Group #14576739 — subgroups

Subgroups — C₂×D₁₆×D₁₉ #14576739

Order 2432.

440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₂×D₈×D₁₉	C₂	1	2	yes	maximal, complemented
2	C₂×D₃₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597283	C₂	1	2	yes	maximal, complemented
4	D₁₆×D₁₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×D₁₉	—	2	2	no	—
8	C₂×D₈×C₁₉	C₂²	1	2	yes	complemented
9	C₂×#64525	—	2	2	no	—
10	D₈×D₁₉	—	2	4	no	—
11	D₈×D₁₉	C₂²	1	8	yes	complemented
12	C₂×D₁₅₂	C₂²	1	2	yes	complemented
13	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×D₁₆	C₂²	1	4	yes	complemented
15	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	#10597283	C₂²	1	8	yes	complemented
17	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
18	D₃₀₄	C₂²	1	4	yes	complemented
19	C₁₆×D₁₉	C₂²	1	4	yes	complemented
20	C₂³×D₁₉	—	4	2	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×C₂²⋊D₁₉	—	4	2	no	—
23	D₄×D₁₉	—	2	8	no	—
24	D₄×D₁₉	—	4	4	no	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
27	D₈×C₁₉	—	2	2	no	—
28	D₈×C₁₉	C₂³	1	4	yes	complemented
29	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
30	#64525	—	2	8	no	—
31	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
32	D₁₅₂	—	2	2	no	—
33	D₁₅₂	C₂³	1	4	yes	complemented
34	C₈×D₁₉	D₄	1	2	yes	—
35	C₈×D₁₉	C₂³	1	2	yes	—
36	C₁₆×C₁₉	C₂³	1	2	yes	complemented
37	C₁₉⋊C₁₆	C₂³	1	2	yes	complemented
38	C₂³×C₁₉	—	4	2	no	—
39	C₂²×D₁₉	—	4	2	no	—
40	C₂²×D₁₉	—	4	8	no	—
41	C₂²×D₁₉	—	8	8	no	—
42	C₂²×D₁₉	D₈	1	1	yes	characteristic
43	D₄×C₁₉	—	2	4	no	—
44	D₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²⋊D₁₉	—	4	8	no	—
47	C₂×Dic₁₉	D₈	1	1	yes	characteristic
48	D₇₆	—	2	4	no	—
49	D₇₆	—	4	2	no	—
50	C₄×D₁₉	D₈	1	2	yes	—
51	C₄×D₁₉	C₂×D₄	1	2	yes	—
52	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₈×C₁₉	C₂⁴	1	1	yes	characteristic
54	C₁₉⋊C₈	C₂×D₄	1	2	yes	—
55	C₂²×D₁₆	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	—	4	4	no	—
57	C₂²×C₁₉	—	8	4	no	—
58	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
59	C₂×D₁₉	—	4	4	no	—
60	C₂×D₁₉	—	8	4	no	—
61	C₂×D₁₉	—	8	16	no	—
62	C₂×D₁₉	D₁₆	1	4	yes	direct product factor
63	C₂×D₁₉	C₂×D₈	1	2	yes	—
64	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
65	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
66	Dic₁₉	C₂×D₈	1	2	yes	—
67	C₂²×D₈	—	19	2	no	—
68	C₂×D₁₆	—	19	2	no	—
69	C₂×D₁₆	—	19	8	no	—
70	C₂×D₁₆	—	19	1	no	—
71	C₂×D₁₆	D₁₉	1	1	yes	characteristic, direct product factor
72	C₂²×C₁₆	—	19	1	no	—
73	C₂×C₁₉	—	8	4	no	—
74	C₂×C₁₉	C₂×D₁₆	1	2	yes	complemented
75	C₂×C₁₉	C₂²×D₈	1	1	yes	characteristic
76	D₁₉	—	8	4	no	—
77	D₁₉	C₂×D₁₆	1	4	yes	direct product factor
78	C₂²×D₄	—	38	2	no	—
79	C₂×D₈	—	19	8	no	—
80	C₂×D₈	—	19	2	no	—
81	C₂×D₈	—	38	4	no	—
82	C₂×D₈	—	38	2	no	—
83	C₂×D₈	C₂×D₁₉	1	2	yes	complemented
84	C₂²×C₈	—	19	1	no	—
85	D₁₆	—	19	8	no	—
86	D₁₆	—	19	4	no	—
87	D₁₆	C₂×D₁₉	1	4	yes	direct product factor
88	C₂×C₁₆	—	19	1	no	—
89	C₂×C₁₆	—	19	4	no	—
90	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
91	C₁₉	C₂²×D₁₆	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	—	76	2	no	—
93	C₂×D₄	—	2	2	no	—
94	C₂×D₄	—	38	8	no	—
95	C₂×D₄	—	38	2	no	—
96	C₂×D₄	—	76	4	no	—
97	C₂×D₄	—	76	2	no	—
98	C₂²×C₄	—	19	1	no	—
99	D₈	—	2	2	no	—
100	D₈	—	19	4	no	—
101	D₈	—	38	8	no	—
102	D₈	—	38	2	no	—
103	D₈	C₂²×D₁₉	1	4	yes	complemented
104	C₂×C₈	—	19	1	no	—
105	C₂×C₈	—	19	2	no	—
106	C₂×C₈	—	19	2	no	—
107	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
108	C₁₆	—	19	2	no	—
109	C₁₆	C₂²×D₁₉	1	2	yes	complemented
110	C₂³	—	4	2	no	—
111	C₂³	—	19	1	no	—
112	C₂³	—	76	8	no	—
113	C₂³	—	76	2	no	—
114	C₂³	—	152	8	no	—
115	D₄	—	2	4	no	—
116	D₄	—	4	2	no	—
117	D₄	—	38	4	no	—
118	D₄	—	76	8	no	—
119	D₄	—	76	2	no	—
120	C₂×C₄	—	19	1	no	—
121	C₂×C₄	—	19	2	no	—
122	C₂×C₄	—	19	2	no	—
123	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
124	C₈	—	19	2	no	—
125	C₈	D₄×D₁₉	1	1	yes	characteristic
126	C₈	C₂³×D₁₉	1	1	yes	characteristic
127	C₂²	—	4	4	no	—
128	C₂²	—	8	4	no	—
129	C₂²	—	19	2	no	—
130	C₂²	—	19	4	no	—
131	C₂²	—	76	4	no	—
132	C₂²	—	152	16	no	—
133	C₂²	—	152	4	no	—
134	C₂²	D₈×D₁₉	1	1	yes	characteristic
135	C₄	—	19	2	no	—
136	C₄	D₈×D₁₉	1	1	yes	characteristic
137	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
138	C₂	—	8	4	no	—
139	C₂	—	19	4	no	—
140	C₂	—	152	4	no	—
141	C₂	D₁₆×D₁₉	1	2	yes	direct product factor
142	C₂	C₂×D₈×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₈×D₁₉

C₂

yes

maximal, complemented

C₂×D₃₀₄

C₂

yes

maximal, characteristic, complemented

C₂×#10597283

C₂

yes

maximal, complemented

D₁₆×D₁₉

C₂

yes

maximal, direct product factor

C₂×C₁₆×D₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₂

yes

maximal, characteristic, complemented

C₂×D₄×D₁₉

—

C₂×D₈×C₁₉

C₂²

yes

complemented

C₂×#64525

—

D₈×D₁₉

—

D₈×D₁₉

C₂²

yes

complemented

C₂×D₁₅₂

C₂²

yes

complemented

C₂×C₈×D₁₉

C₂²

yes

characteristic

C₁₉×D₁₆

C₂²

yes

complemented

C₂×C₁₆×C₁₉

C₂²

yes

characteristic, complemented

#10597283

C₂²

yes

complemented

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic, complemented

D₃₀₄

C₂²

yes

complemented

C₁₆×D₁₉

C₂²

yes

complemented

C₂³×D₁₉

—

C₂×D₄×C₁₉

—

C₂×C₂²⋊D₁₉

—

D₄×D₁₉

—

D₄×D₁₉

—

C₂×D₇₆

—

C₂×C₄×D₁₉

D₄

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

C₂³

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

characteristic

#64525

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

D₁₅₂

—

D₁₅₂

C₂³

yes

complemented

C₈×D₁₉

D₄

yes

—

C₈×D₁₉

C₂³

yes

—

C₁₆×C₁₉

C₂³

yes

complemented

C₁₉⋊C₁₆

C₂³

yes

complemented

C₂³×C₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

D₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

D₇₆

—

D₇₆

—

C₄×D₁₉

D₈

yes

—

C₄×D₁₉

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂⁴

yes

characteristic

C₁₉⋊C₈

C₂×D₄

yes

—

C₂²×D₁₆

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

D₁₆

yes

direct product factor

C₂×D₁₉

C₂×D₈

yes

—

C₄×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

C₂×D₈

yes

—

C₂²×D₈

—

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

D₁₉

yes

characteristic, direct product factor

C₂²×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₂×D₁₆

yes

complemented

C₂×C₁₉

C₂²×D₈

yes

characteristic

D₁₉

—

D₁₉

C₂×D₁₆

yes

direct product factor

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

complemented

C₂²×C₈

—

D₁₆

—

D₁₆

—

D₁₆

C₂×D₁₉

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic, complemented

C₁₉

C₂²×D₁₆

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

100

D₈

—

101

D₈

—

102

D₈

—

103

D₈

C₂²×D₁₉

yes

complemented

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂²×D₁₉

yes

characteristic

108

C₁₆

—

109

C₁₆

C₂²×D₁₉

yes

complemented

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

152

—

115

D₄

—

116

D₄

—

117

D₄

—

118

D₄

—

119

D₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

D₄×D₁₉

yes

characteristic

124

C₈

—

125

C₈

D₄×D₁₉

yes

characteristic

126

C₈

C₂³×D₁₉

yes

characteristic

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

152

—

133

C₂²

—

152

—

134

C₂²

D₈×D₁₉

yes

characteristic

135

C₄

—

136

C₄

D₈×D₁₉

yes

characteristic

137

C₄

C₂×D₄×D₁₉

yes

characteristic

138

C₂

—

139

C₂

—

140

C₂

—

152

—

141

C₂

D₁₆×D₁₉

yes

direct product factor

142

C₂

C₂×D₈×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₈×C₁₉	C₂⁴
Frattini	C₈	C₂³×D₁₉
Fitting	C₂×C₁₉×D₁₆	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	C₂×D₁₆	D₁₉
hypocenter	C₁₉	C₂²×D₁₆
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₈×C₁₉

C₂⁴

Frattini

C₈

C₂³×D₁₉

Fitting

C₂×C₁₉×D₁₆

C₂

socle

C₂²×C₁₉

C₂×D₈

hypercenter

C₂×D₁₆

D₁₉

hypocenter

C₁₉

C₂²×D₁₆

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. C₂×D₈×D₁₉	C₂	semidirect
2. C₂×D₃₀₄	C₂	semidirect
3. C₂×#10597283	C₂	semidirect
4. D₁₆×D₁₉	C₂	direct (N × H)
5. C₂×C₁₆×D₁₉	C₂	semidirect
6. C₂×C₁₉×D₁₆	C₂	semidirect
8. C₂×D₈×C₁₉	C₂²	semidirect
11. D₈×D₁₉	C₂²	semidirect
12. C₂×D₁₅₂	C₂²	semidirect
14. C₁₉×D₁₆	C₂²	semidirect
15. C₂×C₁₆×C₁₉	C₂²	semidirect
16. #10597283	C₂²	semidirect
17. C₂×C₁₉⋊C₁₆	C₂²	semidirect
18. D₃₀₄	C₂²	semidirect
19. C₁₆×D₁₉	C₂²	semidirect
28. D₈×C₁₉	C₂³	semidirect
33. D₁₅₂	C₂³	semidirect
36. C₁₆×C₁₉	C₂³	semidirect
37. C₁₉⋊C₁₆	C₂³	semidirect
62. C₂×D₁₉	D₁₆	direct (N × H)
71. C₂×D₁₆	D₁₉	direct (N × H)
74. C₂×C₁₉	C₂×D₁₆	semidirect
77. D₁₉	C₂×D₁₆	direct (N × H)
83. C₂×D₈	C₂×D₁₉	semidirect
87. D₁₆	C₂×D₁₉	direct (N × H)
90. C₂×C₁₆	C₂×D₁₉	semidirect
91. C₁₉	C₂²×D₁₆	semidirect
103. D₈	C₂²×D₁₉	semidirect
109. C₁₆	C₂²×D₁₉	semidirect
141. C₂	D₁₆×D₁₉	direct (N × H)

H ≅ G/N

type

1. C₂×D₈×D₁₉

C₂

semidirect

2. C₂×D₃₀₄

C₂

semidirect

3. C₂×#10597283

C₂

semidirect

4. D₁₆×D₁₉

C₂

direct (N × H)

5. C₂×C₁₆×D₁₉

C₂

semidirect

6. C₂×C₁₉×D₁₆

C₂

semidirect

8. C₂×D₈×C₁₉

C₂²

semidirect

11. D₈×D₁₉

C₂²

semidirect

12. C₂×D₁₅₂

C₂²

semidirect

14. C₁₉×D₁₆

C₂²

semidirect

15. C₂×C₁₆×C₁₉

C₂²

semidirect

16. #10597283

C₂²

semidirect

17. C₂×C₁₉⋊C₁₆

C₂²

semidirect

18. D₃₀₄

C₂²

semidirect

19. C₁₆×D₁₉

C₂²

semidirect

28. D₈×C₁₉

C₂³

semidirect

33. D₁₅₂

C₂³

semidirect

36. C₁₆×C₁₉

C₂³

semidirect

37. C₁₉⋊C₁₆

C₂³

semidirect

62. C₂×D₁₉

D₁₆

direct (N × H)

71. C₂×D₁₆

D₁₉

direct (N × H)

74. C₂×C₁₉

C₂×D₁₆

semidirect

77. D₁₉

C₂×D₁₆

direct (N × H)

83. C₂×D₈

C₂×D₁₉

semidirect

87. D₁₆

C₂×D₁₉

direct (N × H)

90. C₂×C₁₆

C₂×D₁₉

semidirect

91. C₁₉

C₂²×D₁₆

semidirect

103. D₈

C₂²×D₁₉

semidirect

109. C₁₆

C₂²×D₁₉

semidirect

141. C₂

D₁₆×D₁₉

direct (N × H)

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

subgroup	index
C₂×D₈×D₁₉	2
C₂×D₃₀₄	2
C₂×#10597283	2
D₁₆×D₁₉	2
C₂×C₁₆×D₁₉	2
C₂×C₁₉×D₁₆	2
C₂²×D₁₆	19

subgroup

index

C₂×D₈×D₁₉

C₂×D₃₀₄

C₂×#10597283

D₁₆×D₁₉

C₂×C₁₆×D₁₉

C₂×C₁₉×D₁₆

C₂²×D₁₆

Subgroups — C₂×D₁₆×D₁₉ #14576739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×D16×D19 #14576739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₆×D₁₉ #14576739