Subgroups — C₅×C₇×C₃⋊D₁₄₁ #44444121

Order 29610.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₁₄₁	—	3	4	no	maximal
3	C₇×C₃⋊D₁₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₄₇	D₃	1	4	yes	complemented
5	C₅×C₃⋊D₁₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₄₇	—	9	1	no	Hall
7	C₃²×C₇×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₁₄₁	—	3	4	no	—
10	C₅×C₇×C₄₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₅×D₁₄₁	—	3	4	no	—
12	C₃×C₇×C₄₇	C₅×D₃	1	4	yes	complemented
13	C₃⋊D₁₄₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₄₇	D₃×C₇	1	4	yes	complemented
15	C₇×D₄₇	—	9	1	no	Hall
16	C₅×C₇×C₃⋊D₃	—	47	1	no	maximal, Hall
17	C₅×D₄₇	—	9	1	no	Hall
18	C₃²×C₄₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
19	C₇×C₄₇	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅×C₇	D₄₇	1	1	yes	characteristic, complemented, Hall
21	D₁₄₁	—	3	4	no	—
22	C₅×C₄₇	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	C₅×D₃×C₇	—	141	4	no	—
24	C₃×C₄₇	C₅×D₃×C₇	1	4	yes	complemented
25	C₇×C₃⋊D₃	—	47	1	no	Hall
26	C₃×C₅×C₇	D₁₄₁	1	4	yes	complemented
27	D₄₇	—	9	1	no	Hall
28	C₅×C₃⋊D₃	—	47	1	no	Hall
29	C₂×C₅×C₇	—	423	1	no	Hall
30	C₃²×C₇	C₅×D₄₇	1	1	yes	characteristic, complemented, Hall
31	C₄₇	C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
32	C₃²×C₅	C₇×D₄₇	1	1	yes	characteristic, complemented, Hall
33	D₃×C₇	—	141	4	no	—
34	C₅×C₇	C₃⋊D₁₄₁	1	1	yes	characteristic, direct product factor, Hall
35	C₅×D₃	—	141	4	no	—
36	C₃×C₇	C₅×D₁₄₁	1	4	yes	complemented
37	C₃⋊D₃	—	47	1	no	Hall
38	C₃×C₅	C₇×D₁₄₁	1	4	yes	complemented
39	C₂×C₇	—	423	1	no	Hall
40	C₂×C₅	—	423	1	no	Hall
41	C₃²	C₅×C₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×C₃⋊D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	141	4	no	—
44	C₅	C₇×C₃⋊D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₇×D₁₄₁	1	4	yes	complemented
46	C₂	—	423	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	C₃⋊D₁₄₁
commutator, cosocle, hypocenter	C₃²×C₄₇	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₄₇	C₂
LCS	G ▷ C₃²×C₄₇
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₄₇	C₂	semidirect
3. C₇×C₃⋊D₁₄₁	C₅	direct (N × H)
4. C₃×C₅×C₇×C₄₇	D₃	semidirect
5. C₅×C₃⋊D₁₄₁	C₇	direct (N × H)
7. C₃²×C₇×C₄₇	C₂×C₅	semidirect
8. C₃²×C₅×C₄₇	C₂×C₇	semidirect
10. C₅×C₇×C₄₇	C₃⋊D₃	semidirect
12. C₃×C₇×C₄₇	C₅×D₃	semidirect
13. C₃⋊D₁₄₁	C₅×C₇	direct (N × H)
14. C₃×C₅×C₄₇	D₃×C₇	semidirect
18. C₃²×C₄₇	C₂×C₅×C₇	semidirect
19. C₇×C₄₇	C₅×C₃⋊D₃	semidirect
20. C₃²×C₅×C₇	D₄₇	semidirect
22. C₅×C₄₇	C₇×C₃⋊D₃	semidirect
24. C₃×C₄₇	C₅×D₃×C₇	semidirect
26. C₃×C₅×C₇	D₁₄₁	semidirect
30. C₃²×C₇	C₅×D₄₇	semidirect
31. C₄₇	C₅×C₇×C₃⋊D₃	semidirect
32. C₃²×C₅	C₇×D₄₇	semidirect
34. C₅×C₇	C₃⋊D₁₄₁	direct (N × H)
36. C₃×C₇	C₅×D₁₄₁	semidirect
38. C₃×C₅	C₇×D₁₄₁	semidirect
41. C₃²	C₅×C₇×D₄₇	semidirect
42. C₇	C₅×C₃⋊D₁₄₁	direct (N × H)
44. C₅	C₇×C₃⋊D₁₄₁	direct (N × H)
45. C₃	C₅×C₇×D₁₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₄₇	2
C₅×C₇×D₁₄₁	3
C₇×C₃⋊D₁₄₁	5
C₅×C₃⋊D₁₄₁	7
C₅×C₇×C₃⋊D₃	47

Subgroups — C5×C7×C3⋊D141 #44444121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₃⋊D₁₄₁ #44444121