Group #22580243 — subgroups

Subgroups — D₁₃⋊C₃×D₁₉⋊C₃ #22580243

Order 8892.

120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉⋊C₃×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₁₃⋊C₃)⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	D₁₉×D₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	#13093361⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
7	#13093360⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
8	C₁₃⋊C₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
9	#13093367	C₂×C₃	1	1	yes	characteristic, complemented
10	#13093366	C₂×C₃	1	1	yes	characteristic, complemented
11	#13093365	C₂×C₃	1	1	yes	characteristic, complemented
12	#13093364	C₂×C₃	1	1	yes	characteristic, complemented
13	(C₁₃⋊C₃)⋊D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₁₉×D₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
15	#13093361	C₂×C₃	1	1	yes	characteristic, complemented
16	#13093360	C₂×C₃	1	1	yes	characteristic, complemented
17	D₁₉×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
18	(C₁₉⋊C₃)⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
19	D₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
20	C₁₃×D₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
21	D₁₃×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
22	#10625203	C₂²×C₃	1	1	yes	characteristic, complemented
23	#10625202	C₂²×C₃	1	1	yes	characteristic, complemented
24	C₁₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
25	C₁₉×C₁₃⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×D₁₉⋊C₃	—	13	1	no	maximal, Hall
27	D₂₄₇	C₂×C₃²	1	1	yes	characteristic, complemented
28	C₁₃×D₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
29	C₁₉×D₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
30	C₂×C₃×D₁₃⋊C₃	—	19	1	no	maximal, Hall
31	C₂×C₃×C₁₉⋊C₃	—	13	1	no	—
32	C₃×D₁₉⋊C₃	—	13	1	no	—
33	C₃×D₁₉⋊C₃	—	13	1	no	—
34	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₁₃⋊C₃	—	19	1	no	—
36	C₃×D₁₃⋊C₃	—	19	1	no	—
37	C₃×D₁₃⋊C₃	—	19	1	no	—
38	C₂×C₃×D₁₉	—	13	1	no	—
39	C₂×D₁₉⋊C₃	—	13	1	no	—
40	C₂×D₁₉⋊C₃	—	13	1	no	—
41	C₂×D₁₉⋊C₃	—	13	1	no	—
42	C₃×C₁₉⋊C₃	—	13	1	no	Hall
43	C₂×C₃×D₁₃	—	19	1	no	—
44	C₂×D₁₃⋊C₃	—	19	1	no	—
45	C₂×D₁₃⋊C₃	—	19	1	no	—
46	C₂×D₁₃⋊C₃	—	19	1	no	—
47	C₃×C₁₃⋊C₃	—	19	1	no	Hall
48	C₂×C₃×C₁₉	—	13	1	no	—
49	C₃×D₁₉	—	13	1	no	—
50	C₃×D₁₉	—	13	1	no	—
51	C₂×C₁₉⋊C₃	—	13	1	no	—
52	C₂×C₁₉⋊C₃	—	13	1	no	—
53	C₂×C₁₉⋊C₃	—	13	1	no	—
54	D₁₉⋊C₃	—	13	1	no	—
55	D₁₉⋊C₃	—	13	1	no	—
56	D₁₉⋊C₃	—	13	1	no	—
57	D₁₉⋊C₃	—	13	1	no	—
58	D₁₉⋊C₃	—	13	1	no	—
59	D₁₉⋊C₃	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
60	C₂×C₃×C₁₃	—	19	1	no	—
61	C₃×D₁₃	—	19	1	no	—
62	C₃×D₁₃	—	19	1	no	—
63	C₂×C₁₃⋊C₃	—	19	1	no	—
64	C₂×C₁₃⋊C₃	—	19	1	no	—
65	C₂×C₁₃⋊C₃	—	19	1	no	—
66	D₁₃⋊C₃	—	19	1	no	—
67	D₁₃⋊C₃	—	19	1	no	—
68	D₁₃⋊C₃	—	19	1	no	—
69	D₁₃⋊C₃	—	19	1	no	—
70	D₁₃⋊C₃	—	19	1	no	—
71	D₁₃⋊C₃	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
72	C₂×D₁₉	—	13	1	no	Hall
73	C₃×C₁₉	—	13	1	no	—
74	C₁₉⋊C₃	—	13	1	no	—
75	C₁₉⋊C₃	—	13	1	no	—
76	C₁₉⋊C₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
77	C₂×D₁₃	—	19	1	no	Hall
78	C₃×C₁₃	—	19	1	no	—
79	C₁₃⋊C₃	—	19	1	no	—
80	C₁₃⋊C₃	—	19	1	no	—
81	C₁₃⋊C₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
82	C₂×C₁₉	—	13	1	no	—
83	D₁₉	—	13	1	no	—
84	D₁₉	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
85	C₂²×C₃²	—	247	1	no	Hall
86	C₂×C₁₃	—	19	1	no	—
87	D₁₃	—	19	1	no	—
88	D₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
89	C₁₉	C₂×C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
90	C₂×C₃²	—	247	1	no	—
91	C₂×C₃²	—	247	1	no	—
92	C₂×C₃²	—	247	1	no	—
93	C₁₃	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₃	—	247	1	no	—
95	C₂²×C₃	—	247	1	no	—
96	C₂²×C₃	—	247	1	no	—
97	C₂²×C₃	—	247	1	no	—
98	C₃²	—	247	1	no	Sylow
99	C₂×C₃	—	13	1	no	—
100	C₂×C₃	—	19	1	no	—
101	C₂×C₃	—	247	1	no	—
102	C₂×C₃	—	247	1	no	—
103	C₂×C₃	—	247	1	no	—
104	C₂×C₃	—	247	1	no	—
105	C₂×C₃	—	247	1	no	—
106	C₂×C₃	—	247	1	no	—
107	C₂×C₃	—	247	1	no	—
108	C₂×C₃	—	247	1	no	—
109	C₂×C₃	—	247	1	no	—
110	C₂×C₃	—	247	1	no	—
111	C₂²	—	247	1	no	Sylow
112	C₃	—	13	1	no	—
113	C₃	—	19	1	no	—
114	C₃	—	247	1	no	—
115	C₃	—	247	1	no	—
116	C₂	—	13	1	no	—
117	C₂	—	19	1	no	—
118	C₂	—	247	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃⋊C₃×D₁₉⋊C₃

C₂

yes

maximal, characteristic, complemented

C₁₉⋊C₃×D₁₃⋊C₃

C₂

yes

maximal, characteristic, complemented

(C₁₃⋊C₃)⋊(D₁₉⋊C₃)

C₂

yes

maximal, characteristic, complemented

D₁₃×D₁₉⋊C₃

C₃

yes

maximal, characteristic, complemented

D₁₉×D₁₃⋊C₃

C₃

yes

maximal, characteristic, complemented

#13093361⋊C₂

C₃

yes

maximal, characteristic, complemented

#13093360⋊C₂

C₃

yes

maximal, characteristic, complemented

C₁₃⋊C₃×C₁₉⋊C₃

C₂²

yes

characteristic, complemented, Hall

#13093367

C₂×C₃

yes

characteristic, complemented

#13093366

C₂×C₃

yes

characteristic, complemented

#13093365

C₂×C₃

yes

characteristic, complemented

#13093364

C₂×C₃

yes

characteristic, complemented

(C₁₃⋊C₃)⋊D₁₉

C₂×C₃

yes

characteristic, complemented

C₁₉×D₁₃⋊C₃

C₂×C₃

yes

characteristic, complemented

#13093361

C₂×C₃

yes

characteristic, complemented

#13093360

C₂×C₃

yes

characteristic, complemented

D₁₉×C₁₃⋊C₃

C₂×C₃

yes

characteristic, complemented

(C₁₉⋊C₃)⋊D₁₃

C₂×C₃

yes

characteristic, complemented

D₁₃×C₁₉⋊C₃

C₂×C₃

yes

characteristic, complemented

C₁₃×D₁₉⋊C₃

C₂×C₃

yes

characteristic, complemented

D₁₃×D₁₉

C₃²

yes

characteristic, complemented, Hall

#10625203

C₂²×C₃

yes

characteristic, complemented

#10625202

C₂²×C₃

yes

characteristic, complemented

C₁₃×C₁₉⋊C₃

C₂²×C₃

yes

characteristic, complemented

C₁₉×C₁₃⋊C₃

C₂²×C₃

yes

characteristic, complemented

C₂×C₃×D₁₉⋊C₃

—

maximal, Hall

D₂₄₇

C₂×C₃²

yes

characteristic, complemented

C₁₃×D₁₉

C₂×C₃²

yes

characteristic, complemented

C₁₉×D₁₃

C₂×C₃²

yes

characteristic, complemented

C₂×C₃×D₁₃⋊C₃

—

maximal, Hall

C₂×C₃×C₁₉⋊C₃

—

C₃×D₁₉⋊C₃

—

C₃×D₁₉⋊C₃

—

C₁₃×C₁₉

C₂²×C₃²

yes

characteristic, complemented, Hall

C₂×C₃×C₁₃⋊C₃

—

C₃×D₁₃⋊C₃

—

C₃×D₁₃⋊C₃

—

C₂×C₃×D₁₉

—

C₂×D₁₉⋊C₃

—

C₂×D₁₉⋊C₃

—

C₂×D₁₉⋊C₃

—

C₃×C₁₉⋊C₃

—

Hall

C₂×C₃×D₁₃

—

C₂×D₁₃⋊C₃

—

C₂×D₁₃⋊C₃

—

C₂×D₁₃⋊C₃

—

C₃×C₁₃⋊C₃

—

Hall

C₂×C₃×C₁₉

—

C₃×D₁₉

—

C₃×D₁₉

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

D₁₃⋊C₃

yes

characteristic, direct product factor

C₂×C₃×C₁₃

—

C₃×D₁₃

—

C₃×D₁₃

—

C₂×C₁₃⋊C₃

—

C₂×C₁₃⋊C₃

—

C₂×C₁₃⋊C₃

—

D₁₃⋊C₃

—

D₁₃⋊C₃

—

D₁₃⋊C₃

—

D₁₃⋊C₃

—

D₁₃⋊C₃

—

D₁₃⋊C₃

D₁₉⋊C₃

yes

characteristic, direct product factor

C₂×D₁₉

—

Hall

C₃×C₁₉

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

C₂×D₁₃⋊C₃

yes

characteristic, complemented

C₂×D₁₃

—

Hall

C₃×C₁₃

—

C₁₃⋊C₃

—

C₁₃⋊C₃

—

C₁₃⋊C₃

C₂×D₁₉⋊C₃

yes

characteristic, complemented

C₂×C₁₉

—

D₁₉

—

D₁₉

C₃×D₁₃⋊C₃

yes

characteristic, complemented

C₂²×C₃²

—

247

Hall

C₂×C₁₃

—

D₁₃

—

D₁₃

C₃×D₁₉⋊C₃

yes

characteristic, complemented

C₁₉

C₂×C₃×D₁₃⋊C₃

yes

characteristic, complemented, Sylow

C₂×C₃²

—

247

—

C₂×C₃²

—

247

—

C₂×C₃²

—

247

—

C₁₃

C₂×C₃×D₁₉⋊C₃

yes

characteristic, complemented, Sylow

C₂²×C₃

—

247

—

C₂²×C₃

—

247

—

C₂²×C₃

—

247

—

C₂²×C₃

—

247

—

C₃²

—

247

Sylow

C₂×C₃

—

100

C₂×C₃

—

101

C₂×C₃

—

247

—

102

C₂×C₃

—

247

—

103

C₂×C₃

—

247

—

104

C₂×C₃

—

247

—

105

C₂×C₃

—

247

—

106

C₂×C₃

—

247

—

107

C₂×C₃

—

247

—

108

C₂×C₃

—

247

—

109

C₂×C₃

—

247

—

110

C₂×C₃

—

247

—

111

C₂²

—

247

Sylow

112

C₃

—

113

C₃

—

114

C₃

—

247

—

115

C₃

—

247

—

116

C₂

—

117

C₂

—

118

C₂

—

247

—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₉	C₂²×C₃²
LCS	G ▷ C₁₃×C₁₉
UCS	C₁

subgroup

G/H

center, Frattini, hypercenter

C₁

commutator, Fitting, socle, hypocenter

C₁₃×C₁₉

C₂²×C₃²

LCS

G ▷ C₁₃×C₁₉

UCS

C₁

N	H ≅ G/N	type
1. C₁₃⋊C₃×D₁₉⋊C₃	C₂	semidirect
2. C₁₉⋊C₃×D₁₃⋊C₃	C₂	semidirect
3. (C₁₃⋊C₃)⋊(D₁₉⋊C₃)	C₂	semidirect
4. D₁₃×D₁₉⋊C₃	C₃	semidirect
5. D₁₉×D₁₃⋊C₃	C₃	semidirect
6. #13093361⋊C₂	C₃	semidirect
7. #13093360⋊C₂	C₃	semidirect
8. C₁₃⋊C₃×C₁₉⋊C₃	C₂²	semidirect
9. #13093367	C₂×C₃	semidirect
10. #13093366	C₂×C₃	semidirect
11. #13093365	C₂×C₃	semidirect
12. #13093364	C₂×C₃	semidirect
13. (C₁₃⋊C₃)⋊D₁₉	C₂×C₃	semidirect
14. C₁₉×D₁₃⋊C₃	C₂×C₃	semidirect
15. #13093361	C₂×C₃	semidirect
16. #13093360	C₂×C₃	semidirect
17. D₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
18. (C₁₉⋊C₃)⋊D₁₃	C₂×C₃	semidirect
19. D₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
20. C₁₃×D₁₉⋊C₃	C₂×C₃	semidirect
21. D₁₃×D₁₉	C₃²	semidirect
22. #10625203	C₂²×C₃	semidirect
23. #10625202	C₂²×C₃	semidirect
24. C₁₃×C₁₉⋊C₃	C₂²×C₃	semidirect
25. C₁₉×C₁₃⋊C₃	C₂²×C₃	semidirect
27. D₂₄₇	C₂×C₃²	semidirect
28. C₁₃×D₁₉	C₂×C₃²	semidirect
29. C₁₉×D₁₃	C₂×C₃²	semidirect
34. C₁₃×C₁₉	C₂²×C₃²	semidirect
59. D₁₉⋊C₃	D₁₃⋊C₃	direct (N × H)
71. D₁₃⋊C₃	D₁₉⋊C₃	direct (N × H)
76. C₁₉⋊C₃	C₂×D₁₃⋊C₃	semidirect
81. C₁₃⋊C₃	C₂×D₁₉⋊C₃	semidirect
84. D₁₉	C₃×D₁₃⋊C₃	semidirect
88. D₁₃	C₃×D₁₉⋊C₃	semidirect
89. C₁₉	C₂×C₃×D₁₃⋊C₃	semidirect
93. C₁₃	C₂×C₃×D₁₉⋊C₃	semidirect

H ≅ G/N

type

1. C₁₃⋊C₃×D₁₉⋊C₃

C₂

semidirect

2. C₁₉⋊C₃×D₁₃⋊C₃

C₂

semidirect

3. (C₁₃⋊C₃)⋊(D₁₉⋊C₃)

C₂

semidirect

4. D₁₃×D₁₉⋊C₃

C₃

semidirect

5. D₁₉×D₁₃⋊C₃

C₃

semidirect

6. #13093361⋊C₂

C₃

semidirect

7. #13093360⋊C₂

C₃

semidirect

8. C₁₃⋊C₃×C₁₉⋊C₃

C₂²

semidirect

9. #13093367

C₂×C₃

semidirect

10. #13093366

C₂×C₃

semidirect

11. #13093365

C₂×C₃

semidirect

12. #13093364

C₂×C₃

semidirect

13. (C₁₃⋊C₃)⋊D₁₉

C₂×C₃

semidirect

14. C₁₉×D₁₃⋊C₃

C₂×C₃

semidirect

15. #13093361

C₂×C₃

semidirect

16. #13093360

C₂×C₃

semidirect

17. D₁₉×C₁₃⋊C₃

C₂×C₃

semidirect

18. (C₁₉⋊C₃)⋊D₁₃

C₂×C₃

semidirect

19. D₁₃×C₁₉⋊C₃

C₂×C₃

semidirect

20. C₁₃×D₁₉⋊C₃

C₂×C₃

semidirect

21. D₁₃×D₁₉

C₃²

semidirect

22. #10625203

C₂²×C₃

semidirect

23. #10625202

C₂²×C₃

semidirect

24. C₁₃×C₁₉⋊C₃

C₂²×C₃

semidirect

25. C₁₉×C₁₃⋊C₃

C₂²×C₃

semidirect

27. D₂₄₇

C₂×C₃²

semidirect

28. C₁₃×D₁₉

C₂×C₃²

semidirect

29. C₁₉×D₁₃

C₂×C₃²

semidirect

34. C₁₃×C₁₉

C₂²×C₃²

semidirect

59. D₁₉⋊C₃

D₁₃⋊C₃

direct (N × H)

71. D₁₃⋊C₃

D₁₉⋊C₃

direct (N × H)

76. C₁₉⋊C₃

C₂×D₁₃⋊C₃

semidirect

81. C₁₃⋊C₃

C₂×D₁₉⋊C₃

semidirect

84. D₁₉

C₃×D₁₃⋊C₃

semidirect

88. D₁₃

C₃×D₁₉⋊C₃

semidirect

89. C₁₉

C₂×C₃×D₁₃⋊C₃

semidirect

93. C₁₃

C₂×C₃×D₁₉⋊C₃

semidirect

Subgroups — D₁₃⋊C₃×D₁₉⋊C₃ #22580243

Conjugacy classes of subgroups

Complements

Subgroups — D13⋊C3×D19⋊C3 #22580243

Conjugacy classes of subgroups

Complements

Subgroups — D₁₃⋊C₃×D₁₉⋊C₃ #22580243