Group #18014286 — subgroups

Subgroups — C₁₉×#8327 #18014286

Order 4864.

684 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 158 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×#541	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1479	C₂	1	4	yes	maximal, complemented
3	C₁₉×#1458	C₂	1	2	yes	maximal
4	C₁₉×#541	—	2	8	no	—
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₂×C₁₉×#126	—	2	2	no	—
7	C₂×C₁₉×#125	—	2	2	no	—
8	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
10	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₁₉×#431	C₂²	1	4	yes	—
13	C₁₉×Q₈⋊C₈	—	2	8	no	—
14	C₁₉×#324	—	2	2	no	—
15	C₁₉×#323	—	2	2	no	—
16	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₁₉×C₄⋊Q₈	—	2	4	no	—
19	C₁₉×#126	—	2	16	no	—
20	C₁₉×#125	—	2	16	no	—
21	C₁₉×#125	—	2	4	no	—
22	C₁₉×C₂²⋊Q₈	—	2	4	no	—
23	C₁₉×C₂²⋊Q₈	—	2	4	no	—
24	C₄×Q₈×C₁₉	—	2	4	no	—
25	C₄×Q₈×C₁₉	D₄	1	8	yes	—
26	C₁₉×#117	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₁₉×C₄⋊C₈	—	2	4	no	—
39	C₁₉×C₂²⋊C₈	—	2	4	no	—
40	C₄×C₈×C₁₉	—	2	4	no	—
41	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×Q₈×C₁₉	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	8	no	—
44	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	4	no	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₁₉	—	4	4	no	—
54	C₄⋊C₄×C₁₉	—	2	8	no	—
55	C₄⋊C₄×C₁₉	—	2	8	no	—
56	C₄⋊C₄×C₁₉	—	2	8	no	—
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	8	no	—
59	C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
61	C₂²⋊C₄×C₁₉	—	2	8	no	—
62	C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	2	8	no	—
65	C₄²×C₁₉	C₂×D₄	1	4	yes	—
66	#8327	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂³×C₁₉	—	2	1	no	—
68	C₂³×C₁₉	—	2	2	no	—
69	C₂³×C₁₉	—	4	2	no	—
70	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	Q₈×C₁₉	—	2	8	no	—
72	Q₈×C₁₉	—	4	4	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	4	no	—
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	4	4	no	—
81	C₂×C₄×C₁₉	—	4	4	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
84	C₂×C₄×C₁₉	#120	1	4	yes	—
85	C₂×C₄×C₁₉	#131	1	4	yes	—
86	C₈×C₁₉	—	8	4	no	—
87	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
88	#1479	C₂×C₁₉	1	4	yes	complemented
89	#1458	C₂×C₁₉	1	2	yes	—
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	—	4	1	no	—
93	C₂²×C₁₉	—	8	2	no	—
94	C₂²×C₁₉	#379	1	1	yes	characteristic
95	C₂²×C₁₉	#408	1	2	yes	—
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	—	4	4	no	—
99	C₄×C₁₉	—	4	1	no	—
100	C₄×C₁₉	—	4	4	no	—
101	C₄×C₁₉	#408	1	4	yes	—
102	#541	—	2	8	no	—
103	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
104	C₂×#126	—	2	2	no	—
105	C₂×#125	—	2	2	no	—
106	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
107	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
108	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
109	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
110	#431	C₂²×C₁₉	1	4	yes	—
111	Q₈⋊C₈	—	2	8	no	—
112	#324	—	2	2	no	—
113	#323	—	2	2	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	—	8	1	no	—
116	C₂×C₁₉	#1780	1	1	yes	characteristic
117	C₂×C₁₉	#1796	1	2	yes	—
118	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
119	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
120	C₄⋊Q₈	—	2	4	no	—
121	#126	—	2	16	no	—
122	#125	—	2	16	no	—
123	#125	—	2	4	no	—
124	C₂²⋊Q₈	—	2	4	no	—
125	C₂²⋊Q₈	—	2	4	no	—
126	C₄×Q₈	—	2	4	no	—
127	C₄×Q₈	D₄×C₁₉	1	8	yes	—
128	#117	—	2	4	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
134	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
135	C₂×C₂²⋊C₄	—	2	2	no	—
136	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
137	C₂×C₄²	—	2	2	no	—
138	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
139	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
140	C₄⋊C₈	—	2	4	no	—
141	C₂²⋊C₈	—	2	4	no	—
142	C₄×C₈	—	2	4	no	—
143	C₁₉	#8327	1	1	yes	characteristic, direct product factor, Sylow
144	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
145	C₂×Q₈	—	2	2	no	—
146	C₂×Q₈	—	2	8	no	—
147	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	4	no	—
152	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
153	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
154	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
156	C₂×C₈	—	4	4	no	—
157	C₄⋊C₄	—	2	8	no	—
158	C₄⋊C₄	—	2	8	no	—
159	C₄⋊C₄	—	2	8	no	—
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	—	2	8	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
164	C₂²⋊C₄	—	2	8	no	—
165	C₂²⋊C₄	—	2	4	no	—
166	C₄²	—	2	2	no	—
167	C₄²	—	2	8	no	—
168	C₄²	C₂×D₄×C₁₉	1	4	yes	—
169	C₂³	—	2	1	no	—
170	C₂³	—	2	2	no	—
171	C₂³	—	4	2	no	—
172	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
173	Q₈	—	2	8	no	—
174	Q₈	—	4	4	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
186	C₂×C₄	C₁₉×#120	1	4	yes	—
187	C₂×C₄	C₁₉×#131	1	4	yes	—
188	C₈	—	8	4	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	4	1	no	—
191	C₂²	—	4	2	no	—
192	C₂²	—	8	2	no	—
193	C₂²	C₁₉×#379	1	1	yes	characteristic
194	C₂²	C₁₉×#408	1	2	yes	—
195	C₄	—	2	4	no	—
196	C₄	—	4	1	no	—
197	C₄	—	4	4	no	—
198	C₄	—	4	4	no	—
199	C₄	—	4	2	no	—
200	C₄	C₁₉×#408	1	4	yes	—
201	C₂	—	2	2	no	—
202	C₂	—	8	1	no	—
203	C₂	C₁₉×#1780	1	1	yes	characteristic
204	C₂	C₁₉×#1796	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#541

C₂

yes

maximal, characteristic

C₁₉×#1479

C₂

yes

maximal, complemented

C₁₉×#1458

C₂

yes

maximal

C₁₉×#541

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₁₉×#126

—

C₂×C₁₉×#125

—

C₂×C₁₉×#125

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊Q₈

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

—

C₁₉×Q₈⋊C₈

—

C₁₉×#324

—

C₁₉×#323

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#126

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

#8327

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₂×#541

C₂×C₁₉

yes

characteristic

#1479

C₂×C₁₉

yes

complemented

#1458

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#379

yes

characteristic

C₂²×C₁₉

#408

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

#408

yes

—

102

#541

—

103

C₂×C₄⋊Q₈

C₄×C₁₉

yes

characteristic

104

C₂×#126

—

105

C₂×#125

—

106

C₂×#125

C₄×C₁₉

yes

characteristic

107

C₂×C₂²⋊Q₈

C₄×C₁₉

yes

—

108

C₂×C₄×Q₈

C₂²×C₁₉

yes

—

109

C₂×#117

C₂²×C₁₉

yes

characteristic

110

#431

C₂²×C₁₉

yes

—

111

Q₈⋊C₈

—

112

#324

—

113

#323

—

114

C₂×C₁₉

—

115

C₂×C₁₉

—

116

C₂×C₁₉

#1780

yes

characteristic

117

C₂×C₁₉

#1796

yes

—

118

C₂²×Q₈

C₂×C₄×C₁₉

yes

—

119

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

120

C₄⋊Q₈

—

121

#126

—

122

#125

—

123

#125

—

124

C₂²⋊Q₈

—

125

C₂²⋊Q₈

—

126

C₄×Q₈

—

127

C₄×Q₈

D₄×C₁₉

yes

—

128

#117

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

134

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

137

C₂×C₄²

—

138

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

139

C₂×C₄²

C₂³×C₁₉

yes

characteristic

140

C₄⋊C₈

—

141

C₂²⋊C₈

—

142

C₄×C₈

—

143

C₁₉

#8327

yes

characteristic, direct product factor, Sylow

144

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×Q₈

C₂²⋊C₄×C₁₉

yes

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

153

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

154

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

155

C₂²×C₄

C₂×D₄×C₁₉

yes

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

C₂²⋊C₄×C₁₉

yes

—

164

C₂²⋊C₄

—

165

C₂²⋊C₄

—

166

C₄²

—

167

C₄²

—

168

C₄²

C₂×D₄×C₁₉

yes

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

173

Q₈

—

174

Q₈

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

—

186

C₂×C₄

C₁₉×#120

yes

—

187

C₂×C₄

C₁₉×#131

yes

—

188

C₈

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

C₁₉×#379

yes

characteristic

194

C₂²

C₁₉×#408

yes

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

C₁₉×#408

yes

—

201

C₂

—

202

C₂

—

203

C₂

C₁₉×#1780

yes

characteristic

204

C₂

C₁₉×#1796

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#379

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1479	C₂	semidirect
66. #8327	C₁₉	direct (N × H)
88. #1479	C₂×C₁₉	semidirect
143. C₁₉	#8327	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1479

C₂

semidirect

66. #8327

C₁₉

direct (N × H)

88. #1479

C₂×C₁₉

semidirect

143. C₁₉

#8327

direct (N × H)

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

subgroup	index
C₂×C₁₉×#541	2
C₁₉×#1479	2
C₁₉×#1458	2
#8327	19

subgroup

index

C₂×C₁₉×#541

C₁₉×#1479

C₁₉×#1458

#8327

Subgroups — C₁₉×#8327 #18014286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8327 #18014286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8327 #18014286