Subgroups — D₃×C₇₁×C₅²⋊C₃ #44544071

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	C₅²×D₃×C₇₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇₁×C₅²⋊C₃	—	3	1	no	maximal
4	C₇₁×C₅²⋊C₃	—	2	1	no	—
5	C₇₁×C₅²⋊C₃	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₅²×C₇₁	—	3	1	no	Hall
8	C₅×D₃×C₇₁	—	3	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	C₂×C₅×C₇₁	—	9	2	no	—
13	C₃²×C₇₁	—	25	1	no	Hall
14	D₃×C₅²⋊C₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×C₇₁	—	75	1	no	—
16	D₃×C₇₁	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
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	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
22	C₅²×D₃	C₃×C₇₁	1	1	yes	characteristic, complemented
23	C₂×C₅²⋊C₃	—	3	1	no	—
24	C₂×C₇₁	—	3	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, direct product factor
28	C₇₁	D₃×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅²	—	3	1	no	Hall
30	C₅×D₃	—	3	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	C₂×C₅	—	9	2	no	—
35	C₃²	—	25	1	no	Sylow
36	C₂×C₃	—	75	1	no	—
37	D₃	C₇₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
38	C₅	—	3	2	no	—
39	C₃	—	25	1	no	—
40	C₃	—	50	1	no	—
41	C₃	C₂×C₇₁×C₅²⋊C₃	1	1	yes	characteristic, complemented
42	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	D₃×C₅²⋊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. C₅²×D₃×C₇₁	C₃	semidirect
5. C₇₁×C₅²⋊C₃	D₃	direct (N × H)
6. C₃×C₅²×C₇₁	C₂×C₃	semidirect
9. C₅²×C₇₁	C₃×D₃	semidirect
14. D₃×C₅²⋊C₃	C₇₁	direct (N × H)
16. D₃×C₇₁	C₅²⋊C₃	direct (N × H)
18. C₃×C₅²⋊C₃	C₂×C₇₁	semidirect
21. C₃×C₇₁	C₂×C₅²⋊C₃	semidirect
22. C₅²×D₃	C₃×C₇₁	semidirect
25. C₃×C₅²	C₂×C₃×C₇₁	semidirect
27. C₅²⋊C₃	D₃×C₇₁	direct (N × H)
28. C₇₁	D₃×C₅²⋊C₃	direct (N × H)
31. C₅²	C₃×D₃×C₇₁	semidirect
37. D₃	C₇₁×C₅²⋊C₃	direct (N × H)
41. C₃	C₂×C₇₁×C₅²⋊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
C₅²×D₃×C₇₁	3
C₂×C₇₁×C₅²⋊C₃	3
C₃×D₃×C₇₁	25
D₃×C₅²⋊C₃	71

Subgroups — D3×C71×C52⋊C3 #44544071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇₁×C₅²⋊C₃ #44544071