Group #18072970 — subgroups

Subgroups — #18072970

Order 4864.

414 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 179 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	#14563380	C₂	1	2	yes	maximal
2	C₄×#10597272	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊#1273	C₂	1	2	yes	maximal
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597272	C₄	1	2	yes	—
7	C₂×#10597272	C₄	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
11	#11926298	C₄	1	4	yes	—
12	#11926298	C₄	1	4	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₉	—	2	2	no	—
25	C₄×C₈×C₁₉	—	2	2	no	—
26	C₄×C₈×C₁₉	—	2	2	no	—
27	#10597272	—	2	4	no	—
28	#10597272	—	2	4	no	—
29	C₄×C₁₉⋊C₈	—	2	1	no	—
30	C₄×C₁₉⋊C₈	—	2	1	no	—
31	C₄×C₁₉⋊C₈	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
35	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
36	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
37	C₂²×Dic₁₉	C₄²	1	2	yes	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	2	4	no	—
41	C₂×C₈×C₁₉	—	2	4	no	—
42	C₂×C₈×C₁₉	—	2	4	no	—
43	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
44	C₄²×C₁₉	#41	1	2	yes	—
45	C₄²×C₁₉	#41	1	1	yes	characteristic
46	C₄²×C₁₉	#41	1	1	yes	characteristic
47	C₄×Dic₁₉	—	2	2	no	—
48	C₄×Dic₁₉	—	2	2	no	—
49	C₄×Dic₁₉	—	2	4	no	—
50	C₄×Dic₁₉	—	2	4	no	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	4	no	—
54	C₂×C₁₉⋊C₈	—	2	4	no	—
55	C₂×C₁₉⋊C₈	—	2	4	no	—
56	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
57	#8134	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#117	1	2	yes	—
61	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#117	1	2	yes	—
63	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
64	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
65	C₂×C₄×C₁₉	#131	1	4	yes	—
66	C₂×C₄×C₁₉	#131	1	4	yes	—
67	C₂×Dic₁₉	—	2	1	no	—
68	C₂×Dic₁₉	—	2	1	no	—
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	2	2	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₈×C₁₉	—	2	4	no	—
75	C₈×C₁₉	—	4	4	no	—
76	C₁₉⋊C₈	—	2	4	no	—
77	C₁₉⋊C₈	—	4	4	no	—
78	#1744	—	19	2	no	—
79	C₄×#97	—	19	1	no	—
80	#1273	—	19	2	no	—
81	#1273	—	19	1	no	—
82	#1273	D₁₉	1	1	yes	characteristic
83	C₂²×C₁₉	#376	1	1	yes	characteristic
84	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
85	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
86	C₂²×C₁₉	#405	1	2	yes	—
87	C₂²×C₁₉	#405	1	2	yes	—
88	C₄×C₁₉	#432	1	2	yes	—
89	C₄×C₁₉	#432	1	2	yes	—
90	C₄×C₁₉	#433	1	4	yes	—
91	C₄×C₁₉	#433	1	4	yes	—
92	Dic₁₉	—	4	1	no	—
93	Dic₁₉	—	4	2	no	—
94	Dic₁₉	—	4	1	no	—
95	C₂×#97	—	19	2	no	—
96	C₂×#97	—	19	2	no	—
97	C₂×C₄×C₈	—	19	1	no	—
98	C₂×C₄×C₈	—	19	2	no	—
99	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
100	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
101	C₄³	—	19	1	no	—
102	#336	—	19	4	no	—
103	#336	—	19	4	no	—
104	C₂×C₁₉	#1453	1	1	yes	characteristic
105	C₂×C₁₉	#1453	1	2	yes	—
106	C₂×C₁₉	#1453	1	1	yes	characteristic
107	C₂×C₁₉	#1745	1	1	yes	characteristic
108	C₂×C₁₉	#1746	1	2	yes	—
109	C₂²×C₈	—	19	2	no	—
110	C₂²×C₈	—	19	4	no	—
111	C₂²×C₈	C₄×D₁₉	1	4	yes	—
112	C₂²×C₈	C₄×D₁₉	1	2	yes	—
113	C₂×C₄²	—	19	2	no	—
114	C₂×C₄²	—	19	2	no	—
115	C₂×C₄²	—	19	1	no	—
116	C₂×C₄²	—	19	1	no	—
117	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
118	#97	—	38	4	no	—
119	#97	—	38	4	no	—
120	C₄×C₈	—	2	2	no	—
121	C₄×C₈	—	2	2	no	—
122	C₄×C₈	—	2	2	no	—
123	C₄×C₈	—	38	1	no	—
124	C₄×C₈	—	38	2	no	—
125	C₄×C₈	—	38	1	no	—
126	C₄×C₈	—	38	2	no	—
127	C₁₉	#8134	1	1	yes	characteristic, complemented, Sylow
128	C₂²×C₄	—	19	1	no	—
129	C₂²×C₄	—	19	1	no	—
130	C₂²×C₄	—	19	2	no	—
131	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
132	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	—	19	4	no	—
139	C₂×C₈	—	38	2	no	—
140	C₂×C₈	—	38	2	no	—
141	C₂×C₈	—	38	4	no	—
142	C₂×C₈	—	38	4	no	—
143	C₂×C₈	—	38	4	no	—
144	C₂×C₈	#64515	1	4	yes	—
145	C₄²	—	38	2	no	—
146	C₄²	—	38	4	no	—
147	C₄²	—	38	2	no	—
148	C₄²	—	38	4	no	—
149	C₄²	#64543	1	2	yes	—
150	C₄²	#64543	1	1	yes	characteristic
151	C₄²	#64545	1	1	yes	characteristic
152	C₂³	C₄²×D₁₉	1	1	yes	characteristic
153	C₂×C₄	—	38	1	no	—
154	C₂×C₄	—	38	1	no	—
155	C₂×C₄	—	38	2	no	—
156	C₂×C₄	—	38	2	no	—
157	C₂×C₄	—	38	2	no	—
158	C₂×C₄	—	38	2	no	—
159	C₂×C₄	—	38	2	no	—
160	C₂×C₄	#10597323	1	1	yes	characteristic
161	C₂×C₄	#10597323	1	2	yes	—
162	C₂×C₄	#10597338	1	1	yes	characteristic
163	C₂×C₄	#10597338	1	2	yes	—
164	C₂×C₄	C₂×#64515	1	2	yes	—
165	C₂×C₄	#10597347	1	4	yes	—
166	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
167	C₂×C₄	#10597353	1	4	yes	—
168	C₈	—	2	4	no	—
169	C₈	—	4	4	no	—
170	C₈	—	38	4	no	—
171	C₈	—	76	4	no	—
172	C₂²	#11926389	1	1	yes	characteristic
173	C₂²	C₄×#64515	1	1	yes	characteristic
174	C₂²	#11926496	1	1	yes	characteristic
175	C₂²	#11926498	1	2	yes	—
176	C₂²	#11926501	1	2	yes	—
177	C₄	—	76	1	no	—
178	C₄	—	76	2	no	—
179	C₄	—	76	1	no	—
180	C₄	#11926598	1	2	yes	—
181	C₄	#11926600	1	2	yes	—
182	C₄	#11926602	1	4	yes	—
183	C₄	#11926604	1	4	yes	—
184	C₂	#14561929	1	1	yes	characteristic
185	C₂	#14561931	1	2	yes	—
186	C₂	#14561933	1	1	yes	characteristic
187	C₂	#14563382	1	1	yes	characteristic
188	C₂	#14563385	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563380

C₂

yes

maximal

C₄×#10597272

C₂

yes

maximal, characteristic

C₁₉⋊#1273

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal, characteristic

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×#10597272

C₄

yes

—

C₂×#10597272

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926298

C₄

yes

—

#11926298

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#10597272

—

#10597272

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×Dic₁₉

C₄²

yes

characteristic

C₂²×Dic₁₉

C₄²

yes

characteristic

C₂²×Dic₁₉

C₄²

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

M₁₆

yes

—

#8134

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1744

—

C₄×#97

—

#1273

—

#1273

—

#1273

D₁₉

yes

characteristic

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

C₄×M₁₆

yes

characteristic

C₂²×C₁₉

C₄×M₁₆

yes

characteristic

C₂²×C₁₉

#405

yes

—

C₂²×C₁₉

#405

yes

—

C₄×C₁₉

#432

yes

—

C₄×C₁₉

#432

yes

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#433

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

100

C₂×C₄×C₈

C₂×D₁₉

yes

—

101

C₄³

—

102

#336

—

103

#336

—

104

C₂×C₁₉

#1453

yes

characteristic

105

C₂×C₁₉

#1453

yes

—

106

C₂×C₁₉

#1453

yes

characteristic

107

C₂×C₁₉

#1745

yes

characteristic

108

C₂×C₁₉

#1746

yes

—

109

C₂²×C₈

—

110

C₂²×C₈

—

111

C₂²×C₈

C₄×D₁₉

yes

—

112

C₂²×C₈

C₄×D₁₉

yes

—

113

C₂×C₄²

—

114

C₂×C₄²

—

115

C₂×C₄²

—

116

C₂×C₄²

—

117

C₂×C₄²

C₂²×D₁₉

yes

characteristic

118

#97

—

119

#97

—

120

C₄×C₈

—

121

C₄×C₈

—

122

C₄×C₈

—

123

C₄×C₈

—

124

C₄×C₈

—

125

C₄×C₈

—

126

C₄×C₈

—

127

C₁₉

#8134

yes

characteristic, complemented, Sylow

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

132

C₂²×C₄

C₂×C₄×D₁₉

yes

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

#64515

yes

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₄²

—

149

C₄²

#64543

yes

—

150

C₄²

#64543

yes

characteristic

151

C₄²

#64545

yes

characteristic

152

C₂³

C₄²×D₁₉

yes

characteristic

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

#10597323

yes

characteristic

161

C₂×C₄

#10597323

yes

—

162

C₂×C₄

#10597338

yes

characteristic

163

C₂×C₄

#10597338

yes

—

164

C₂×C₄

C₂×#64515

yes

—

165

C₂×C₄

#10597347

yes

—

166

C₂×C₄

M₁₆×D₁₉

yes

—

167

C₂×C₄

#10597353

yes

—

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

#11926389

yes

characteristic

173

C₂²

C₄×#64515

yes

characteristic

174

C₂²

#11926496

yes

characteristic

175

C₂²

#11926498

yes

—

176

C₂²

#11926501

yes

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

#11926598

yes

—

181

C₄

#11926600

yes

—

182

C₄

#11926602

yes

—

183

C₄

#11926604

yes

—

184

C₂

#14561929

yes

characteristic

185

C₂

#14561931

yes

—

186

C₂

#14561933

yes

characteristic

187

C₂

#14563382

yes

characteristic

188

C₂

#14563385

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂×C₄²
Fitting	C₁₉×#1273	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#8134
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator, socle, prime radical

C₂³×C₁₉

C₂×C₄²

Fitting

C₁₉×#1273

C₂

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
127. C₁₉	#8134	semidirect

H ≅ G/N

type

127. C₁₉

#8134

semidirect

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

subgroup	index
#14563380	2
C₄×#10597272	2
C₁₉⋊#1273	2
C₁₉×#1273	2
#8134	19

subgroup

index

#14563380

C₄×#10597272

C₁₉⋊#1273

C₁₉×#1273

#8134

Subgroups — #18072970

Conjugacy classes of subgroups

Complements

Maximal subgroups