Group #18038676 — subgroups

Subgroups — C₁₉×#32717 #18038676

Order 4864.

848 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 848 conjugacy classes of subgroups — too many to draw. Only its 206 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	C₁₉×#2616	C₂	1	2	yes	maximal
2	C₁₉×#2075	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2036	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2001	C₂	1	3	yes	maximal, complemented
5	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
9	C₂×C₁₉×#107	C₂²	1	3	yes	—
10	C₂×C₁₉×#103	C₂²	1	6	yes	—
11	C₂×C₁₉×C₂²⋊C₈	C₂²	1	3	yes	—
12	C₂×C₁₉×C₂²⋊C₈	C₂²	1	3	yes	—
13	C₁₉×#395	—	2	2	no	—
14	C₁₉×#394	—	2	6	no	—
15	C₁₉×#380	C₂²	1	6	yes	—
16	C₁₉×#340	C₂²	1	3	yes	—
17	C₁₉×#340	C₂²	1	3	yes	—
18	C₂×#41×C₁₉	—	4	3	no	—
19	C₂×#41×C₁₉	—	4	3	no	—
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
22	C₂²×D₄×C₁₉	D₄	1	3	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂×Q₁₆×C₁₉	—	4	3	no	—
25	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
27	C₁₉×C₂²⋊Q₈	—	4	6	no	—
28	C₁₉×C₂²⋊Q₈	—	4	6	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
33	C₁₉×#107	—	4	3	no	—
34	C₁₉×#103	—	4	6	no	—
35	C₁₉×C₂²⋊C₈	—	4	3	no	—
36	C₁₉×C₂²⋊C₈	—	4	3	no	—
37	C₁₉×#95	—	2	6	no	—
38	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
39	#41×C₁₉	—	4	12	no	—
40	#41×C₁₉	—	4	4	no	—
41	C₂×Q₈×C₁₉	—	2	6	no	—
42	C₂×Q₈×C₁₉	—	2	6	no	—
43	C₂×Q₈×C₁₉	—	4	3	no	—
44	C₂×D₄×C₁₉	—	4	6	no	—
45	C₂×D₄×C₁₉	—	4	3	no	—
46	C₂²×C₄×C₁₉	—	2	6	no	—
47	C₂²×C₄×C₁₉	—	2	6	no	—
48	C₂²×C₄×C₁₉	—	2	3	no	—
49	C₂²×C₄×C₁₉	—	2	3	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	2	6	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
53	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
54	Q₁₆×C₁₉	—	4	4	no	—
55	C₂×C₈×C₁₉	—	2	3	no	—
56	C₂×C₈×C₁₉	—	2	6	no	—
57	C₂×C₈×C₁₉	—	2	3	no	—
58	C₄⋊C₄×C₁₉	—	2	6	no	—
59	C₄⋊C₄×C₁₉	—	2	6	no	—
60	C₄⋊C₄×C₁₉	—	4	12	no	—
61	C₂²⋊C₄×C₁₉	—	4	12	no	—
62	C₂²⋊C₄×C₁₉	—	8	6	no	—
63	#32717	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂³×C₁₉	—	2	6	no	—
65	C₂³×C₁₉	—	2	3	no	—
66	C₂³×C₁₉	—	2	3	no	—
67	C₂³×C₁₉	—	2	3	no	—
68	C₂³×C₁₉	—	2	6	no	—
69	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	4	no	—
71	Q₈×C₁₉	—	4	6	no	—
72	Q₈×C₁₉	—	4	2	no	—
73	D₄×C₁₉	—	4	12	no	—
74	C₂×C₄×C₁₉	—	2	6	no	—
75	C₂×C₄×C₁₉	—	2	3	no	—
76	C₂×C₄×C₁₉	—	4	3	no	—
77	C₂×C₄×C₁₉	—	4	6	no	—
78	C₂×C₄×C₁₉	—	4	3	no	—
79	C₂×C₄×C₁₉	—	4	6	no	—
80	C₂×C₄×C₁₉	—	4	6	no	—
81	C₂×C₄×C₁₉	—	4	6	no	—
82	C₂×C₄×C₁₉	—	4	6	no	—
83	C₂×C₄×C₁₉	H(5,𝔽₂)	1	3	yes	—
84	C₂×C₄×C₁₉	H(5,𝔽₂)	1	3	yes	—
85	C₈×C₁₉	—	4	3	no	—
86	C₈×C₁₉	—	4	1	no	—
87	#2616	C₂×C₁₉	1	2	yes	—
88	#2075	C₂×C₁₉	1	3	yes	complemented
89	#2036	C₂×C₁₉	1	6	yes	complemented
90	#2001	C₂×C₁₉	1	3	yes	complemented
91	#1780	C₂×C₁₉	1	1	yes	characteristic
92	C₂²×C₁₉	—	4	6	no	—
93	C₂²×C₁₉	—	4	3	no	—
94	C₂²×C₁₉	—	4	6	no	—
95	C₂²×C₁₉	—	4	3	no	—
96	C₂²×C₁₉	—	4	3	no	—
97	C₂²×C₁₉	#534	1	3	yes	—
98	C₂²×C₁₉	#576	1	1	yes	characteristic
99	C₂²×C₁₉	#578	1	3	yes	—
100	C₄×C₁₉	—	4	3	no	—
101	C₄×C₁₉	—	8	6	no	—
102	C₄×C₁₉	—	8	2	no	—
103	C₄×C₁₉	#560	1	3	yes	—
104	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
105	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
106	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
107	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
108	C₂×#107	C₂²×C₁₉	1	3	yes	—
109	C₂×#103	C₂²×C₁₉	1	6	yes	—
110	C₂×C₂²⋊C₈	C₂²×C₁₉	1	3	yes	—
111	C₂×C₂²⋊C₈	C₂²×C₁₉	1	3	yes	—
112	#395	—	2	2	no	—
113	#394	—	2	6	no	—
114	#380	C₂²×C₁₉	1	6	yes	—
115	#340	C₂²×C₁₉	1	3	yes	—
116	#340	C₂²×C₁₉	1	3	yes	—
117	C₂×C₁₉	—	8	3	no	—
118	C₂×C₁₉	#2812	1	1	yes	characteristic
119	C₂×C₁₉	#3202	1	3	yes	—
120	C₂×C₁₉	#3203	1	3	yes	—
121	C₂×#41	—	4	3	no	—
122	C₂×#41	—	4	3	no	—
123	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
124	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
125	C₂²×D₄	D₄×C₁₉	1	3	yes	—
126	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
127	C₂×Q₁₆	—	4	3	no	—
128	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
129	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
130	C₂²⋊Q₈	—	4	6	no	—
131	C₂²⋊Q₈	—	4	6	no	—
132	C₂×C₄⋊C₄	—	2	6	no	—
133	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
134	C₂×C₂²⋊C₄	—	2	6	no	—
135	C₂×C₂²⋊C₄	—	2	6	no	—
136	#107	—	4	3	no	—
137	#103	—	4	6	no	—
138	C₂²⋊C₈	—	4	3	no	—
139	C₂²⋊C₈	—	4	3	no	—
140	#95	—	2	6	no	—
141	C₁₉	#32717	1	1	yes	characteristic, direct product factor, Sylow
142	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
143	#41	—	4	12	no	—
144	#41	—	4	4	no	—
145	C₂×Q₈	—	2	6	no	—
146	C₂×Q₈	—	2	6	no	—
147	C₂×Q₈	—	4	3	no	—
148	C₂×D₄	—	4	6	no	—
149	C₂×D₄	—	4	3	no	—
150	C₂²×C₄	—	2	3	no	—
151	C₂²×C₄	—	2	3	no	—
152	C₂²×C₄	—	2	6	no	—
153	C₂²×C₄	—	2	6	no	—
154	C₂²×C₄	—	2	6	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
157	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
158	Q₁₆	—	4	4	no	—
159	C₂×C₈	—	2	6	no	—
160	C₂×C₈	—	2	3	no	—
161	C₂×C₈	—	2	3	no	—
162	C₄⋊C₄	—	2	6	no	—
163	C₄⋊C₄	—	2	6	no	—
164	C₄⋊C₄	—	4	12	no	—
165	C₂²⋊C₄	—	4	12	no	—
166	C₂²⋊C₄	—	8	6	no	—
167	C₂³	—	2	6	no	—
168	C₂³	—	2	3	no	—
169	C₂³	—	2	3	no	—
170	C₂³	—	2	3	no	—
171	C₂³	—	2	6	no	—
172	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
173	Q₈	—	4	4	no	—
174	Q₈	—	4	6	no	—
175	Q₈	—	4	2	no	—
176	D₄	—	4	12	no	—
177	C₂×C₄	—	2	6	no	—
178	C₂×C₄	—	2	3	no	—
179	C₂×C₄	—	4	6	no	—
180	C₂×C₄	—	4	3	no	—
181	C₂×C₄	—	4	3	no	—
182	C₂×C₄	—	4	6	no	—
183	C₂×C₄	—	4	6	no	—
184	C₂×C₄	—	4	6	no	—
185	C₂×C₄	—	4	6	no	—
186	C₂×C₄	C₁₉×H(5,𝔽₂)	1	3	yes	—
187	C₂×C₄	C₁₉×H(5,𝔽₂)	1	3	yes	—
188	C₈	—	4	3	no	—
189	C₈	—	4	1	no	—
190	C₂²	—	4	6	no	—
191	C₂²	—	4	3	no	—
192	C₂²	—	4	6	no	—
193	C₂²	—	4	3	no	—
194	C₂²	—	4	3	no	—
195	C₂²	C₁₉×#534	1	3	yes	—
196	C₂²	C₁₉×#576	1	1	yes	characteristic
197	C₂²	C₁₉×#578	1	3	yes	—
198	C₄	—	4	3	no	—
199	C₄	—	8	6	no	—
200	C₄	—	8	2	no	—
201	C₄	C₁₉×#560	1	3	yes	—
202	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
203	C₂	—	8	3	no	—
204	C₂	C₁₉×#2812	1	1	yes	characteristic
205	C₂	C₁₉×#3202	1	3	yes	—
206	C₂	C₁₉×#3203	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2616

C₂

yes

maximal

C₁₉×#2075

C₂

yes

maximal, complemented

C₁₉×#2036

C₂

yes

maximal, complemented

C₁₉×#2001

C₂

yes

maximal, complemented

C₁₉×#1780

C₂

yes

maximal, characteristic

C₂²×#41×C₁₉

C₂²

yes

characteristic

C₂²×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊Q₈

C₂²

yes

—

C₂×C₁₉×#107

C₂²

yes

—

C₂×C₁₉×#103

C₂²

yes

—

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

—

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#395

—

C₁₉×#394

—

C₁₉×#380

C₂²

yes

—

C₁₉×#340

C₂²

yes

—

C₁₉×#340

C₂²

yes

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×Q₈×C₁₉

C₂³

yes

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₁₉×#107

—

C₁₉×#103

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂×D₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂⁴

yes

characteristic

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#32717

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×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

H(5,𝔽₂)

yes

—

C₂×C₄×C₁₉

H(5,𝔽₂)

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#2616

C₂×C₁₉

yes

—

#2075

C₂×C₁₉

yes

complemented

#2036

C₂×C₁₉

yes

complemented

#2001

C₂×C₁₉

yes

complemented

#1780

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#534

yes

—

C₂²×C₁₉

#576

yes

characteristic

C₂²×C₁₉

#578

yes

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

#560

yes

—

104

C₄×C₁₉

H(3,𝔽₄)

yes

characteristic

105

C₂²×#41

C₂²×C₁₉

yes

characteristic

106

C₂²×Q₁₆

C₂²×C₁₉

yes

characteristic

107

C₂×C₂²⋊Q₈

C₂²×C₁₉

yes

—

108

C₂×#107

C₂²×C₁₉

yes

—

109

C₂×#103

C₂²×C₁₉

yes

—

110

C₂×C₂²⋊C₈

C₂²×C₁₉

yes

—

111

C₂×C₂²⋊C₈

C₂²×C₁₉

yes

—

112

#395

—

113

#394

—

114

#380

C₂²×C₁₉

yes

—

115

#340

C₂²×C₁₉

yes

—

116

#340

C₂²×C₁₉

yes

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#2812

yes

characteristic

119

C₂×C₁₉

#3202

yes

—

120

C₂×C₁₉

#3203

yes

—

121

C₂×#41

—

122

C₂×#41

—

123

C₂²×Q₈

D₄×C₁₉

yes

characteristic

124

C₂²×Q₈

C₂³×C₁₉

yes

—

125

C₂²×D₄

D₄×C₁₉

yes

—

126

C₂³×C₄

C₂³×C₁₉

yes

—

127

C₂×Q₁₆

—

128

C₂²×C₈

C₂³×C₁₉

yes

characteristic

129

C₂²×C₈

C₂³×C₁₉

yes

—

130

C₂²⋊Q₈

—

131

C₂²⋊Q₈

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

C₂³×C₁₉

yes

—

134

C₂×C₂²⋊C₄

—

135

C₂×C₂²⋊C₄

—

136

#107

—

137

#103

—

138

C₂²⋊C₈

—

139

C₂²⋊C₈

—

140

#95

—

141

C₁₉

#32717

yes

characteristic, direct product factor, Sylow

142

C₂⁴

C₂×D₄×C₁₉

yes

—

143

#41

—

144

#41

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

C₂×D₄×C₁₉

yes

—

157

C₂²×C₄

C₂⁴×C₁₉

yes

characteristic

158

Q₁₆

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₂²⋊C₄

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

C₂²×D₄×C₁₉

yes

characteristic

173

Q₈

—

174

Q₈

—

175

Q₈

—

176

D₄

—

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

—

186

C₂×C₄

C₁₉×H(5,𝔽₂)

yes

—

187

C₂×C₄

C₁₉×H(5,𝔽₂)

yes

—

188

C₈

—

189

C₈

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

C₁₉×#534

yes

—

196

C₂²

C₁₉×#576

yes

characteristic

197

C₂²

C₁₉×#578

yes

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

C₁₉×#560

yes

—

202

C₄

C₁₉×H(3,𝔽₄)

yes

characteristic

203

C₂

—

204

C₂

C₁₉×#2812

yes

characteristic

205

C₂

C₁₉×#3202

yes

—

206

C₂

C₁₉×#3203

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₉

prime radical

C₂²×#41×C₁₉

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2075	C₂	semidirect
3. C₁₉×#2036	C₂	semidirect
4. C₁₉×#2001	C₂	semidirect
63. #32717	C₁₉	direct (N × H)
88. #2075	C₂×C₁₉	semidirect
89. #2036	C₂×C₁₉	semidirect
90. #2001	C₂×C₁₉	semidirect
141. C₁₉	#32717	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2075

C₂

semidirect

3. C₁₉×#2036

C₂

semidirect

4. C₁₉×#2001

C₂

semidirect

63. #32717

C₁₉

direct (N × H)

88. #2075

C₂×C₁₉

semidirect

89. #2036

C₂×C₁₉

semidirect

90. #2001

C₂×C₁₉

semidirect

141. C₁₉

#32717

direct (N × H)

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

subgroup	index
C₁₉×#2616	2
C₁₉×#2075	2
C₁₉×#2036	2
C₁₉×#2001	2
C₁₉×#1780	2
#32717	19

subgroup

index

C₁₉×#2616

C₁₉×#2075

C₁₉×#2036

C₁₉×#2001

C₁₉×#1780

#32717

Subgroups — C₁₉×#32717 #18038676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#32717 #18038676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32717 #18038676