Group #18014718 — subgroups

Subgroups — C₁₉×#8759 #18014718

Order 4864.

474 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2312	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1462	C₂	1	2	yes	maximal
3	C₁₉×#1305	C₂	1	4	yes	maximal, complemented
4	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×#407	C₂²	1	4	yes	—
6	C₁₉×#388	—	2	4	no	—
7	C₁₉×#380	C₂²	1	2	yes	—
8	C₁₉×#379	C₄	1	2	yes	—
9	C₄×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
10	C₁₉×#323	—	2	4	no	—
11	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×M₁₆×C₁₉	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
17	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
21	C₂×C₄²×C₁₉	—	2	2	no	—
22	C₁₉×C₂²⋊C₈	—	2	4	no	—
23	C₁₉×C₂²⋊C₈	—	2	4	no	—
24	C₁₉×#95	—	2	2	no	—
25	C₁₉×#95	—	2	2	no	—
26	C₂⁴×C₁₉	—	2	2	no	—
27	C₂⁴×C₁₉	—	4	2	no	—
28	C₂⁴×C₁₉	—	8	1	no	—
29	C₂⁴×C₁₉	—	8	1	no	—
30	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
31	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	—	2	4	no	—
34	C₂²×C₄×C₁₉	—	8	1	no	—
35	C₂²×C₄×C₁₉	—	8	1	no	—
36	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
38	C₂²×C₄×C₁₉	#41	1	4	yes	—
39	M₁₆×C₁₉	—	8	4	no	—
40	C₂×C₈×C₁₉	—	4	4	no	—
41	C₄⋊C₄×C₁₉	—	8	2	no	—
42	C₂²⋊C₄×C₁₉	—	2	8	no	—
43	C₂²⋊C₄×C₁₉	—	4	4	no	—
44	C₂²⋊C₄×C₁₉	—	8	2	no	—
45	C₂²⋊C₄×C₁₉	—	8	2	no	—
46	C₄²×C₁₉	—	8	2	no	—
47	#8759	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	—	2	2	no	—
50	C₂³×C₁₉	—	2	4	no	—
51	C₂³×C₁₉	—	4	1	no	—
52	C₂³×C₁₉	—	4	1	no	—
53	C₂³×C₁₉	—	4	4	no	—
54	C₂³×C₁₉	—	4	2	no	—
55	C₂³×C₁₉	—	4	2	no	—
56	C₂³×C₁₉	—	8	2	no	—
57	C₂³×C₁₉	—	8	2	no	—
58	C₂³×C₁₉	—	8	8	no	—
59	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂³×C₁₉	#117	1	2	yes	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	4	4	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	—	4	4	no	—
66	C₂×C₄×C₁₉	—	4	4	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	—	8	2	no	—
69	C₂×C₄×C₁₉	#123	1	4	yes	—
70	C₈×C₁₉	—	8	4	no	—
71	#2312	C₂×C₁₉	1	1	yes	characteristic
72	#1462	C₂×C₁₉	1	2	yes	—
73	#1305	C₂×C₁₉	1	4	yes	complemented
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	2	no	—
77	C₂²×C₁₉	—	2	2	no	—
78	C₂²×C₁₉	—	2	2	no	—
79	C₂²×C₁₉	—	4	4	no	—
80	C₂²×C₁₉	—	4	2	no	—
81	C₂²×C₁₉	—	4	2	no	—
82	C₂²×C₁₉	—	4	2	no	—
83	C₂²×C₁₉	—	8	4	no	—
84	C₂²×C₁₉	—	8	8	no	—
85	C₂²×C₁₉	#381	1	1	yes	characteristic
86	C₂²×C₁₉	#413	1	2	yes	—
87	C₄×C₁₉	—	2	4	no	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	—	8	4	no	—
90	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
91	#407	C₂²×C₁₉	1	4	yes	—
92	#388	—	2	4	no	—
93	#380	C₂²×C₁₉	1	2	yes	—
94	#379	C₄×C₁₉	1	2	yes	—
95	C₄×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
96	#323	—	2	4	no	—
97	C₂×C₁₉	—	2	2	no	—
98	C₂×C₁₉	—	4	2	no	—
99	C₂×C₁₉	—	8	2	no	—
100	C₂×C₁₉	#1822	1	1	yes	characteristic
101	C₂×C₁₉	#1828	1	1	yes	characteristic
102	C₂×C₁₉	#1829	1	1	yes	characteristic
103	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
104	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
105	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
106	C₂×M₁₆	—	2	4	no	—
107	C₂×C₄⋊C₄	—	2	2	no	—
108	C₂×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
112	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
113	C₂×C₄²	—	2	2	no	—
114	C₂²⋊C₈	—	2	4	no	—
115	C₂²⋊C₈	—	2	4	no	—
116	#95	—	2	2	no	—
117	#95	—	2	2	no	—
118	C₁₉	#8759	1	1	yes	characteristic, direct product factor, Sylow
119	C₂⁴	—	2	2	no	—
120	C₂⁴	—	4	2	no	—
121	C₂⁴	—	8	1	no	—
122	C₂⁴	—	8	1	no	—
123	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
124	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	—	2	4	no	—
127	C₂²×C₄	—	8	1	no	—
128	C₂²×C₄	—	8	1	no	—
129	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
130	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
131	C₂²×C₄	#41×C₁₉	1	4	yes	—
132	M₁₆	—	8	4	no	—
133	C₂×C₈	—	4	4	no	—
134	C₄⋊C₄	—	8	2	no	—
135	C₂²⋊C₄	—	2	8	no	—
136	C₂²⋊C₄	—	4	4	no	—
137	C₂²⋊C₄	—	8	2	no	—
138	C₂²⋊C₄	—	8	2	no	—
139	C₄²	—	8	2	no	—
140	C₂³	—	2	2	no	—
141	C₂³	—	2	2	no	—
142	C₂³	—	2	4	no	—
143	C₂³	—	4	1	no	—
144	C₂³	—	4	1	no	—
145	C₂³	—	4	4	no	—
146	C₂³	—	4	2	no	—
147	C₂³	—	4	2	no	—
148	C₂³	—	8	2	no	—
149	C₂³	—	8	2	no	—
150	C₂³	—	8	8	no	—
151	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
152	C₂³	C₁₉×#117	1	2	yes	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	4	no	—
156	C₂×C₄	—	4	2	no	—
157	C₂×C₄	—	4	4	no	—
158	C₂×C₄	—	4	4	no	—
159	C₂×C₄	—	4	4	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	C₁₉×#123	1	4	yes	—
162	C₈	—	8	4	no	—
163	C₂²	—	2	1	no	—
164	C₂²	—	2	1	no	—
165	C₂²	—	2	2	no	—
166	C₂²	—	2	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	4	4	no	—
169	C₂²	—	4	2	no	—
170	C₂²	—	4	2	no	—
171	C₂²	—	4	2	no	—
172	C₂²	—	8	4	no	—
173	C₂²	—	8	8	no	—
174	C₂²	C₁₉×#381	1	1	yes	characteristic
175	C₂²	C₁₉×#413	1	2	yes	—
176	C₄	—	2	4	no	—
177	C₄	—	4	2	no	—
178	C₄	—	8	4	no	—
179	C₂	—	2	2	no	—
180	C₂	—	4	2	no	—
181	C₂	—	8	2	no	—
182	C₂	C₁₉×#1822	1	1	yes	characteristic
183	C₂	C₁₉×#1828	1	1	yes	characteristic
184	C₂	C₁₉×#1829	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2312

C₂

yes

maximal, characteristic

C₁₉×#1462

C₂

yes

maximal

C₁₉×#1305

C₂

yes

maximal, complemented

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#407

C₂²

yes

—

C₁₉×#388

—

C₁₉×#380

C₂²

yes

—

C₁₉×#379

C₄

yes

—

C₄×C₂²⋊C₄×C₁₉

C₄

yes

—

C₁₉×#323

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#8759

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#123

yes

—

C₈×C₁₉

—

#2312

C₂×C₁₉

yes

characteristic

#1462

C₂×C₁₉

yes

—

#1305

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

#413

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

characteristic

#407

C₂²×C₁₉

yes

—

#388

—

#380

C₂²×C₁₉

yes

—

#379

C₄×C₁₉

yes

—

C₄×C₂²⋊C₄

C₄×C₁₉

yes

—

#323

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

100

C₂×C₁₉

#1822

yes

characteristic

101

C₂×C₁₉

#1828

yes

characteristic

102

C₂×C₁₉

#1829

yes

characteristic

103

C₂⁵

C₂×C₄×C₁₉

yes

characteristic

104

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

105

C₂³×C₄

C₂³×C₁₉

yes

characteristic

106

C₂×M₁₆

—

107

C₂×C₄⋊C₄

—

108

C₂×C₂²⋊C₄

—

109

C₂×C₂²⋊C₄

—

110

C₂×C₂²⋊C₄

—

111

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

—

112

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

113

C₂×C₄²

—

114

C₂²⋊C₈

—

115

C₂²⋊C₈

—

116

#95

—

117

#95

—

118

C₁₉

#8759

yes

characteristic, direct product factor, Sylow

119

C₂⁴

—

120

C₂⁴

—

121

C₂⁴

—

122

C₂⁴

—

123

C₂⁴

C₂²⋊C₄×C₁₉

yes

—

124

C₂⁴

C₂²×C₄×C₁₉

yes

characteristic

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

130

C₂²×C₄

C₂×D₄×C₁₉

yes

—

131

C₂²×C₄

#41×C₁₉

yes

—

132

M₁₆

—

133

C₂×C₈

—

134

C₄⋊C₄

—

135

C₂²⋊C₄

—

136

C₂²⋊C₄

—

137

C₂²⋊C₄

—

138

C₂²⋊C₄

—

139

C₄²

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

152

C₂³

C₁₉×#117

yes

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

C₁₉×#123

yes

—

162

C₈

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

C₁₉×#381

yes

characteristic

175

C₂²

C₁₉×#413

yes

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₂

—

180

C₂

—

181

C₂

—

182

C₂

C₁₉×#1822

yes

characteristic

183

C₂

C₁₉×#1828

yes

characteristic

184

C₂

C₁₉×#1829

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#381

commutator

C₂⁴

C₂²×C₄×C₁₉

Frattini, cosocle

C₂³×C₄

C₂³×C₁₉

prime radical

C₂⁵×C₁₉

C₂×C₄

LCS

G ▷ C₂⁴ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1305	C₂	semidirect
47. #8759	C₁₉	direct (N × H)
73. #1305	C₂×C₁₉	semidirect
118. C₁₉	#8759	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1305

C₂

semidirect

47. #8759

C₁₉

direct (N × H)

73. #1305

C₂×C₁₉

semidirect

118. C₁₉

#8759

direct (N × H)

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

subgroup	index
C₁₉×#2312	2
C₁₉×#1462	2
C₁₉×#1305	2
#8759	19

subgroup

index

C₁₉×#2312

C₁₉×#1462

C₁₉×#1305

#8759

Subgroups — C₁₉×#8759 #18014718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8759 #18014718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8759 #18014718