Subgroups — C₁₉×C₃⋊#10587722 #44527928

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#63270	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×#10587722	—	3	1	no	maximal
3	C₁₉×D₂₇₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#63270	—	2	1	no	—
5	C₁₉×#63270	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×C₃⋊(D₁₃⋊C₃)	—	7	1	no	maximal, Hall
8	C₁₉×D₉₁	—	3	1	no	Hall
9	C₁₉×C₃⋊AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
10	C₃×C₁₉×C₁₃⋊C₃	—	7	1	no	Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃⋊#10587722	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₉×D₃₉	—	7	1	no	—
14	C₁₉×D₁₃⋊C₃	—	21	1	no	—
15	C₃×C₁₉×ΓL(1,𝔽₈)	—	13	1	no	Hall
16	C₃×#63270	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₉×D₂₁	—	13	1	no	—
18	C₁₉×AGL(1,𝔽₇)	—	39	1	no	—
19	C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₁₉×C₁₃⋊C₃	—	7	1	no	—
21	C₁₉×C₁₃⋊C₃	—	14	1	no	—
22	D₂₇₃	C₃×C₁₉	1	1	yes	characteristic, complemented
23	#10587722	—	3	1	no	—
24	C₁₉×D₁₃	—	21	1	no	Hall
25	C₃×C₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₁₉×ΓL(1,𝔽₈)	—	13	1	no	—
27	C₁₉×ΓL(1,𝔽₈)	—	26	1	no	—
28	C₃×D₃×C₁₉	—	91	1	no	Hall
29	C₃×C₇×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
30	#63270	—	2	1	no	—
31	#63270	D₃×C₁₉	1	1	yes	characteristic, complemented
32	D₇×C₁₉	—	39	1	no	Hall
33	C₁₃×C₁₉	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
34	C₃⋊(D₁₃⋊C₃)	—	7	1	no	Hall
35	D₉₁	—	3	1	no	Hall
36	C₃²×C₁₉	—	91	1	no	Hall
37	C₇×C₁₉	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
38	C₃⋊AGL(1,𝔽₇)	—	13	1	no	Hall
39	C₃×C₁₃⋊C₃	—	7	1	no	Hall
40	C₂×C₃×C₁₉	—	273	1	no	—
41	D₃×C₁₉	—	91	1	no	—
42	C₇×C₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
43	D₃₉	—	7	1	no	—
44	D₁₃⋊C₃	—	21	1	no	—
45	C₃×ΓL(1,𝔽₈)	—	13	1	no	Hall
46	C₃×C₁₉	—	91	1	no	—
47	C₃×C₁₉	—	182	1	no	—
48	C₃×C₁₉	#10587722	1	1	yes	characteristic, complemented
49	D₂₁	—	13	1	no	—
50	AGL(1,𝔽₇)	—	39	1	no	—
51	C₃×C₁₃	C₁₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	—	7	1	no	—
53	C₁₃⋊C₃	—	14	1	no	—
54	C₂×C₁₉	—	273	1	no	Hall
55	D₁₃	—	21	1	no	Hall
56	C₃×C₇	C₁₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	—	13	1	no	—
58	ΓL(1,𝔽₈)	—	26	1	no	—
59	C₁₉	C₃⋊#10587722	1	1	yes	characteristic, direct product factor, Sylow
60	C₃×D₃	—	91	1	no	Hall
61	D₇	—	39	1	no	Hall
62	C₁₃	C₁₉×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	91	1	no	Sylow
64	C₇	C₁₉×C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	273	1	no	—
66	D₃	—	91	1	no	—
67	C₃	—	91	1	no	—
68	C₃	—	182	1	no	—
69	C₃	C₁₉×#10587722	1	1	yes	characteristic, complemented
70	C₂	—	273	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊#10587722
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#63270	C₂	semidirect
3. C₁₉×D₂₇₃	C₃	semidirect
5. C₁₉×#63270	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
12. C₃⋊#10587722	C₁₉	direct (N × H)
16. C₃×#63270	C₂×C₁₉	semidirect
19. C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	semidirect
22. D₂₇₃	C₃×C₁₉	semidirect
25. C₃×C₇×C₁₉	D₁₃⋊C₃	semidirect
29. C₃×C₇×C₁₃	C₂×C₃×C₁₉	semidirect
31. #63270	D₃×C₁₉	semidirect
33. C₁₃×C₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
37. C₇×C₁₉	C₃⋊(D₁₃⋊C₃)	semidirect
42. C₇×C₁₃	C₃×D₃×C₁₉	semidirect
48. C₃×C₁₉	#10587722	semidirect
51. C₃×C₁₃	C₁₉×AGL(1,𝔽₇)	semidirect
56. C₃×C₇	C₁₉×D₁₃⋊C₃	semidirect
59. C₁₉	C₃⋊#10587722	direct (N × H)
62. C₁₃	C₁₉×C₃⋊AGL(1,𝔽₇)	semidirect
64. C₇	C₁₉×C₃⋊(D₁₃⋊C₃)	semidirect
69. C₃	C₁₉×#10587722	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#63270	2
C₁₉×#10587722	3
C₁₉×D₂₇₃	3
C₁₉×C₃⋊(D₁₃⋊C₃)	7
C₁₉×C₃⋊AGL(1,𝔽₇)	13
C₃⋊#10587722	19

Subgroups — C19×C3⋊#10587722 #44527928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#10587722 #44527928