Group #14571940 — subgroups

Subgroups — #14571940

Order 2432.

556 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 169 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×C₄²×D₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926440	C₂	1	2	yes	maximal, complemented
3	#11926425	C₂	1	4	yes	maximal, complemented
4	#11926415	C₂	1	4	yes	maximal
5	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926401	C₂	1	2	yes	maximal
7	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
9	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#125	—	2	4	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₄²×D₁₉	—	2	4	no	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₁₉⋊#95	C₂²	1	4	yes	—
22	C₁₉⋊#95	C₂²	1	4	yes	—
23	C₂³×D₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₉	C₂³	1	4	yes	—
28	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	C₂³	1	2	yes	—
30	C₂×C₄×D₁₉	—	2	4	no	—
31	C₂×C₄×D₁₉	—	2	4	no	—
32	C₂×C₄×D₁₉	—	2	2	no	—
33	C₂×C₄×D₁₉	—	2	2	no	—
34	C₂×C₄×D₁₉	—	2	4	no	—
35	C₂×C₄×D₁₉	Q₈	1	4	yes	—
36	C₄⋊C₄×C₁₉	—	2	8	no	—
37	C₄⋊C₄×C₁₉	—	2	4	no	—
38	C₄²×C₁₉	D₄	1	4	yes	—
39	(C₂×D₁₉)⋊C₄	—	2	8	no	—
40	C₄⋊Dic₁₉	—	2	4	no	—
41	Dic₁₉⋊C₄	—	2	8	no	—
42	C₄×Dic₁₉	—	2	4	no	—
43	C₄×Dic₁₉	—	2	2	no	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂²×D₁₉	—	2	1	no	—
46	C₂²×D₁₉	—	2	1	no	—
47	C₂²×D₁₉	—	2	2	no	—
48	C₂²×D₁₉	C₂×Q₈	1	2	yes	—
49	C₂²×D₁₉	#41	1	4	yes	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
58	C₂×C₄×C₁₉	#41	1	2	yes	—
59	C₂×Dic₁₉	—	2	1	no	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	2	1	no	—
62	C₂×Dic₁₉	—	2	2	no	—
63	C₂×Dic₁₉	—	2	4	no	—
64	C₂×Dic₁₉	—	2	4	no	—
65	C₂×Dic₁₉	—	2	4	no	—
66	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
67	C₂×Dic₁₉	#41	1	4	yes	—
68	C₄×D₁₉	—	2	16	no	—
69	C₄×D₁₉	—	2	8	no	—
70	#2851	—	19	1	no	maximal, Sylow
71	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
72	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
73	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
74	C₂²×C₁₉	C₂×#41	1	2	yes	—
75	C₂²×C₁₉	C₂×#41	1	2	yes	—
76	C₂×D₁₉	—	2	2	no	—
77	C₂×D₁₉	—	2	4	no	—
78	C₂×D₁₉	—	2	4	no	—
79	C₂×D₁₉	—	2	2	no	—
80	C₂×D₁₉	#125	1	4	yes	complemented
81	C₄×C₁₉	—	2	4	no	—
82	C₄×C₁₉	—	4	4	no	—
83	C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
84	Dic₁₉	—	2	2	no	—
85	Dic₁₉	—	2	4	no	—
86	Dic₁₉	—	4	4	no	—
87	C₂×#125	D₁₉	1	1	yes	characteristic, complemented
88	C₂²×C₄²	—	19	1	no	—
89	#389	—	19	2	no	—
90	#387	—	19	4	no	—
91	#385	—	19	4	no	—
92	#382	—	19	1	no	—
93	#380	—	19	2	no	—
94	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₁₉	#525	1	2	yes	—
96	C₂×C₁₉	C₂×#125	1	1	yes	characteristic
97	C₂×C₁₉	#529	1	2	yes	—
98	C₂×C₁₉	#533	1	1	yes	characteristic
99	D₁₉	—	2	4	no	—
100	C₂³×C₄	—	19	1	no	—
101	C₂³×C₄	—	19	2	no	—
102	#125	—	2	4	no	—
103	C₂×C₄⋊C₄	—	19	2	no	—
104	C₂×C₄⋊C₄	—	19	4	no	—
105	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
106	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
107	C₂×C₂²⋊C₄	—	19	4	no	—
108	C₂×C₄²	—	19	2	no	—
109	C₂×C₄²	—	19	1	no	—
110	C₂×C₄²	—	38	4	no	—
111	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
112	#95	—	19	4	no	—
113	#95	—	19	4	no	—
114	#95	—	19	4	no	—
115	C₁₉	#2851	1	1	yes	characteristic, complemented, Sylow
116	C₂⁴	—	19	1	no	—
117	C₂²×C₄	—	19	1	no	—
118	C₂²×C₄	—	19	2	no	—
119	C₂²×C₄	—	19	4	no	—
120	C₂²×C₄	—	19	4	no	—
121	C₂²×C₄	—	38	4	no	—
122	C₂²×C₄	—	38	4	no	—
123	C₂²×C₄	—	38	2	no	—
124	C₂²×C₄	—	38	4	no	—
125	C₂²×C₄	—	38	2	no	—
126	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
127	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
128	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
129	C₄⋊C₄	—	2	8	no	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	38	8	no	—
132	C₄⋊C₄	—	38	4	no	—
133	C₂²⋊C₄	—	38	8	no	—
134	C₄²	—	38	4	no	—
135	C₄²	—	38	2	no	—
136	C₄²	C₂²⋊D₁₉	1	4	yes	—
137	C₂³	—	19	2	no	—
138	C₂³	—	19	4	no	—
139	C₂³	—	38	1	no	—
140	C₂³	—	38	2	no	—
141	C₂³	—	38	1	no	—
142	C₂³	C₂³×D₁₉	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	19	2	no	—
149	C₂×C₄	—	19	4	no	—
150	C₂×C₄	—	38	16	no	—
151	C₂×C₄	—	38	1	no	—
152	C₂×C₄	—	38	2	no	—
153	C₂×C₄	—	38	2	no	—
154	C₂×C₄	—	38	1	no	—
155	C₂×C₄	—	38	8	no	—
156	C₂×C₄	—	38	4	no	—
157	C₂×C₄	—	38	4	no	—
158	C₂×C₄	—	38	4	no	—
159	C₂×C₄	Q₈×D₁₉	1	2	yes	—
160	C₂×C₄	#64545	1	2	yes	—
161	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
162	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
163	C₂²	—	19	4	no	—
164	C₂²	—	38	4	no	—
165	C₂²	—	38	4	no	—
166	C₂²	—	38	2	no	—
167	C₂²	—	38	2	no	—
168	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
169	C₂²	C₂×#64545	1	1	yes	characteristic
170	C₂²	#41×D₁₉	1	2	yes	—
171	C₂²	#41×D₁₉	1	2	yes	—
172	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
173	C₄	—	2	4	no	—
174	C₄	—	4	4	no	—
175	C₄	—	38	4	no	—
176	C₄	—	38	2	no	—
177	C₄	—	76	4	no	—
178	C₄	#10597392	1	4	yes	—
179	C₂	—	38	4	no	—
180	C₂	C₂×#10597392	1	1	yes	characteristic
181	C₂	#11927051	1	2	yes	—
182	C₂	#125×D₁₉	1	1	yes	characteristic
183	C₂	#11927079	1	2	yes	—
184	C₂	#11927100	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₁₉

C₂

yes

maximal, characteristic

#11926440

C₂

yes

maximal, complemented

#11926425

C₂

yes

maximal, complemented

#11926415

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic, complemented

#11926401

C₂

yes

maximal

C₂×C₁₉×#125

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

—

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₄²×D₁₉

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

Q₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×Q₈

yes

—

C₂²×D₁₉

#41

yes

—

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×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

#41

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

#2851

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

#125

yes

complemented

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

D₁₉

yes

characteristic, complemented

C₂²×C₄²

—

—

—

—

—

—

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

C₂×C₁₉

#525

yes

—

C₂×C₁₉

C₂×#125

yes

characteristic

C₂×C₁₉

#529

yes

—

C₂×C₁₉

#533

yes

characteristic

D₁₉

—

100

C₂³×C₄

—

101

C₂³×C₄

—

102

#125

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

106

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

107

C₂×C₂²⋊C₄

—

108

C₂×C₄²

—

109

C₂×C₄²

—

110

C₂×C₄²

—

111

C₂×C₄²

C₂×D₁₉

yes

characteristic

112

#95

—

113

#95

—

114

#95

—

115

C₁₉

#2851

yes

characteristic, complemented, Sylow

116

C₂⁴

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₂²×D₁₉

yes

—

127

C₂²×C₄

C₂²×D₁₉

yes

—

128

C₂²×C₄

C₂²×D₁₉

yes

characteristic

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₂²⋊C₄

—

134

C₄²

—

135

C₄²

—

136

C₄²

C₂²⋊D₁₉

yes

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

C₂³×D₁₉

yes

characteristic

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

Q₈×D₁₉

yes

—

160

C₂×C₄

#64545

yes

—

161

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

162

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

C₂×Q₈×D₁₉

yes

characteristic

169

C₂²

C₂×#64545

yes

characteristic

170

C₂²

#41×D₁₉

yes

—

171

C₂²

#41×D₁₉

yes

—

172

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

#10597392

yes

—

179

C₂

—

180

C₂

C₂×#10597392

yes

characteristic

181

C₂

#11927051

yes

—

182

C₂

#125×D₁₉

yes

characteristic

183

C₂

#11927079

yes

—

184

C₂

#11927100

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#125	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#2851
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

C₂³×D₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
2. #11926440	C₂	semidirect
3. #11926425	C₂	semidirect
5. #11926410	C₂	semidirect
7. C₂×C₁₉×#125	C₂	semidirect
80. C₂×D₁₉	#125	semidirect
87. C₂×#125	D₁₉	semidirect
115. C₁₉	#2851	semidirect

H ≅ G/N

type

2. #11926440

C₂

semidirect

3. #11926425

C₂

semidirect

5. #11926410

C₂

semidirect

7. C₂×C₁₉×#125

C₂

semidirect

80. C₂×D₁₉

#125

semidirect

87. C₂×#125

D₁₉

semidirect

115. C₁₉

#2851

semidirect

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

subgroup	index
C₂×C₄²×D₁₉	2
#11926440	2
#11926425	2
#11926415	2
#11926410	2
#11926401	2
C₂×C₁₉×#125	2
#2851	19

subgroup

index

C₂×C₄²×D₁₉

C₂×C₁₉×#125

Subgroups — #14571940

Conjugacy classes of subgroups

Complements

Maximal subgroups