Group #14571685 — subgroups

Subgroups — #14571685

Order 2432.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597321	C₂	1	1	yes	maximal, characteristic
2	#11926479	C₂	1	2	yes	maximal, complemented
3	#11926470	C₂	1	2	yes	maximal, complemented
4	#11926466	C₂	1	4	yes	maximal, complemented
5	#11926464	C₂	1	2	yes	maximal, complemented
6	#11926461	C₂	1	2	yes	maximal
7	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₁₉×#125	—	2	4	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
18	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
19	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
20	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
21	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
22	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
23	#10597321	—	2	4	no	—
24	C₁₉⋊#95	C₂²	1	2	yes	—
25	C₁₉⋊#95	C₂²	1	2	yes	—
26	C₁₉⋊#95	C₂²	1	4	yes	—
27	C₂³×D₁₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₁₉	C₂³	1	2	yes	—
34	C₂²×Dic₁₉	C₂³	1	4	yes	—
35	C₂×D₇₆	—	2	2	no	—
36	C₂×D₇₆	—	4	2	no	—
37	C₂×Dic₃₈	—	2	2	no	—
38	C₂×Dic₃₈	—	4	2	no	—
39	C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₄²×C₁₉	D₄	1	4	yes	—
44	(C₂×D₁₉)⋊C₄	—	2	4	no	—
45	(C₂×D₁₉)⋊C₄	—	2	4	no	—
46	(C₂×D₁₉)⋊C₄	—	4	4	no	—
47	(C₂×D₁₉)⋊C₄	—	4	4	no	—
48	C₄⋊Dic₁₉	—	4	2	no	—
49	Dic₁₉⋊C₄	—	4	4	no	—
50	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
51	C₂²×D₁₉	—	2	2	no	—
52	C₂²×D₁₉	—	2	2	no	—
53	C₂²×D₁₉	—	2	4	no	—
54	C₂²×D₁₉	—	2	4	no	—
55	C₂²×D₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	C₂×Dic₁₉	—	2	2	no	—
69	C₂×Dic₁₉	—	2	4	no	—
70	C₂×Dic₁₉	—	2	4	no	—
71	C₂×Dic₁₉	—	2	4	no	—
72	C₂×Dic₁₉	—	2	4	no	—
73	D₇₆	—	4	4	no	—
74	Dic₃₈	—	4	4	no	—
75	#2820	—	19	1	no	maximal, Sylow
76	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
77	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
78	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
79	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
80	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
81	C₂×D₁₉	—	4	2	no	—
82	C₂×D₁₉	—	4	2	no	—
83	C₂×D₁₉	—	4	2	no	—
84	C₂×D₁₉	—	4	4	no	—
85	C₂×D₁₉	—	4	4	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	Dic₁₉	—	4	2	no	—
92	Dic₁₉	—	4	4	no	—
93	C₂×#125	D₁₉	1	1	yes	characteristic, complemented
94	C₂×#124	—	19	1	no	—
95	#399	—	19	2	no	—
96	#397	—	19	2	no	—
97	#396	—	19	4	no	—
98	#395	—	19	2	no	—
99	#394	—	19	2	no	—
100	#382	—	19	1	no	—
101	C₂×C₁₉	#535	1	1	yes	characteristic
102	C₂×C₁₉	#536	1	1	yes	characteristic
103	C₂×C₁₉	#537	1	1	yes	characteristic
104	C₂×C₁₉	#562	1	2	yes	—
105	C₂×C₁₉	#563	1	2	yes	—
106	D₁₉	—	8	2	no	—
107	C₂²×Q₈	—	19	1	no	—
108	C₂²×D₄	—	19	1	no	—
109	#125	—	2	4	no	—
110	#124	—	38	4	no	—
111	C₂×C₄⋊C₄	—	19	2	no	—
112	C₂×C₄⋊C₄	—	19	4	no	—
113	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
114	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
115	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
116	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
117	C₂×C₂²⋊C₄	—	19	2	no	—
118	C₂×C₂²⋊C₄	—	19	2	no	—
119	C₂×C₂²⋊C₄	—	19	4	no	—
120	C₂×C₂²⋊C₄	—	19	4	no	—
121	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
122	#95	—	19	2	no	—
123	#95	—	19	2	no	—
124	#95	—	19	4	no	—
125	C₁₉	#2820	1	1	yes	characteristic, complemented, Sylow
126	C₂⁴	—	19	2	no	—
127	C₂×Q₈	—	38	2	no	—
128	C₂×Q₈	—	76	2	no	—
129	C₂×D₄	—	38	2	no	—
130	C₂×D₄	—	76	2	no	—
131	C₂²×C₄	—	19	4	no	—
132	C₂²×C₄	—	19	2	no	—
133	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
134	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
135	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
136	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
137	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	2	2	no	—
140	C₄⋊C₄	—	2	2	no	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	76	4	no	—
143	C₄⋊C₄	—	76	2	no	—
144	C₂²⋊C₄	—	38	4	no	—
145	C₂²⋊C₄	—	38	4	no	—
146	C₂²⋊C₄	—	76	4	no	—
147	C₂²⋊C₄	—	76	4	no	—
148	C₄²	C₂²⋊D₁₉	1	4	yes	—
149	C₂³	—	38	4	no	—
150	C₂³	—	38	2	no	—
151	C₂³	—	38	4	no	—
152	C₂³	—	38	2	no	—
153	C₂³	—	38	2	no	—
154	C₂³	C₂³×D₁₉	1	1	yes	characteristic
155	Q₈	—	76	4	no	—
156	D₄	—	76	4	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	38	4	no	—
167	C₂×C₄	—	38	4	no	—
168	C₂×C₄	—	38	4	no	—
169	C₂×C₄	—	38	4	no	—
170	C₂×C₄	—	38	2	no	—
171	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
172	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
173	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
174	C₂²	—	76	4	no	—
175	C₂²	—	76	2	no	—
176	C₂²	—	76	2	no	—
177	C₂²	—	76	2	no	—
178	C₂²	—	76	4	no	—
179	C₂²	#10597433	1	2	yes	—
180	C₂²	#10597435	1	2	yes	—
181	C₂²	#10597435	1	1	yes	characteristic
182	C₂²	#10597436	1	1	yes	characteristic
183	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
184	C₄	—	2	2	no	—
185	C₄	—	2	2	no	—
186	C₄	—	2	2	no	—
187	C₄	—	4	2	no	—
188	C₄	—	4	2	no	—
189	C₄	—	76	2	no	—
190	C₄	—	76	4	no	—
191	C₂	—	152	2	no	—
192	C₂	#11927108	1	1	yes	characteristic
193	C₂	#11927118	1	1	yes	characteristic
194	C₂	#11927122	1	1	yes	characteristic
195	C₂	#11927292	1	2	yes	—
196	C₂	#11927298	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597321

C₂

yes

maximal, characteristic

#11926479

C₂

yes

maximal, complemented

#11926470

C₂

yes

maximal, complemented

#11926466

C₂

yes

maximal, complemented

#11926464

C₂

yes

maximal, complemented

#11926461

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#125

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597321

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

Dic₃₈

—

#2820

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

D₁₉

yes

characteristic, complemented

—

—

—

—

—

—

100

#382

—

101

C₂×C₁₉

#535

yes

characteristic

102

C₂×C₁₉

#536

yes

characteristic

103

C₂×C₁₉

#537

yes

characteristic

104

C₂×C₁₉

#562

yes

—

105

C₂×C₁₉

#563

yes

—

106

D₁₉

—

107

C₂²×Q₈

—

108

C₂²×D₄

—

109

#125

—

110

#124

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

114

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

115

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

116

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

117

C₂×C₂²⋊C₄

—

118

C₂×C₂²⋊C₄

—

119

C₂×C₂²⋊C₄

—

120

C₂×C₂²⋊C₄

—

121

C₂×C₄²

C₂×D₁₉

yes

characteristic

122

#95

—

123

#95

—

124

#95

—

125

C₁₉

#2820

yes

characteristic, complemented, Sylow

126

C₂⁴

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×D₁₉

yes

—

134

C₂²×C₄

C₂²×D₁₉

yes

—

135

C₂²×C₄

C₂²×D₁₉

yes

characteristic

136

C₂²×C₄

C₂²×D₁₉

yes

characteristic

137

C₂²×C₄

C₂²×D₁₉

yes

characteristic

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₂²⋊C₄

—

145

C₂²⋊C₄

—

146

C₂²⋊C₄

—

147

C₂²⋊C₄

—

148

C₄²

C₂²⋊D₁₉

yes

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

C₂³×D₁₉

yes

characteristic

155

Q₈

—

156

D₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

172

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

173

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

#10597433

yes

—

180

C₂²

#10597435

yes

—

181

C₂²

#10597435

yes

characteristic

182

C₂²

#10597436

yes

characteristic

183

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₂

—

152

—

192

C₂

#11927108

yes

characteristic

193

C₂

#11927118

yes

characteristic

194

C₂

#11927122

yes

characteristic

195

C₂

#11927292

yes

—

196

C₂

#11927298

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#125	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#2820
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#125

C₂

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
2. #11926479	C₂	semidirect
3. #11926470	C₂	semidirect
4. #11926466	C₂	semidirect
5. #11926464	C₂	semidirect
7. #11926410	C₂	semidirect
8. C₂×C₁₉×#125	C₂	semidirect
93. C₂×#125	D₁₉	semidirect
125. C₁₉	#2820	semidirect

H ≅ G/N

type

2. #11926479

C₂

semidirect

3. #11926470

C₂

semidirect

4. #11926466

C₂

semidirect

5. #11926464

C₂

semidirect

7. #11926410

C₂

semidirect

8. C₂×C₁₉×#125

C₂

semidirect

93. C₂×#125

D₁₉

semidirect

125. C₁₉

#2820

semidirect

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

subgroup	index
C₂×#10597321	2
#11926479	2
#11926470	2
#11926466	2
#11926464	2
#11926461	2
#11926410	2
C₂×C₁₉×#125	2
#2820	19

subgroup

index

C₂×C₁₉×#125

Subgroups — #14571685

Conjugacy classes of subgroups

Complements

Maximal subgroups