Subgroups — C₇×C₃⋊#13093361 #44527916

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#10625203	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×#13093361	—	3	1	no	maximal
3	C₇×C₁₃×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×#10625203	—	2	1	no	—
5	C₇×#10625203	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃⋊#13093361	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×D₁₉	—	3	1	no	Hall
9	C₇×C₃⋊(D₁₉⋊C₃)	—	13	1	no	maximal, Hall
10	C₃×#10625203	C₂×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	D₃×C₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
13	C₁₃×D₅₇	C₃×C₇	1	1	yes	characteristic, complemented
14	#13093361	—	3	1	no	—
15	C₃×C₇×C₁₉⋊C₃	—	13	1	no	Hall
16	C₃×C₇×C₁₃⋊C₃	—	19	1	no	Hall
17	C₇×D₅₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₇×D₁₉⋊C₃	—	39	1	no	—
19	C₃×C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
20	#10625203	—	2	1	no	—
21	#10625203	D₃×C₇	1	1	yes	characteristic, complemented
22	D₃×C₇×C₁₃	—	19	1	no	—
23	C₂×C₇×C₁₃⋊C₃	—	57	1	no	—
24	C₁₃×D₁₉	—	3	1	no	Hall
25	C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₇×C₁₉⋊C₃	—	13	1	no	—
27	C₇×C₁₉⋊C₃	—	26	1	no	—
28	C₃⋊(D₁₉⋊C₃)	—	13	1	no	Hall
29	C₃×C₇×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
30	C₇×C₁₃⋊C₃	—	19	1	no	—
31	C₇×C₁₃⋊C₃	—	38	1	no	—
32	C₇×D₁₉	—	3	1	no	Hall
33	C₁₃×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
34	D₃×C₁₃⋊C₃	—	19	1	no	Hall
35	C₂×C₇×C₁₃	—	57	1	no	Hall
36	C₃×C₁₉⋊C₃	—	13	1	no	Hall
37	C₇×C₁₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
38	C₃×D₃×C₇	—	247	1	no	Hall
39	C₃×C₁₃⋊C₃	—	19	1	no	Hall
40	D₅₇	C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
41	D₁₉⋊C₃	—	39	1	no	—
42	C₇×C₁₃	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Hall
43	D₃×C₁₃	—	19	1	no	—
44	C₂×C₁₃⋊C₃	—	57	1	no	—
45	C₃²×C₇	—	247	1	no	Hall
46	C₃×C₁₉	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	—	13	1	no	—
48	C₁₉⋊C₃	—	26	1	no	—
49	C₂×C₃×C₇	—	741	1	no	—
50	D₃×C₇	—	19	1	no	—
51	C₃×C₁₃	C₇×D₁₉⋊C₃	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	—	19	1	no	—
53	C₁₃⋊C₃	—	38	1	no	—
54	D₁₉	—	3	1	no	Hall
55	C₂×C₁₃	—	57	1	no	Hall
56	C₃×C₇	—	494	1	no	—
57	C₃×C₇	—	247	1	no	—
58	C₃×C₇	#13093361	1	1	yes	characteristic, complemented
59	C₁₉	D₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃×D₃	—	247	1	no	Hall
61	C₂×C₇	—	57	1	no	Hall
62	C₁₃	C₇×C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	247	1	no	Sylow
64	C₇	C₃⋊#13093361	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₃	—	741	1	no	—
66	D₃	—	19	1	no	—
67	C₃	—	494	1	no	—
68	C₃	—	247	1	no	—
69	C₃	C₇×#13093361	1	1	yes	characteristic, complemented
70	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊#13093361
commutator, cosocle, hypocenter	C₃×C₁₃×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#10625203	C₂	semidirect
3. C₇×C₁₃×D₅₇	C₃	semidirect
5. C₇×#10625203	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₃⋊#13093361	C₇	direct (N × H)
10. C₃×#10625203	C₂×C₇	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
13. C₁₃×D₅₇	C₃×C₇	semidirect
17. C₇×D₅₇	C₁₃⋊C₃	semidirect
19. C₃×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
21. #10625203	D₃×C₇	semidirect
25. C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
29. C₃×C₇×C₁₃	D₁₉⋊C₃	semidirect
33. C₁₃×C₁₉	C₃×D₃×C₇	semidirect
37. C₇×C₁₉	D₃×C₁₃⋊C₃	semidirect
40. D₅₇	C₇×C₁₃⋊C₃	semidirect
42. C₇×C₁₃	C₃⋊(D₁₉⋊C₃)	semidirect
46. C₃×C₁₉	C₂×C₇×C₁₃⋊C₃	semidirect
51. C₃×C₁₃	C₇×D₁₉⋊C₃	semidirect
58. C₃×C₇	#13093361	semidirect
59. C₁₉	D₃×C₇×C₁₃⋊C₃	semidirect
62. C₁₃	C₇×C₃⋊(D₁₉⋊C₃)	semidirect
64. C₇	C₃⋊#13093361	direct (N × H)
69. C₃	C₇×#13093361	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×#10625203	2
C₇×#13093361	3
C₇×C₁₃×D₅₇	3
C₃⋊#13093361	7
C₇×C₃⋊(D₁₉⋊C₃)	13
D₃×C₇×C₁₃⋊C₃	19

Subgroups — C7×C3⋊#13093361 #44527916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊#13093361 #44527916