Subgroups — C₇×C₁₃⋊C₃×D₁₉⋊C₃ #44527648

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃⋊C₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×#13093361	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#13093360	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×D₁₉×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₇×C₁₃×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₇×#10625203	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×#10625202	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₃⋊C₃×D₁₉⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₁₃×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×D₁₉⋊C₃	—	13	1	no	maximal, Hall
13	C₁₃⋊C₃×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
16	#13093361	C₃×C₇	1	1	yes	characteristic, complemented
17	#13093360	C₃×C₇	1	1	yes	characteristic, complemented
18	D₁₉×C₁₃⋊C₃	C₃×C₇	1	1	yes	characteristic, complemented
19	C₁₃×D₁₉⋊C₃	C₃×C₇	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₉⋊C₃	—	13	1	no	Hall
21	C₃×C₇×C₁₃⋊C₃	—	19	1	no	Hall
22	C₃×C₇×D₁₉	—	13	1	no	—
23	C₇×D₁₉⋊C₃	—	13	1	no	—
24	C₇×D₁₉⋊C₃	—	13	1	no	—
25	C₇×D₁₉⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	#10625203	C₂×C₃×C₇	1	1	yes	characteristic, complemented
27	#10625202	C₂×C₃×C₇	1	1	yes	characteristic, complemented
28	C₁₃×C₁₉⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
29	C₁₉×C₁₃⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
30	C₂×C₃×C₇×C₁₃	—	19	1	no	—
31	C₂×C₇×C₁₃⋊C₃	—	19	1	no	—
32	C₂×C₇×C₁₃⋊C₃	—	19	1	no	—
33	C₂×C₇×C₁₃⋊C₃	—	19	1	no	—
34	C₁₃×D₁₉	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
35	C₃×C₇×C₁₉	—	13	1	no	—
36	C₇×C₁₉⋊C₃	—	13	1	no	—
37	C₇×C₁₉⋊C₃	—	13	1	no	—
38	C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₃×D₁₉⋊C₃	—	13	1	no	Hall
40	C₃×C₇×C₁₃	—	19	1	no	—
41	C₇×C₁₃⋊C₃	—	19	1	no	—
42	C₇×C₁₃⋊C₃	—	19	1	no	—
43	C₇×C₁₃⋊C₃	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
44	C₇×D₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
45	C₁₃×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₃⋊C₃	—	19	1	no	Hall
47	C₂×C₇×C₁₃	—	19	1	no	Hall
48	C₃×C₁₉⋊C₃	—	13	1	no	Hall
49	C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃²×C₇	—	247	1	no	Hall
51	C₃×C₁₃⋊C₃	—	19	1	no	Hall
52	C₃×D₁₉	—	13	1	no	—
53	D₁₉⋊C₃	—	13	1	no	—
54	D₁₉⋊C₃	—	13	1	no	—
55	D₁₉⋊C₃	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
56	C₇×C₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₁₃	—	19	1	no	—
58	C₂×C₁₃⋊C₃	—	19	1	no	—
59	C₂×C₁₃⋊C₃	—	19	1	no	—
60	C₂×C₁₃⋊C₃	—	19	1	no	—
61	C₃²×C₇	—	247	1	no	Hall
62	C₃×C₁₉	—	13	1	no	—
63	C₁₉⋊C₃	—	13	1	no	—
64	C₁₉⋊C₃	—	13	1	no	—
65	C₁₉⋊C₃	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
66	C₂×C₃×C₇	—	19	1	no	—
67	C₂×C₃×C₇	—	247	1	no	—
68	C₂×C₃×C₇	—	247	1	no	—
69	C₂×C₃×C₇	—	247	1	no	—
70	C₃×C₁₃	—	19	1	no	—
71	C₁₃⋊C₃	—	19	1	no	—
72	C₁₃⋊C₃	—	19	1	no	—
73	C₁₃⋊C₃	C₇×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
74	D₁₉	C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
75	C₂×C₁₃	—	19	1	no	Hall
76	C₃×C₇	—	13	1	no	—
77	C₃×C₇	—	19	1	no	—
78	C₃×C₇	—	247	1	no	—
79	C₃×C₇	—	247	1	no	—
80	C₁₉	C₂×C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃²	—	247	1	no	Hall
82	C₂×C₇	—	19	1	no	Hall
83	C₁₃	C₃×C₇×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
84	C₃²	—	247	1	no	Sylow
85	C₇	C₁₃⋊C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₃	—	19	1	no	—
87	C₂×C₃	—	247	1	no	—
88	C₂×C₃	—	247	1	no	—
89	C₂×C₃	—	247	1	no	—
90	C₃	—	13	1	no	—
91	C₃	—	19	1	no	—
92	C₃	—	247	1	no	—
93	C₃	—	247	1	no	—
94	C₂	—	19	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃⋊C₃×C₁₉⋊C₃	C₂	semidirect
2. C₇×#13093361	C₃	semidirect
3. C₇×#13093360	C₃	semidirect
4. C₇×D₁₉×C₁₃⋊C₃	C₃	semidirect
5. C₇×C₁₃×D₁₉⋊C₃	C₃	semidirect
6. C₇×#10625203	C₂×C₃	semidirect
7. C₇×#10625202	C₂×C₃	semidirect
8. C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
9. C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
10. C₁₃⋊C₃×D₁₉⋊C₃	C₇	direct (N × H)
11. C₇×C₁₃×D₁₉	C₃²	semidirect
13. C₁₃⋊C₃×C₁₉⋊C₃	C₂×C₇	semidirect
14. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
16. #13093361	C₃×C₇	semidirect
17. #13093360	C₃×C₇	semidirect
18. D₁₉×C₁₃⋊C₃	C₃×C₇	semidirect
19. C₁₃×D₁₉⋊C₃	C₃×C₇	semidirect
25. C₇×D₁₉⋊C₃	C₁₃⋊C₃	direct (N × H)
26. #10625203	C₂×C₃×C₇	semidirect
27. #10625202	C₂×C₃×C₇	semidirect
28. C₁₃×C₁₉⋊C₃	C₂×C₃×C₇	semidirect
29. C₁₉×C₁₃⋊C₃	C₂×C₃×C₇	semidirect
34. C₁₃×D₁₉	C₃²×C₇	semidirect
38. C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	semidirect
43. C₇×C₁₃⋊C₃	D₁₉⋊C₃	direct (N × H)
44. C₇×D₁₉	C₃×C₁₃⋊C₃	semidirect
45. C₁₃×C₁₉	C₂×C₃²×C₇	semidirect
49. C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
55. D₁₉⋊C₃	C₇×C₁₃⋊C₃	direct (N × H)
56. C₇×C₁₃	C₃×D₁₉⋊C₃	semidirect
65. C₁₉⋊C₃	C₂×C₇×C₁₃⋊C₃	semidirect
73. C₁₃⋊C₃	C₇×D₁₉⋊C₃	direct (N × H)
74. D₁₉	C₃×C₇×C₁₃⋊C₃	semidirect
80. C₁₉	C₂×C₃×C₇×C₁₃⋊C₃	semidirect
83. C₁₃	C₃×C₇×D₁₉⋊C₃	semidirect
85. C₇	C₁₃⋊C₃×D₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃⋊C₃×C₁₉⋊C₃	2
C₇×#13093361	3
C₇×#13093360	3
C₇×D₁₉×C₁₃⋊C₃	3
C₇×C₁₃×D₁₉⋊C₃	3
C₁₃⋊C₃×D₁₉⋊C₃	7
C₃×C₇×D₁₉⋊C₃	13
C₂×C₃×C₇×C₁₃⋊C₃	19

Subgroups — C7×C13⋊C3×D19⋊C3 #44527648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃⋊C₃×D₁₉⋊C₃ #44527648