅)⋊C₃	3
C₃×D₃×C₇₁	25
C₃⋊((C₅⋊D₅)⋊C₃)	71

Subgroups — C71×C3⋊((C5⋊D5)⋊C3) #44544075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×C₃⋊((C₅⋊D₅)⋊C₃) #44544075