Group #18017498 — subgroups

Subgroups — C₁₉×#11539 #18017498

Order 4864.

270 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2960	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2166	C₂	1	2	yes	maximal
3	C₁₉×#1328	C₂	1	2	yes	maximal
4	C₁₉×#1327	C₂	1	2	yes	maximal
5	C₁₉×#533	C₄	1	1	yes	characteristic
6	C₁₉×#446	—	2	2	no	—
7	C₈×Q₈×C₁₉	—	2	2	no	—
8	C₁₉×#424	C₄	1	1	yes	characteristic
9	C₁₉×#424	C₂²	1	1	yes	characteristic
10	C₁₉×#423	C₂²	1	1	yes	characteristic
11	C₁₉×#405	C₄	1	1	yes	characteristic
12	C₁₉×#405	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
14	C₁₉×#364	—	2	2	no	—
15	C₁₉×#349	C₂²	1	4	yes	—
16	C₁₉×#347	—	2	2	no	—
17	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₁₉×C₄⋊Q₈	—	2	1	no	—
22	C₁₉×#125	—	2	1	no	—
23	C₁₉×C₂²⋊Q₈	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
26	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₉×M₃₂	—	2	4	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×#97	—	2	1	no	—
33	C₁₉×#97	D₄	1	2	yes	—
34	C₄×C₈×C₁₉	—	2	1	no	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₄×C₈×C₁₉	—	2	1	no	—
37	C₄×C₈×C₁₉	D₄	1	2	yes	—
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	1	no	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	M₁₆×C₁₉	—	4	1	no	—
42	M₁₆×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	4	1	no	—
47	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
50	C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂²⋊C₄×C₁₉	M₁₆	1	2	yes	—
56	C₄²×C₁₉	—	2	1	no	—
57	C₄²×C₁₉	—	2	1	no	—
58	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
60	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
61	C₁₆×C₁₉	—	4	4	no	—
62	#11539	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
64	Q₈×C₁₉	—	4	4	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
74	C₈×C₁₉	—	2	2	no	—
75	C₈×C₁₉	—	2	1	no	—
76	C₈×C₁₉	—	4	1	no	—
77	C₈×C₁₉	—	4	1	no	—
78	C₈×C₁₉	#101	1	2	yes	—
79	#2960	C₂×C₁₉	1	1	yes	characteristic
80	#2166	C₂×C₁₉	1	2	yes	—
81	#1328	C₂×C₁₉	1	2	yes	—
82	#1327	C₂×C₁₉	1	2	yes	—
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	—	4	1	no	—
85	C₂²×C₁₉	#407	1	1	yes	characteristic
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	1	no	—
88	C₄×C₁₉	—	4	1	no	—
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	#410	1	1	yes	characteristic
92	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
93	#533	C₄×C₁₉	1	1	yes	characteristic
94	#446	—	2	2	no	—
95	C₈×Q₈	—	2	2	no	—
96	#424	C₄×C₁₉	1	1	yes	characteristic
97	#424	C₂²×C₁₉	1	1	yes	characteristic
98	#423	C₂²×C₁₉	1	1	yes	characteristic
99	#405	C₄×C₁₉	1	1	yes	characteristic
100	#405	C₂²×C₁₉	1	1	yes	characteristic
101	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
102	#364	—	2	2	no	—
103	#349	C₂²×C₁₉	1	4	yes	—
104	#347	—	2	2	no	—
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	—	4	1	no	—
107	C₂×C₁₉	#1467	1	1	yes	characteristic
108	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
109	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
110	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
111	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
112	C₄⋊Q₈	—	2	1	no	—
113	#125	—	2	1	no	—
114	C₂²⋊Q₈	—	2	2	no	—
115	C₄×Q₈	—	2	2	no	—
116	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
117	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
118	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
119	M₃₂	—	2	4	no	—
120	C₄⋊C₈	—	2	2	no	—
121	C₄⋊C₈	—	2	2	no	—
122	C₄⋊C₈	—	2	2	no	—
123	#97	—	2	1	no	—
124	#97	D₄×C₁₉	1	2	yes	—
125	C₄×C₈	—	2	1	no	—
126	C₄×C₈	—	2	1	no	—
127	C₄×C₈	—	2	1	no	—
128	C₄×C₈	D₄×C₁₉	1	2	yes	—
129	C₁₉	#11539	1	1	yes	characteristic, direct product factor, Sylow
130	C₂×Q₈	—	2	2	no	—
131	C₂²×C₄	—	2	1	no	—
132	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
133	M₁₆	—	4	1	no	—
134	M₁₆	—	4	1	no	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	4	1	no	—
139	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
141	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	2	1	no	—
145	C₄⋊C₄	—	2	1	no	—
146	C₂²⋊C₄	—	2	1	no	—
147	C₂²⋊C₄	M₁₆×C₁₉	1	2	yes	—
148	C₄²	—	2	1	no	—
149	C₄²	—	2	1	no	—
150	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
151	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
152	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
153	C₁₆	—	4	4	no	—
154	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
155	Q₈	—	4	4	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
164	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
165	C₈	—	2	2	no	—
166	C₈	—	2	1	no	—
167	C₈	—	4	1	no	—
168	C₈	—	4	1	no	—
169	C₈	C₁₉×#101	1	2	yes	—
170	C₂²	—	2	1	no	—
171	C₂²	—	4	1	no	—
172	C₂²	C₁₉×#407	1	1	yes	characteristic
173	C₄	—	2	2	no	—
174	C₄	—	2	1	no	—
175	C₄	—	4	1	no	—
176	C₄	—	4	2	no	—
177	C₄	—	4	2	no	—
178	C₄	C₁₉×#410	1	1	yes	characteristic
179	C₄	C₂×C₁₉×#101	1	1	yes	characteristic
180	C₂	—	2	1	no	—
181	C₂	—	4	1	no	—
182	C₂	C₁₉×#1467	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2960

C₂

yes

maximal, characteristic

C₁₉×#2166

C₂

yes

maximal

C₁₉×#1328

C₂

yes

maximal

C₁₉×#1327

C₂

yes

maximal

C₁₉×#533

C₄

yes

characteristic

C₁₉×#446

—

C₈×Q₈×C₁₉

—

C₁₉×#424

C₄

yes

characteristic

C₁₉×#424

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#405

C₄

yes

characteristic

C₁₉×#405

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#364

—

C₁₉×#349

C₂²

yes

—

C₁₉×#347

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂³

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂×C₄

yes

characteristic

C₁₉×#117

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×M₃₂

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₆×C₁₉

—

#11539

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×M₁₆

yes

characteristic

Q₈×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

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#101

yes

—

#2960

C₂×C₁₉

yes

characteristic

#2166

C₂×C₁₉

yes

—

#1328

C₂×C₁₉

yes

—

#1327

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#407

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

characteristic

#446

—

C₈×Q₈

—

#424

C₄×C₁₉

yes

characteristic

#424

C₂²×C₁₉

yes

characteristic

#423

C₂²×C₁₉

yes

characteristic

#405

C₄×C₁₉

yes

characteristic

100

#405

C₂²×C₁₉

yes

characteristic

101

C₂×C₄×C₈

C₄×C₁₉

yes

characteristic

102

#364

—

103

#349

C₂²×C₁₉

yes

—

104

#347

—

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#1467

yes

characteristic

108

C₂×M₁₆

C₂×C₄×C₁₉

yes

characteristic

109

C₂×M₁₆

C₂³×C₁₉

yes

characteristic

110

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

111

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

112

C₄⋊Q₈

—

113

#125

—

114

C₂²⋊Q₈

—

115

C₄×Q₈

—

116

#117

C₂×C₄×C₁₉

yes

characteristic

117

#117

C₂×C₄×C₁₉

yes

characteristic

118

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

119

M₃₂

—

120

C₄⋊C₈

—

121

C₄⋊C₈

—

122

C₄⋊C₈

—

123

#97

—

124

#97

D₄×C₁₉

yes

—

125

C₄×C₈

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₄×C₈

D₄×C₁₉

yes

—

129

C₁₉

#11539

yes

characteristic, direct product factor, Sylow

130

C₂×Q₈

—

131

C₂²×C₄

—

132

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

133

M₁₆

—

134

M₁₆

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

140

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

141

C₂×C₈

C₂×D₄×C₁₉

yes

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₂²⋊C₄

—

147

C₂²⋊C₄

M₁₆×C₁₉

yes

—

148

C₄²

—

149

C₄²

—

150

C₄²

C₂²⋊C₄×C₁₉

yes

—

151

C₄²

M₁₆×C₁₉

yes

characteristic

152

C₄²

M₁₆×C₁₉

yes

characteristic

153

C₁₆

—

154

C₂³

C₂×M₁₆×C₁₉

yes

characteristic

155

Q₈

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

164

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

165

C₈

—

166

C₈

—

167

C₈

—

168

C₈

—

169

C₈

C₁₉×#101

yes

—

170

C₂²

—

171

C₂²

—

172

C₂²

C₁₉×#407

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

C₁₉×#410

yes

characteristic

179

C₄

C₂×C₁₉×#101

yes

characteristic

180

C₂

—

181

C₂

—

182

C₂

C₁₉×#1467

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#1467
prime radical	C₂³×C₁₉	C₂×M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₁₉×#405 ◁ G

subgroup

G/H

center

C₄×C₁₉

#410

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×M₁₆

C₂³×C₁₉

socle

C₂×C₁₉

#1467

prime radical

C₂³×C₁₉

C₂×M₁₆

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₁₉×#405 ◁ G

N	H ≅ G/N	type
62. #11539	C₁₉	direct (N × H)
129. C₁₉	#11539	direct (N × H)

H ≅ G/N

type

62. #11539

C₁₉

direct (N × H)

129. C₁₉

#11539

direct (N × H)

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

subgroup	index
C₁₉×#2960	2
C₁₉×#2166	2
C₁₉×#1328	2
C₁₉×#1327	2
#11539	19

subgroup

index

C₁₉×#2960

C₁₉×#2166

C₁₉×#1328

C₁₉×#1327

#11539

Subgroups — C₁₉×#11539 #18017498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11539 #18017498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11539 #18017498