Group #18020129 — subgroups

Subgroups — C₁₉×#14170 #18020129

Order 4864.

1494 conjugacy classes of subgroups; only the 494 normal subgroups are shown.

normal subgroups only

This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 494 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	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#376	C₂	1	2	yes	maximal
3	C₁₉×#1445	C₂	1	4	yes	maximal
4	C₁₉×#1436	C₂	1	8	yes	maximal
5	C₂×C₁₉×#125	—	2	8	no	—
6	C₂×C₁₉×#125	C₄	1	8	yes	complemented
7	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#376	—	2	8	no	—
12	C₂×C₁₉×#95	C₂²	1	16	yes	—
13	C₂×C₁₉×#95	C₂²	1	4	yes	—
14	C₂×C₁₉×#95	C₂²	1	4	yes	—
15	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
16	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
17	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
19	C₁₉×#125	—	2	32	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
26	C₂×C₄²×C₁₉	—	2	8	no	—
27	C₂×C₄²×C₁₉	—	2	16	no	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₉	D₄	1	8	yes	—
30	C₁₉×#95	—	2	8	no	—
31	C₁₉×#95	—	2	8	no	—
32	C₁₉×#95	—	2	32	no	—
33	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	—	2	8	no	—
35	C₂²×C₄×C₁₉	—	2	4	no	—
36	C₂²×C₄×C₁₉	—	2	8	no	—
37	C₂²×C₄×C₁₉	—	2	4	no	—
38	C₂²×C₄×C₁₉	—	2	4	no	—
39	C₂²×C₄×C₁₉	—	2	8	no	—
40	C₂²×C₄×C₁₉	—	2	16	no	—
41	C₂²×C₄×C₁₉	—	2	16	no	—
42	C₂²×C₄×C₁₉	—	2	16	no	—
43	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
49	C₂²×C₄×C₁₉	#41	1	16	yes	—
50	C₄⋊C₄×C₁₉	—	2	16	no	—
51	C₄⋊C₄×C₁₉	—	2	32	no	—
52	C₄²×C₁₉	—	2	32	no	—
53	C₄²×C₁₉	C₂²⋊C₄	1	16	yes	—
54	#14170	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
56	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
57	C₂³×C₁₉	C₂×#41	1	8	yes	—
58	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
59	C₂×C₄×C₁₉	—	2	8	no	—
60	C₂×C₄×C₁₉	—	2	4	no	—
61	C₂×C₄×C₁₉	—	2	8	no	—
62	C₂×C₄×C₁₉	—	2	8	no	—
63	C₂×C₄×C₁₉	—	2	8	no	—
64	C₂×C₄×C₁₉	—	2	8	no	—
65	C₂×C₄×C₁₉	—	2	16	no	—
66	C₂×C₄×C₁₉	—	2	16	no	—
67	C₂×C₄×C₁₉	—	2	32	no	—
68	C₂×C₄×C₁₉	—	4	8	no	—
69	C₂×C₄×C₁₉	—	4	8	no	—
70	C₂×C₄×C₁₉	—	4	8	no	—
71	C₂×C₄×C₁₉	—	4	8	no	—
72	C₂×C₄×C₁₉	—	4	16	no	—
73	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
74	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
75	C₂²×#125	C₂×C₁₉	1	1	yes	characteristic
76	C₂×#376	C₂×C₁₉	1	2	yes	—
77	#1445	C₂×C₁₉	1	4	yes	—
78	#1436	C₂×C₁₉	1	8	yes	—
79	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₁₉	C₄×#41	1	4	yes	—
81	C₂²×C₁₉	#519	1	2	yes	—
82	C₂²×C₁₉	#525	1	4	yes	—
83	C₂²×C₁₉	#532	1	4	yes	—
84	C₂²×C₁₉	#536	1	4	yes	—
85	C₂²×C₁₉	#552	1	16	yes	—
86	C₄×C₁₉	—	2	4	no	—
87	C₄×C₁₉	—	2	8	no	—
88	C₄×C₁₉	—	4	16	no	—
89	C₄×C₁₉	—	4	8	no	—
90	C₂×#125	—	2	8	no	—
91	C₂×#125	C₄×C₁₉	1	8	yes	complemented
92	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
93	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
94	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
95	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
96	#376	—	2	8	no	—
97	C₂×#95	C₂²×C₁₉	1	16	yes	—
98	C₂×#95	C₂²×C₁₉	1	4	yes	—
99	C₂×#95	C₂²×C₁₉	1	4	yes	—
100	C₂×C₁₉	#2297	1	2	yes	—
101	C₂×C₁₉	#2310	1	1	yes	characteristic
102	C₂×C₁₉	#2371	1	4	yes	—
103	C₂×C₁₉	#2611	1	8	yes	—
104	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
105	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
106	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
107	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
108	#125	—	2	32	no	—
109	C₂×C₄⋊C₄	—	2	8	no	—
110	C₂×C₄⋊C₄	—	2	4	no	—
111	C₂×C₄⋊C₄	—	2	4	no	—
112	C₂×C₄⋊C₄	—	2	8	no	—
113	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
114	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
115	C₂×C₄²	—	2	8	no	—
116	C₂×C₄²	—	2	16	no	—
117	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
118	C₂×C₄²	D₄×C₁₉	1	8	yes	—
119	#95	—	2	8	no	—
120	#95	—	2	8	no	—
121	#95	—	2	32	no	—
122	C₁₉	#14170	1	1	yes	characteristic, direct product factor, Sylow
123	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
124	C₂²×C₄	—	2	8	no	—
125	C₂²×C₄	—	2	4	no	—
126	C₂²×C₄	—	2	8	no	—
127	C₂²×C₄	—	2	4	no	—
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	—	2	16	no	—
130	C₂²×C₄	—	2	16	no	—
131	C₂²×C₄	—	2	8	no	—
132	C₂²×C₄	—	2	16	no	—
133	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
134	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
135	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
136	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
137	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
138	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
139	C₂²×C₄	#41×C₁₉	1	16	yes	—
140	C₄⋊C₄	—	2	32	no	—
141	C₄⋊C₄	—	2	16	no	—
142	C₄²	—	2	32	no	—
143	C₄²	C₂²⋊C₄×C₁₉	1	16	yes	—
144	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
145	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
146	C₂³	C₂×#41×C₁₉	1	8	yes	—
147	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	8	no	—
151	C₂×C₄	—	2	8	no	—
152	C₂×C₄	—	2	8	no	—
153	C₂×C₄	—	2	8	no	—
154	C₂×C₄	—	2	16	no	—
155	C₂×C₄	—	2	16	no	—
156	C₂×C₄	—	2	32	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	—	4	8	no	—
159	C₂×C₄	—	4	8	no	—
160	C₂×C₄	—	4	8	no	—
161	C₂×C₄	—	4	16	no	—
162	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
163	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
164	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
165	C₂²	C₄×#41×C₁₉	1	4	yes	—
166	C₂²	C₁₉×#519	1	2	yes	—
167	C₂²	C₁₉×#525	1	4	yes	—
168	C₂²	C₁₉×#532	1	4	yes	—
169	C₂²	C₁₉×#536	1	4	yes	—
170	C₂²	C₁₉×#552	1	16	yes	—
171	C₄	—	2	8	no	—
172	C₄	—	2	4	no	—
173	C₄	—	4	8	no	—
174	C₄	—	4	16	no	—
175	C₂	C₁₉×#2297	1	2	yes	—
176	C₂	C₁₉×#2310	1	1	yes	characteristic
177	C₂	C₁₉×#2371	1	4	yes	—
178	C₂	C₁₉×#2611	1	8	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉×#125

C₂

yes

maximal, characteristic

C₂×C₁₉×#376

C₂

yes

maximal

C₁₉×#1445

C₂

yes

maximal

C₁₉×#1436

C₂

yes

maximal

C₂×C₁₉×#125

—

C₂×C₁₉×#125

C₄

yes

complemented

C₂²×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#376

—

C₂×C₁₉×#95

C₂²

yes

—

C₂×C₁₉×#95

C₂²

yes

—

C₂×C₁₉×#95

C₂²

yes

—

C₂³×C₄×C₁₉

C₂³

yes

—

C₂³×C₄×C₁₉

C₂³

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

—

C₁₉×#125

—

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

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂⁴

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

#14170

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂³×C₄

yes

characteristic

C₂³×C₁₉

C₂²×D₄

yes

—

C₂³×C₁₉

C₂×#41

yes

—

C₂³×C₁₉

2₋¹⁺⁴

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

—

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

C₂×C₂²⋊C₄

yes

—

C₂²×#125

C₂×C₁₉

yes

characteristic

C₂×#376

C₂×C₁₉

yes

—

#1445

C₂×C₁₉

yes

—

#1436

C₂×C₁₉

yes

—

C₂²×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×#41

yes

—

C₂²×C₁₉

#519

yes

—

C₂²×C₁₉

#525

yes

—

C₂²×C₁₉

#532

yes

—

C₂²×C₁₉

#536

yes

—

C₂²×C₁₉

#552

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#125

—

C₂×#125

C₄×C₁₉

yes

complemented

C₂²×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂²×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂²×C₄²

C₂²×C₁₉

yes

—

C₂²×C₄²

C₂²×C₁₉

yes

characteristic

#376

—

C₂×#95

C₂²×C₁₉

yes

—

C₂×#95

C₂²×C₁₉

yes

—

C₂×#95

C₂²×C₁₉

yes

—

100

C₂×C₁₉

#2297

yes

—

101

C₂×C₁₉

#2310

yes

characteristic

102

C₂×C₁₉

#2371

yes

—

103

C₂×C₁₉

#2611

yes

—

104

C₂³×C₄

C₂³×C₁₉

yes

—

105

C₂³×C₄

C₂³×C₁₉

yes

—

106

C₂³×C₄

C₂³×C₁₉

yes

characteristic

107

C₂³×C₄

C₂³×C₁₉

yes

—

108

#125

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

114

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

115

C₂×C₄²

—

116

C₂×C₄²

—

117

C₂×C₄²

C₂×C₄×C₁₉

yes

—

118

C₂×C₄²

D₄×C₁₉

yes

—

119

#95

—

120

#95

—

121

#95

—

122

C₁₉

#14170

yes

characteristic, direct product factor, Sylow

123

C₂⁴

C₂⁴×C₁₉

yes

characteristic

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×C₄×C₁₉

yes

—

134

C₂²×C₄

C₂²×C₄×C₁₉

yes

—

135

C₂²×C₄

C₂²×C₄×C₁₉

yes

—

136

C₂²×C₄

C₂×D₄×C₁₉

yes

—

137

C₂²×C₄

C₂×D₄×C₁₉

yes

—

138

C₂²×C₄

C₂×D₄×C₁₉

yes

—

139

C₂²×C₄

#41×C₁₉

yes

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

—

143

C₄²

C₂²⋊C₄×C₁₉

yes

—

144

C₂³

C₂³×C₄×C₁₉

yes

characteristic

145

C₂³

C₂²×D₄×C₁₉

yes

—

146

C₂³

C₂×#41×C₁₉

yes

—

147

C₂³

C₁₉×2₋¹⁺⁴

yes

—

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

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

—

163

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

—

164

C₂²

C₂²×C₂²⋊C₄×C₁₉

yes

characteristic

165

C₂²

C₄×#41×C₁₉

yes

—

166

C₂²

C₁₉×#519

yes

—

167

C₂²

C₁₉×#525

yes

—

168

C₂²

C₁₉×#532

yes

—

169

C₂²

C₁₉×#536

yes

—

170

C₂²

C₁₉×#552

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₂

C₁₉×#2297

yes

—

176

C₂

C₁₉×#2310

yes

characteristic

177

C₂

C₁₉×#2371

yes

—

178

C₂

C₁₉×#2611

yes

—

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

subgroup

G/H

center, socle, prime radical

C₂⁴×C₁₉

C₂⁴

commutator

C₂³

C₂³×C₄×C₁₉

Frattini, cosocle

C₂⁴

C₂⁴×C₁₉

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂⁴×C₁₉ ◁ G

N	H ≅ G/N	type
6. C₂×C₁₉×#125	C₄	semidirect
54. #14170	C₁₉	direct (N × H)
91. C₂×#125	C₄×C₁₉	semidirect
122. C₁₉	#14170	direct (N × H)

H ≅ G/N

type

6. C₂×C₁₉×#125

C₄

semidirect

54. #14170

C₁₉

direct (N × H)

91. C₂×#125

C₄×C₁₉

semidirect

122. C₁₉

#14170

direct (N × H)

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

subgroup	index
C₂²×C₁₉×#125	2
C₂×C₁₉×#376	2
C₁₉×#1445	2
C₁₉×#1436	2
#14170	19

subgroup

index

C₂²×C₁₉×#125

C₂×C₁₉×#376

C₁₉×#1445

C₁₉×#1436

#14170

Subgroups — C₁₉×#14170 #18020129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#14170 #18020129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14170 #18020129