Group #18019651 — subgroups

Subgroups — C₁₉×#13692 #18019651

Order 4864.

216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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	C₁₉×#2263	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2178	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1422	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1419	C₂	1	2	yes	maximal, complemented
6	C₁₉×#508	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×D₁₆	—	2	1	no	—
8	C₂×C₁₉×D₁₆	C₂²	1	2	yes	—
9	C₁₉×#493	—	2	1	no	—
10	C₁₉×#443	—	2	1	no	—
11	C₁₉×SD₆₄	—	2	2	no	—
12	C₁₉×D₃₂	—	2	2	no	—
13	C₁₉×M₆₄	C₂²	1	2	yes	—
14	C₁₉×#368	C₂²	1	1	yes	characteristic
15	C₁₉×#359	—	2	1	no	—
16	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#135	—	2	1	no	—
18	C₂×D₈×C₁₉	—	2	2	no	—
19	C₂×D₈×C₁₉	—	4	1	no	—
20	C₁₉×#131	—	4	1	no	—
21	C₁₉×#127	—	4	1	no	—
22	C₁₉×Q₃₂	D₄	1	1	yes	characteristic, complemented
23	C₁₉×SD₃₂	—	2	1	no	—
24	C₁₉×D₁₆	—	2	2	no	—
25	C₁₉×D₁₆	—	2	2	no	—
26	C₁₉×D₁₆	—	4	2	no	—
27	C₁₉×D₁₆	D₄	1	1	yes	characteristic, complemented
28	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
30	C₁₉×#108	—	2	1	no	—
31	C₁₉×#104	—	4	1	no	—
32	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₁₉×C₃₂	—	2	2	no	—
34	#41×C₁₉	—	4	1	no	—
35	C₂×D₄×C₁₉	—	4	2	no	—
36	C₂×D₄×C₁₉	—	8	2	no	—
37	Q₁₆×C₁₉	—	2	1	no	—
38	SD₁₆×C₁₉	—	4	1	no	—
39	D₈×C₁₉	—	2	1	no	—
40	D₈×C₁₉	—	4	2	no	—
41	D₈×C₁₉	—	4	2	no	—
42	D₈×C₁₉	—	8	1	no	—
43	D₈×C₁₉	—	8	1	no	—
44	M₁₆×C₁₉	—	4	1	no	—
45	M₁₆×C₁₉	—	8	1	no	—
46	C₂×C₈×C₁₉	—	8	1	no	—
47	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₉	D₈	1	1	yes	characteristic
50	C₁₆×C₁₉	—	2	1	no	—
51	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₁₆×C₁₉	#41	1	1	yes	characteristic
53	#13692	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂³×C₁₉	—	8	2	no	—
55	Q₈×C₁₉	—	4	1	no	—
56	D₄×C₁₉	—	4	1	no	—
57	D₄×C₁₉	—	8	1	no	—
58	D₄×C₁₉	—	8	2	no	—
59	D₄×C₁₉	—	8	2	no	—
60	D₄×C₁₉	—	16	4	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	8	1	no	—
63	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
64	C₈×C₁₉	—	8	1	no	—
65	C₈×C₁₉	D₁₆	1	1	yes	characteristic
66	C₈×C₁₉	D₁₆	1	1	yes	characteristic
67	C₈×C₁₉	#121	1	1	yes	characteristic
68	C₈×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	#2263	C₂×C₁₉	1	2	yes	complemented
70	#2246	C₂×C₁₉	1	1	yes	characteristic, complemented
71	#2178	C₂×C₁₉	1	1	yes	characteristic, complemented
72	#1422	C₂×C₁₉	1	1	yes	characteristic, complemented
73	#1419	C₂×C₁₉	1	2	yes	complemented
74	C₂²×C₁₉	—	8	1	no	—
75	C₂²×C₁₉	—	16	4	no	—
76	C₂²×C₁₉	—	16	2	no	—
77	C₂²×C₁₉	#509	1	1	yes	characteristic
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	—	8	1	no	—
80	C₄×C₁₉	#459	1	1	yes	characteristic
81	C₄×C₁₉	C₂×D₁₆	1	1	yes	characteristic
82	#508	C₂²×C₁₉	1	1	yes	characteristic
83	C₂×D₁₆	—	2	1	no	—
84	C₂×D₁₆	C₂²×C₁₉	1	2	yes	—
85	#493	—	2	1	no	—
86	#443	—	2	1	no	—
87	SD₆₄	—	2	2	no	—
88	D₃₂	—	2	2	no	—
89	M₆₄	C₂²×C₁₉	1	2	yes	—
90	#368	C₂²×C₁₉	1	1	yes	characteristic
91	#359	—	2	1	no	—
92	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
93	C₂×C₁₉	—	2	1	no	—
94	C₂×C₁₉	—	16	1	no	—
95	C₂×C₁₉	—	32	2	no	—
96	C₂×C₁₉	#2206	1	1	yes	characteristic
97	#135	—	2	1	no	—
98	C₂×D₈	—	2	2	no	—
99	C₂×D₈	—	4	1	no	—
100	#131	—	4	1	no	—
101	#127	—	4	1	no	—
102	Q₃₂	D₄×C₁₉	1	1	yes	characteristic, complemented
103	SD₃₂	—	2	1	no	—
104	D₁₆	—	2	2	no	—
105	D₁₆	—	2	2	no	—
106	D₁₆	—	4	2	no	—
107	D₁₆	D₄×C₁₉	1	1	yes	characteristic, complemented
108	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
109	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
110	#108	—	2	1	no	—
111	#104	—	4	1	no	—
112	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
113	C₃₂	—	2	2	no	—
114	C₁₉	#13692	1	1	yes	characteristic, direct product factor, Sylow
115	#41	—	4	1	no	—
116	C₂×D₄	—	4	2	no	—
117	C₂×D₄	—	8	2	no	—
118	Q₁₆	—	2	1	no	—
119	SD₁₆	—	4	1	no	—
120	D₈	—	2	1	no	—
121	D₈	—	4	2	no	—
122	D₈	—	4	2	no	—
123	D₈	—	8	1	no	—
124	D₈	—	8	1	no	—
125	M₁₆	—	4	1	no	—
126	M₁₆	—	8	1	no	—
127	C₂×C₈	—	8	1	no	—
128	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
129	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
130	C₄²	D₈×C₁₉	1	1	yes	characteristic
131	C₁₆	—	2	1	no	—
132	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
133	C₁₆	#41×C₁₉	1	1	yes	characteristic
134	C₂³	—	8	2	no	—
135	Q₈	—	4	1	no	—
136	D₄	—	4	1	no	—
137	D₄	—	8	1	no	—
138	D₄	—	8	2	no	—
139	D₄	—	8	2	no	—
140	D₄	—	16	4	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	8	1	no	—
143	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
144	C₈	—	8	1	no	—
145	C₈	C₁₉×D₁₆	1	1	yes	characteristic
146	C₈	C₁₉×D₁₆	1	1	yes	characteristic
147	C₈	C₁₉×#121	1	1	yes	characteristic
148	C₈	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂²	—	8	1	no	—
150	C₂²	—	16	4	no	—
151	C₂²	—	16	2	no	—
152	C₂²	C₁₉×#509	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	8	1	no	—
155	C₄	C₁₉×#459	1	1	yes	characteristic
156	C₄	C₂×C₁₉×D₁₆	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	16	1	no	—
159	C₂	—	32	2	no	—
160	C₂	C₁₉×#2206	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2263

C₂

yes

maximal, complemented

C₁₉×#2246

C₂

yes

maximal, characteristic, complemented

C₁₉×#2178

C₂

yes

maximal, characteristic, complemented

C₁₉×#1422

C₂

yes

maximal, characteristic, complemented

C₁₉×#1419

C₂

yes

maximal, complemented

C₁₉×#508

C₂²

yes

characteristic

C₂×C₁₉×D₁₆

—

C₂×C₁₉×D₁₆

C₂²

yes

—

C₁₉×#493

—

C₁₉×#443

—

C₁₉×SD₆₄

—

C₁₉×D₃₂

—

C₁₉×M₆₄

C₂²

yes

—

C₁₉×#368

C₂²

yes

characteristic

C₁₉×#359

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#135

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×#131

—

C₁₉×#127

—

C₁₉×Q₃₂

D₄

yes

characteristic, complemented

C₁₉×SD₃₂

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₁₉×D₁₆

D₄

yes

characteristic, complemented

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#108

—

C₁₉×#104

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

#41×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×D₄

yes

C₁₆×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

D₁₆

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

complemented

#2246

C₂×C₁₉

yes

characteristic, complemented

#2178

C₂×C₁₉

yes

characteristic, complemented

#1422

C₂×C₁₉

yes

characteristic, complemented

#1419

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#509

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#459

yes

characteristic

C₄×C₁₉

C₂×D₁₆

yes

characteristic

#508

C₂²×C₁₉

yes

characteristic

C₂×D₁₆

—

C₂×D₁₆

C₂²×C₁₉

yes

—

#493

—

#443

—

SD₆₄

—

D₃₂

—

M₆₄

C₂²×C₁₉

yes

—

#368

C₂²×C₁₉

yes

characteristic

#359

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2206

yes

characteristic

#135

—

C₂×D₈

—

C₂×D₈

—

100

#131

—

101

#127

—

102

Q₃₂

D₄×C₁₉

yes

characteristic, complemented

103

SD₃₂

—

104

D₁₆

—

105

D₁₆

—

106

D₁₆

—

107

D₁₆

D₄×C₁₉

yes

characteristic, complemented

108

C₂×C₁₆

D₄×C₁₉

yes

characteristic

109

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

110

#108

—

111

#104

—

112

C₄×C₈

D₄×C₁₉

yes

characteristic

113

C₃₂

—

114

C₁₉

#13692

yes

characteristic, direct product factor, Sylow

115

#41

—

116

C₂×D₄

—

117

C₂×D₄

—

118

Q₁₆

—

119

SD₁₆

—

120

D₈

—

121

D₈

—

122

D₈

—

123

D₈

—

124

D₈

—

125

M₁₆

—

126

M₁₆

—

127

C₂×C₈

—

128

C₂×C₈

D₈×C₁₉

yes

characteristic

129

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

130

C₄²

D₈×C₁₉

yes

characteristic

131

C₁₆

—

132

C₁₆

C₂×D₄×C₁₉

yes

characteristic

133

C₁₆

#41×C₁₉

yes

characteristic

134

C₂³

—

135

Q₈

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

144

C₈

—

145

C₈

C₁₉×D₁₆

yes

characteristic

146

C₈

C₁₉×D₁₆

yes

characteristic

147

C₈

C₁₉×#121

yes

characteristic

148

C₈

C₁₉×AGL(1,ℤ/8)

yes

characteristic

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

C₁₉×#509

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

C₁₉×#459

yes

characteristic

156

C₄

C₂×C₁₉×D₁₆

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

C₁₉×#2206

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#2206

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2263	C₂	semidirect
2. C₁₉×#2246	C₂	semidirect
3. C₁₉×#2178	C₂	semidirect
4. C₁₉×#1422	C₂	semidirect
5. C₁₉×#1419	C₂	semidirect
22. C₁₉×Q₃₂	D₄	semidirect
27. C₁₉×D₁₆	D₄	semidirect
53. #13692	C₁₉	direct (N × H)
69. #2263	C₂×C₁₉	semidirect
70. #2246	C₂×C₁₉	semidirect
71. #2178	C₂×C₁₉	semidirect
72. #1422	C₂×C₁₉	semidirect
73. #1419	C₂×C₁₉	semidirect
102. Q₃₂	D₄×C₁₉	semidirect
107. D₁₆	D₄×C₁₉	semidirect
114. C₁₉	#13692	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2263

C₂

semidirect

2. C₁₉×#2246

C₂

semidirect

3. C₁₉×#2178

C₂

semidirect

4. C₁₉×#1422

C₂

semidirect

5. C₁₉×#1419

C₂

semidirect

22. C₁₉×Q₃₂

D₄

semidirect

27. C₁₉×D₁₆

D₄

semidirect

53. #13692

C₁₉

direct (N × H)

69. #2263

C₂×C₁₉

semidirect

70. #2246

C₂×C₁₉

semidirect

71. #2178

C₂×C₁₉

semidirect

72. #1422

C₂×C₁₉

semidirect

73. #1419

C₂×C₁₉

semidirect

102. Q₃₂

D₄×C₁₉

semidirect

107. D₁₆

D₄×C₁₉

semidirect

114. C₁₉

#13692

direct (N × H)

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

subgroup	index
C₁₉×#2263	2
C₁₉×#2246	2
C₁₉×#2178	2
C₁₉×#1422	2
C₁₉×#1419	2
#13692	19

subgroup

index

C₁₉×#2263

C₁₉×#2246

C₁₉×#2178

C₁₉×#1422

C₁₉×#1419

#13692

Subgroups — C₁₉×#13692 #18019651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13692 #18019651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13692 #18019651