Subgroups — C₃×#23780575 #44527877

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	#23780575	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×D₂₄₇	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×(C₁₃⋊C₃)⋊D₁₉	—	7	1	no	maximal, Hall
7	C₇×D₂₄₇	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	C₃×#10587717	—	19	1	no	maximal, Hall
12	C₃×D₂₄₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	(C₁₃⋊C₃)⋊D₁₉	—	7	3	no	—
14	C₃×C₁₉×ΓL(1,𝔽₈)	—	13	1	no	Hall
15	C₃×#63271	D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×D₁₉	—	13	1	no	—
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	C₃×C₇×D₁₃	—	19	1	no	—
21	#10587717	—	19	3	no	—
22	D₂₄₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	D₁₃⋊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	complemented
28	C₇×D₁₉	—	13	1	no	Hall
29	C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃⋊C₃	—	133	1	no	Hall
31	C₇×D₁₃	—	19	1	no	Hall
32	C₃²×C₁₉	—	91	1	no	Hall
33	C₇×C₁₉	C₃×D₁₃⋊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	—	13	1	no	—
37	C₃×D₁₉	—	91	3	no	—
38	C₇×C₁₃	C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₃×D₁₃	—	19	1	no	—
40	D₁₃⋊C₃	—	133	3	no	—
41	C₃×ΓL(1,𝔽₈)	—	13	1	no	Hall
42	C₃×C₁₉	—	91	3	no	—
43	C₃×C₁₉	#10587717	1	1	yes	characteristic, complemented
44	C₂×C₃×C₇	—	247	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	—	13	1	no	Hall
49	D₁₃	—	19	1	no	Hall
50	C₃×C₇	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	13	3	no	—
52	C₁₉	C₃×#10587717	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	1729	1	no	Hall
54	C₂×C₇	—	247	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×(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	1729	3	no	—
59	C₂×C₃	—	247	1	no	—
60	C₃	—	91	3	no	—
61	C₃	#23780575	1	1	yes	characteristic, direct product factor
62	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#23780575
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. #23780575	C₃	direct (N × H)
3. C₃×C₇×D₂₄₇	C₃	semidirect
4. C₁₉×#63271	C₂×C₃	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₇×D₂₄₇	C₃²	semidirect
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
12. C₃×D₂₄₇	ΓL(1,𝔽₈)	semidirect
15. C₃×#63271	D₁₉	semidirect
18. C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. D₂₄₇	C₃×ΓL(1,𝔽₈)	semidirect
23. C₃×C₇×C₁₉	D₁₃⋊C₃	semidirect
26. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
27. #63271	C₃×D₁₉	semidirect
29. C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
33. C₇×C₁₉	C₃×D₁₃⋊C₃	semidirect
38. C₇×C₁₃	C₃²×D₁₉	semidirect
43. C₃×C₁₉	#10587717	semidirect
46. C₃×C₁₃	ΓL(1,𝔽₈)×D₁₉	semidirect
50. C₃×C₇	(C₁₃⋊C₃)⋊D₁₉	semidirect
52. C₁₉	C₃×#10587717	semidirect
55. C₁₃	C₃×ΓL(1,𝔽₈)×D₁₉	semidirect
57. C₇	C₃×(C₁₃⋊C₃)⋊D₁₉	semidirect
61. C₃	#23780575	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
#23780575	3
C₃×C₇×D₂₄₇	3
C₃×(C₁₃⋊C₃)⋊D₁₉	7
C₃×ΓL(1,𝔽₈)×D₁₉	13
C₃×#10587717	19

Subgroups — C3×#23780575 #44527877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23780575 #44527877