Subgroups — C₃×D₁₉×#63271 #44527883

Order 31122.

96 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	D₁₉×#63271	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#63271	C₂×C₃	1	3	yes	complemented
5	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×D₁₉×C₁₃⋊C₃	—	7	1	no	maximal, Hall
7	C₇×C₁₃×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×ΓL(1,𝔽₈)×D₁₉	—	13	1	no	maximal, Hall
9	C₃×C₁₉×C₁₃⋊C₃	—	7	1	no	Hall
10	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×#63271	—	19	1	no	maximal, Hall
12	C₃×C₁₃×D₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	D₁₉×C₁₃⋊C₃	—	7	3	no	—
14	C₃×C₁₉×ΓL(1,𝔽₈)	—	13	1	no	Hall
15	C₃×#63271	D₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₇×D₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	ΓL(1,𝔽₈)×D₁₉	—	13	3	no	—
18	C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₁₉×C₁₃⋊C₃	—	7	3	no	—
20	C₂×C₃×C₇×C₁₃	—	19	1	no	—
21	C₂×#63271	—	19	3	no	—
22	C₁₃×D₁₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
24	C₁₉×ΓL(1,𝔽₈)	—	13	3	no	—
25	C₃²×D₁₉	—	91	1	no	Hall
26	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
27	#63271	C₃×D₁₉	1	3	yes	direct product factor
28	C₇×D₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃⋊C₃	—	133	1	no	Hall
31	C₂×C₇×C₁₃	—	19	1	no	Hall
32	C₃²×C₁₉	—	91	1	no	Hall
33	C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×ΓL(1,𝔽₈)	—	247	1	no	Hall
35	C₃×C₁₃⋊C₃	—	7	1	no	Hall
36	C₃×D₁₉	—	91	3	no	—
37	C₃×D₁₉	#63271	1	1	yes	characteristic, direct product factor
38	C₇×C₁₃	C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₁₃	—	19	1	no	—
40	C₂×C₁₃⋊C₃	—	133	3	no	—
41	C₃×ΓL(1,𝔽₈)	—	13	1	no	Hall
42	C₃×C₁₉	—	91	3	no	—
43	C₃×C₁₉	C₂×#63271	1	1	yes	characteristic, complemented
44	C₂×C₃×C₇	—	19	1	no	—
45	C₂×ΓL(1,𝔽₈)	—	247	3	no	—
46	C₃×C₁₃	ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic, complemented
47	C₁₃⋊C₃	—	7	3	no	—
48	D₁₉	C₃×#63271	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₁₃	—	19	1	no	Hall
50	C₃×C₇	D₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	13	3	no	—
52	C₁₉	C₂×C₃×#63271	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	1729	1	no	Hall
54	C₂×C₇	—	19	1	no	Hall
55	C₁₃	C₃×ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	91	1	no	Sylow
57	C₇	C₃×D₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	19	1	no	—
59	C₂×C₃	—	1729	3	no	—
60	C₃	—	91	3	no	—
61	C₃	D₁₉×#63271	1	1	yes	characteristic, direct product factor
62	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₉×#63271
commutator, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#63271	C₂	semidirect
2. D₁₉×#63271	C₃	direct (N × H)
3. C₃×C₇×C₁₃×D₁₉	C₃	semidirect
4. C₁₉×#63271	C₂×C₃	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₇×C₁₃×D₁₉	C₃²	semidirect
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
12. C₃×C₁₃×D₁₉	ΓL(1,𝔽₈)	semidirect
15. C₃×#63271	D₁₉	direct (N × H)
16. C₃×C₇×D₁₉	C₁₃⋊C₃	semidirect
18. C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. C₁₃×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
23. C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
26. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
27. #63271	C₃×D₁₉	direct (N × H)
28. C₇×D₁₉	C₃×C₁₃⋊C₃	semidirect
29. C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
33. C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
37. C₃×D₁₉	#63271	direct (N × H)
38. C₇×C₁₃	C₃²×D₁₉	semidirect
43. C₃×C₁₉	C₂×#63271	semidirect
46. C₃×C₁₃	ΓL(1,𝔽₈)×D₁₉	semidirect
48. D₁₉	C₃×#63271	direct (N × H)
50. C₃×C₇	D₁₉×C₁₃⋊C₃	semidirect
52. C₁₉	C₂×C₃×#63271	semidirect
55. C₁₃	C₃×ΓL(1,𝔽₈)×D₁₉	semidirect
57. C₇	C₃×D₁₉×C₁₃⋊C₃	semidirect
61. C₃	D₁₉×#63271	direct (N × H)

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
D₁₉×#63271	3
C₃×C₇×C₁₃×D₁₉	3
C₃×D₁₉×C₁₃⋊C₃	7
C₃×ΓL(1,𝔽₈)×D₁₉	13
C₂×C₃×#63271	19

Subgroups — C3×D19×#63271 #44527883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₉×#63271 #44527883