Group #14561903 — subgroups

Subgroups — #14561903

Order 2432.

520 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 197 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×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉⋊#95	C₂	1	4	yes	maximal
3	C₂×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₉	C₂²	1	2	yes	—
8	C₂³×Dic₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
10	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₉	C₄	1	4	yes	complemented
12	C₁₉⋊#95	—	2	2	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	C₁₉⋊#95	—	2	8	no	—
15	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	—	2	4	no	—
17	C₂²×C₄×C₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	2	4	no	—
20	C₂²×C₄×C₁₉	—	2	4	no	—
21	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	D₄	1	2	yes	—
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×Dic₁₉	—	2	4	no	—
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₂²×Dic₁₉	—	2	2	no	—
28	C₂²×Dic₁₉	—	2	4	no	—
29	C₂²×Dic₁₉	—	2	4	no	—
30	C₂²×Dic₁₉	—	2	2	no	—
31	C₂²×Dic₁₉	—	2	2	no	—
32	C₂²×Dic₁₉	—	2	4	no	—
33	C₂²×Dic₁₉	D₄	1	4	yes	—
34	C₂²×Dic₁₉	Q₈	1	4	yes	—
35	C₄⋊C₄×C₁₉	—	2	8	no	—
36	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂³×C₁₉	C₂×D₄	1	2	yes	—
38	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
41	C₂³×C₁₉	#41	1	4	yes	—
42	C₂³×C₁₉	#41	1	2	yes	—
43	C₂³×C₁₉	#41	1	2	yes	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	2	8	no	—
49	C₂×C₄×C₁₉	—	4	4	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
53	C₂×Dic₁₉	—	2	4	no	—
54	C₂×Dic₁₉	—	2	4	no	—
55	C₂×Dic₁₉	—	2	8	no	—
56	C₂×Dic₁₉	—	2	8	no	—
57	C₂×Dic₁₉	—	4	4	no	—
58	C₂×Dic₁₉	—	4	2	no	—
59	C₂×Dic₁₉	—	4	2	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₂×Dic₁₉	—	4	4	no	—
62	C₂×Dic₁₉	—	4	2	no	—
63	#1445	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₁₉	#117	1	2	yes	—
66	C₂²×C₁₉	C₄×D₄	1	2	yes	—
67	C₂²×C₁₉	C₄×Q₈	1	2	yes	—
68	C₂²×C₁₉	#121	1	2	yes	—
69	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
70	C₂²×C₁₉	C₂²⋊Q₈	1	4	yes	—
71	C₂²×C₁₉	#123	1	4	yes	—
72	C₂²×C₁₉	#123	1	2	yes	—
73	C₂²×C₁₉	#123	1	2	yes	—
74	C₂²×C₁₉	#124	1	1	yes	characteristic
75	C₂²×C₁₉	#124	1	1	yes	characteristic
76	C₂²×C₁₉	#125	1	4	yes	—
77	C₂²×C₁₉	#126	1	4	yes	—
78	C₂²×C₁₉	#127	1	1	yes	characteristic
79	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
80	C₄×C₁₉	—	2	4	no	—
81	C₄×C₁₉	—	4	4	no	—
82	Dic₁₉	—	4	4	no	—
83	Dic₁₉	—	4	4	no	—
84	C₂²×C₄⋊C₄	D₁₉	1	1	yes	characteristic
85	C₂×#95	—	19	4	no	—
86	C₂×#95	—	19	1	no	—
87	C₂×#95	—	19	1	no	—
88	C₂×C₁₉	#381	1	1	yes	characteristic
89	C₂×C₁₉	#387	1	4	yes	—
90	C₂×C₁₉	#390	1	1	yes	characteristic
91	C₂×C₁₉	#391	1	1	yes	characteristic
92	C₂×C₁₉	#397	1	2	yes	—
93	C₂×C₁₉	#398	1	2	yes	—
94	C₂×C₁₉	#399	1	2	yes	—
95	C₂×C₁₉	#400	1	2	yes	—
96	C₂³×C₄	—	19	2	no	—
97	C₂³×C₄	—	19	2	no	—
98	C₂³×C₄	C₂×D₁₉	1	2	yes	—
99	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
100	C₂×C₄⋊C₄	—	2	2	no	—
101	C₂×C₄⋊C₄	—	2	2	no	—
102	C₂×C₄⋊C₄	Dic₁₉	1	4	yes	complemented
103	#95	—	38	8	no	—
104	#95	—	38	2	no	—
105	#95	—	38	2	no	—
106	C₁₉	#1445	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
108	C₂²×C₄	—	2	4	no	—
109	C₂²×C₄	—	2	4	no	—
110	C₂²×C₄	—	2	4	no	—
111	C₂²×C₄	—	2	2	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	—	19	4	no	—
114	C₂²×C₄	—	19	4	no	—
115	C₂²×C₄	—	38	4	no	—
116	C₂²×C₄	—	38	4	no	—
117	C₂²×C₄	—	38	4	no	—
118	C₂²×C₄	—	38	2	no	—
119	C₂²×C₄	—	38	2	no	—
120	C₂²×C₄	—	38	4	no	—
121	C₂²×C₄	—	38	2	no	—
122	C₂²×C₄	—	38	2	no	—
123	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
124	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
125	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
126	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
127	C₄⋊C₄	—	2	8	no	—
128	C₂³	#64541	1	4	yes	—
129	C₂³	D₄×D₁₉	1	2	yes	—
130	C₂³	#64543	1	2	yes	—
131	C₂³	Q₈×D₁₉	1	2	yes	—
132	C₂³	#64545	1	2	yes	—
133	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
134	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
135	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	8	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	4	4	no	—
143	C₂×C₄	—	4	2	no	—
144	C₂×C₄	—	38	4	no	—
145	C₂×C₄	—	38	4	no	—
146	C₂×C₄	—	38	8	no	—
147	C₂×C₄	—	38	8	no	—
148	C₂×C₄	—	76	2	no	—
149	C₂×C₄	—	76	2	no	—
150	C₂×C₄	—	76	4	no	—
151	C₂×C₄	—	76	4	no	—
152	C₂×C₄	—	76	2	no	—
153	C₂×C₄	—	76	2	no	—
154	C₂×C₄	C₂²⋊Dic₁₉	1	4	yes	—
155	C₂²	#10597335	1	4	yes	—
156	C₂²	#10597340	1	4	yes	—
157	C₂²	#10597342	1	4	yes	—
158	C₂²	#10597344	1	4	yes	—
159	C₂²	#10597372	1	2	yes	—
160	C₂²	#10597375	1	2	yes	—
161	C₂²	#10597375	1	2	yes	—
162	C₂²	D₄×Dic₁₉	1	2	yes	—
163	C₂²	#10597382	1	1	yes	characteristic
164	C₂²	#10597384	1	2	yes	—
165	C₂²	#10597386	1	1	yes	characteristic
166	C₂²	#10597390	1	1	yes	characteristic
167	C₂²	Q₈×Dic₁₉	1	2	yes	—
168	C₂²	#10597392	1	2	yes	—
169	C₂²	#10597393	1	1	yes	characteristic
170	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	4	4	no	—
173	C₄	—	76	4	no	—
174	C₄	—	76	4	no	—
175	C₂	#11926407	1	1	yes	characteristic
176	C₂	#11926430	1	4	yes	—
177	C₂	#11926447	1	1	yes	characteristic
178	C₂	#11926451	1	1	yes	characteristic
179	C₂	#11926470	1	2	yes	—
180	C₂	#11926475	1	2	yes	—
181	C₂	#11926479	1	2	yes	—
182	C₂	#11926482	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉⋊#95

C₂

yes

maximal, characteristic

C₂×C₁₉⋊#95

C₂

yes

maximal

C₂×C₁₉⋊#95

C₂

yes

maximal, characteristic

C₂²×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₂³×Dic₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₄

yes

complemented

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂²×Dic₁₉

Q₈

yes

—

C₄⋊C₄×C₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

#41

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

C₂²⋊C₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#1445

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

—

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

C₄×Q₈

yes

—

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#126

yes

—

C₂²×C₁₉

#127

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂²×C₄⋊C₄

D₁₉

yes

characteristic

C₂×#95

—

C₂×#95

—

C₂×#95

—

C₂×C₁₉

#381

yes

characteristic

C₂×C₁₉

#387

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#398

yes

—

C₂×C₁₉

#399

yes

—

C₂×C₁₉

#400

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

Dic₁₉

yes

complemented

103

#95

—

104

#95

—

105

#95

—

106

C₁₉

#1445

yes

characteristic, complemented, Sylow

107

C₂⁴

C₂²×D₁₉

yes

characteristic

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₂×Dic₁₉

yes

—

124

C₂²×C₄

C₂×Dic₁₉

yes

—

125

C₂²×C₄

C₂²⋊D₁₉

yes

—

126

C₂²×C₄

C₂²⋊D₁₉

yes

—

127

C₄⋊C₄

—

128

C₂³

#64541

yes

—

129

C₂³

D₄×D₁₉

yes

—

130

C₂³

#64543

yes

—

131

C₂³

Q₈×D₁₉

yes

—

132

C₂³

#64545

yes

—

133

C₂³

C₂²×Dic₁₉

yes

characteristic

134

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

135

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

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

C₂²⋊Dic₁₉

yes

—

155

C₂²

#10597335

yes

—

156

C₂²

#10597340

yes

—

157

C₂²

#10597342

yes

—

158

C₂²

#10597344

yes

—

159

C₂²

#10597372

yes

—

160

C₂²

#10597375

yes

—

161

C₂²

#10597375

yes

—

162

C₂²

D₄×Dic₁₉

yes

—

163

C₂²

#10597382

yes

characteristic

164

C₂²

#10597384

yes

—

165

C₂²

#10597386

yes

characteristic

166

C₂²

#10597390

yes

characteristic

167

C₂²

Q₈×Dic₁₉

yes

—

168

C₂²

#10597392

yes

—

169

C₂²

#10597393

yes

characteristic

170

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₂

#11926407

yes

characteristic

176

C₂

#11926430

yes

—

177

C₂

#11926447

yes

characteristic

178

C₂

#11926451

yes

characteristic

179

C₂

#11926470

yes

—

180

C₂

#11926475

yes

—

181

C₂

#11926479

yes

—

182

C₂

#11926482

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₁₉
commutator	C₂³×C₁₉	C₂²×C₄
Fitting	C₂²×C₄⋊C₄×C₁₉	C₂
socle, prime radical, cosocle	C₂⁴×C₁₉	C₂³
hypercenter	C₂²×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#1445
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂⁴

C₂²×D₁₉

commutator

C₂³×C₁₉

C₂²×C₄

Fitting

C₂²×C₄⋊C₄×C₁₉

C₂

socle, prime radical, cosocle

C₂⁴×C₁₉

C₂³

hypercenter

C₂²×C₄⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

N	H ≅ G/N	type
11. C₂×C₄⋊C₄×C₁₉	C₄	semidirect
102. C₂×C₄⋊C₄	Dic₁₉	semidirect
106. C₁₉	#1445	semidirect

H ≅ G/N

type

11. C₂×C₄⋊C₄×C₁₉

C₄

semidirect

102. C₂×C₄⋊C₄

Dic₁₉

semidirect

106. C₁₉

#1445

semidirect

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

subgroup	index
C₂×C₁₉⋊#95	2
C₂²×C₄⋊C₄×C₁₉	2
#1445	19

subgroup

index

C₂×C₁₉⋊#95

C₂²×C₄⋊C₄×C₁₉

#1445

Subgroups — #14561903

Conjugacy classes of subgroups

Complements

Maximal subgroups