Subgroups — D₃×C₁₉×#63271 #44527982

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#63271	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#63271	—	3	1	no	maximal
4	C₁₉×#63271	—	2	1	no	—
5	C₁₉×#63271	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₉×C₁₃⋊C₃	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃×C₁₉	—	3	1	no	Hall
9	D₃×C₁₉×ΓL(1,𝔽₈)	—	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	D₃×#63271	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₃×C₁₃×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₂×C₁₉×C₁₃⋊C₃	—	21	1	no	—
15	C₃×C₁₉×ΓL(1,𝔽₈)	—	13	1	no	Hall
16	C₃×#63271	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
17	D₃×C₇×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₂×C₁₉×ΓL(1,𝔽₈)	—	39	1	no	—
19	C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
20	C₁₉×C₁₃⋊C₃	—	7	1	no	—
21	C₁₉×C₁₃⋊C₃	—	14	1	no	—
22	D₃×C₇×C₁₃	C₃×C₁₉	1	1	yes	characteristic, complemented
23	C₂×#63271	—	3	1	no	—
24	C₂×C₁₃×C₁₉	—	3	1	no	Hall
25	C₃×C₇×C₁₉	C₂×C₁₃⋊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	#63271	—	2	1	no	—
31	#63271	D₃×C₁₉	1	1	yes	characteristic, direct product factor
32	C₂×C₇×C₁₉	—	3	1	no	Hall
33	C₁₃×C₁₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
34	D₃×C₁₃⋊C₃	—	7	1	no	Hall
35	C₂×C₇×C₁₃	—	3	1	no	Hall
36	C₃²×C₁₉	—	91	1	no	Hall
37	C₇×C₁₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
38	D₃×ΓL(1,𝔽₈)	—	13	1	no	Hall
39	C₃×C₁₃⋊C₃	—	7	1	no	Hall
40	C₂×C₃×C₁₉	—	273	1	no	—
41	D₃×C₁₉	#63271	1	1	yes	characteristic, direct product factor
42	C₇×C₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
43	D₃×C₁₃	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
44	C₂×C₁₃⋊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	C₂×#63271	1	1	yes	characteristic, complemented
49	D₃×C₇	C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
50	C₂×ΓL(1,𝔽₈)	—	39	1	no	—
51	C₃×C₁₃	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	—	7	1	no	—
53	C₁₃⋊C₃	—	14	1	no	—
54	C₂×C₁₉	—	3	1	no	Hall
55	C₂×C₁₃	—	3	1	no	Hall
56	C₃×C₇	C₂×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	—	13	1	no	—
58	ΓL(1,𝔽₈)	—	26	1	no	—
59	C₁₉	D₃×#63271	1	1	yes	characteristic, direct product factor, Sylow
60	C₃×D₃	—	91	1	no	Hall
61	C₂×C₇	—	3	1	no	Hall
62	C₁₃	D₃×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	91	1	no	Sylow
64	C₇	D₃×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	273	1	no	—
66	D₃	C₁₉×#63271	1	1	yes	characteristic, direct product factor
67	C₃	—	91	1	no	—
68	C₃	—	182	1	no	—
69	C₃	C₂×C₁₉×#63271	1	1	yes	characteristic, complemented
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₃×#63271
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×#63271	C₂	semidirect
2. D₃×C₇×C₁₃×C₁₉	C₃	semidirect
5. C₁₉×#63271	D₃	direct (N × H)
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
12. D₃×#63271	C₁₉	direct (N × H)
13. D₃×C₁₃×C₁₉	ΓL(1,𝔽₈)	semidirect
16. C₃×#63271	C₂×C₁₉	semidirect
17. D₃×C₇×C₁₉	C₁₃⋊C₃	semidirect
19. C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. D₃×C₇×C₁₃	C₃×C₁₉	semidirect
25. C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
29. C₃×C₇×C₁₃	C₂×C₃×C₁₉	semidirect
31. #63271	D₃×C₁₉	direct (N × H)
33. C₁₃×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
37. C₇×C₁₉	D₃×C₁₃⋊C₃	semidirect
41. D₃×C₁₉	#63271	direct (N × H)
42. C₇×C₁₃	C₃×D₃×C₁₉	semidirect
43. D₃×C₁₃	C₁₉×ΓL(1,𝔽₈)	semidirect
48. C₃×C₁₉	C₂×#63271	semidirect
49. D₃×C₇	C₁₉×C₁₃⋊C₃	semidirect
51. C₃×C₁₃	C₂×C₁₉×ΓL(1,𝔽₈)	semidirect
56. C₃×C₇	C₂×C₁₉×C₁₃⋊C₃	semidirect
59. C₁₉	D₃×#63271	direct (N × H)
62. C₁₃	D₃×C₁₉×ΓL(1,𝔽₈)	semidirect
64. C₇	D₃×C₁₉×C₁₃⋊C₃	semidirect
66. D₃	C₁₉×#63271	direct (N × H)
69. C₃	C₂×C₁₉×#63271	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#63271	2
D₃×C₇×C₁₃×C₁₉	3
C₂×C₁₉×#63271	3
D₃×C₁₉×C₁₃⋊C₃	7
D₃×C₁₉×ΓL(1,𝔽₈)	13
D₃×#63271	19

Subgroups — D3×C19×#63271 #44527982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉×#63271 #44527982