Group #18014285 — subgroups

Subgroups — C₁₉×#8326 #18014285

Order 4864.

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

normal subgroups only

This group has 812 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×#540	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1478	C₂	1	4	yes	maximal, complemented
3	C₁₉×#1458	C₂	1	2	yes	maximal, complemented
4	C₁₉×#540	—	2	8	no	—
5	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
6	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
7	C₂×C₁₉×#123	—	2	2	no	—
8	C₂×C₁₉×#121	—	2	2	no	—
9	C₂×C₁₉×#121	C₄	1	2	yes	—
10	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₁₉×#431	C₂²	1	4	yes	—
13	C₁₉×D₄⋊C₈	—	2	8	no	—
14	C₁₉×#324	—	2	2	no	—
15	C₁₉×#323	—	2	2	no	—
16	C₂²×D₄×C₁₉	—	2	2	no	—
17	C₂²×D₄×C₁₉	—	2	2	no	—
18	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	—	2	2	no	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₁₉×#127	—	2	4	no	—
22	C₁₉×#125	—	2	4	no	—
23	C₁₉×#123	—	2	16	no	—
24	C₁₉×#121	—	2	16	no	—
25	C₁₉×#121	—	2	4	no	—
26	C₁₉×#121	—	2	4	no	—
27	C₄×D₄×C₁₉	—	2	4	no	—
28	C₄×D₄×C₁₉	D₄	1	8	yes	—
29	C₁₉×#117	—	2	4	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	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
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	—	2	2	no	—
42	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×D₄×C₁₉	—	2	8	no	—
44	C₂×D₄×C₁₉	—	2	8	no	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	2	8	no	—
47	C₂×D₄×C₁₉	—	8	4	no	—
48	C₂×D₄×C₁₉	—	8	4	no	—
49	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	2	8	no	—
54	C₂²×C₄×C₁₉	—	8	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₉	—	4	4	no	—
60	C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
64	C₂²⋊C₄×C₁₉	—	2	8	no	—
65	C₂²⋊C₄×C₁₉	—	2	8	no	—
66	C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	C₂×D₄	1	4	yes	—
69	#8326	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂³×C₁₉	—	2	1	no	—
71	C₂³×C₁₉	—	2	4	no	—
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	—	4	4	no	—
74	C₂³×C₁₉	—	4	4	no	—
75	C₂³×C₁₉	—	4	2	no	—
76	C₂³×C₁₉	—	4	4	no	—
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	D₄×C₁₉	—	2	8	no	—
79	D₄×C₁₉	—	4	4	no	—
80	D₄×C₁₉	—	8	8	no	—
81	D₄×C₁₉	—	8	8	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	4	4	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	8	8	no	—
91	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
92	C₂×C₄×C₁₉	#120	1	4	yes	—
93	C₂×C₄×C₁₉	#131	1	4	yes	—
94	C₈×C₁₉	—	8	4	no	—
95	C₂×#540	C₂×C₁₉	1	1	yes	characteristic
96	#1478	C₂×C₁₉	1	4	yes	complemented
97	#1458	C₂×C₁₉	1	2	yes	complemented
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	4	4	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	—	4	4	no	—
102	C₂²×C₁₉	—	4	1	no	—
103	C₂²×C₁₉	—	4	4	no	—
104	C₂²×C₁₉	—	8	2	no	—
105	C₂²×C₁₉	—	8	8	no	—
106	C₂²×C₁₉	#379	1	1	yes	characteristic
107	C₂²×C₁₉	#408	1	2	yes	—
108	C₄×C₁₉	—	2	4	no	—
109	C₄×C₁₉	—	4	4	no	—
110	C₄×C₁₉	—	4	2	no	—
111	C₄×C₁₉	—	4	1	no	—
112	C₄×C₁₉	#408	1	4	yes	—
113	#540	—	2	8	no	—
114	C₂×#127	C₄×C₁₉	1	1	yes	characteristic
115	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
116	C₂×#123	—	2	2	no	—
117	C₂×#121	—	2	2	no	—
118	C₂×#121	C₄×C₁₉	1	2	yes	—
119	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
120	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
121	#431	C₂²×C₁₉	1	4	yes	—
122	D₄⋊C₈	—	2	8	no	—
123	#324	—	2	2	no	—
124	#323	—	2	2	no	—
125	C₂×C₁₉	—	2	2	no	—
126	C₂×C₁₉	—	8	1	no	—
127	C₂×C₁₉	—	8	4	no	—
128	C₂×C₁₉	#1780	1	1	yes	characteristic
129	C₂×C₁₉	#1795	1	2	yes	—
130	C₂²×D₄	—	2	2	no	—
131	C₂²×D₄	—	2	2	no	—
132	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
133	C₂³×C₄	—	2	2	no	—
134	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
135	#127	—	2	4	no	—
136	#125	—	2	4	no	—
137	#123	—	2	16	no	—
138	#121	—	2	16	no	—
139	#121	—	2	4	no	—
140	#121	—	2	4	no	—
141	C₄×D₄	—	2	4	no	—
142	C₄×D₄	D₄×C₁₉	1	8	yes	—
143	#117	—	2	4	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
146	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
147	C₂×C₂²⋊C₄	—	2	2	no	—
148	C₂×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
150	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
151	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
152	C₄⋊C₈	—	2	4	no	—
153	C₂²⋊C₈	—	2	4	no	—
154	C₄×C₈	—	2	4	no	—
155	C₁₉	#8326	1	1	yes	characteristic, direct product factor, Sylow
156	C₂⁴	—	2	2	no	—
157	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
158	C₂×D₄	—	2	8	no	—
159	C₂×D₄	—	2	8	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	—	2	8	no	—
162	C₂×D₄	—	8	4	no	—
163	C₂×D₄	—	8	4	no	—
164	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	2	8	no	—
169	C₂²×C₄	—	8	4	no	—
170	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
171	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
172	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
173	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
174	C₂×C₈	—	4	4	no	—
175	C₄⋊C₄	—	2	8	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
179	C₂²⋊C₄	—	2	8	no	—
180	C₂²⋊C₄	—	2	8	no	—
181	C₂²⋊C₄	—	2	4	no	—
182	C₄²	—	2	2	no	—
183	C₄²	C₂×D₄×C₁₉	1	4	yes	—
184	C₂³	—	2	1	no	—
185	C₂³	—	2	4	no	—
186	C₂³	—	2	2	no	—
187	C₂³	—	4	4	no	—
188	C₂³	—	4	4	no	—
189	C₂³	—	4	2	no	—
190	C₂³	—	4	4	no	—
191	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
192	D₄	—	2	8	no	—
193	D₄	—	4	4	no	—
194	D₄	—	8	8	no	—
195	D₄	—	8	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	8	8	no	—
205	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
206	C₂×C₄	C₁₉×#120	1	4	yes	—
207	C₂×C₄	C₁₉×#131	1	4	yes	—
208	C₈	—	8	4	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	4	1	no	—
211	C₂²	—	4	4	no	—
212	C₂²	—	4	4	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	8	no	—
217	C₂²	C₁₉×#379	1	1	yes	characteristic
218	C₂²	C₁₉×#408	1	2	yes	—
219	C₄	—	2	4	no	—
220	C₄	—	4	1	no	—
221	C₄	—	4	4	no	—
222	C₄	—	4	2	no	—
223	C₄	C₁₉×#408	1	4	yes	—
224	C₂	—	2	2	no	—
225	C₂	—	8	4	no	—
226	C₂	—	8	1	no	—
227	C₂	C₁₉×#1780	1	1	yes	characteristic
228	C₂	C₁₉×#1795	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#540

C₂

yes

maximal, characteristic

C₁₉×#1478

C₂

yes

maximal, complemented

C₁₉×#1458

C₂

yes

maximal, complemented

C₁₉×#540

—

C₂×C₁₉×#127

C₄

yes

characteristic

C₂×C₁₉×#125

C₄

yes

characteristic

C₂×C₁₉×#123

—

C₂×C₁₉×#121

—

C₂×C₁₉×#121

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

—

C₁₉×D₄⋊C₈

—

C₁₉×#324

—

C₁₉×#323

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#127

—

C₁₉×#125

—

C₁₉×#123

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

D₄

yes

—

C₁₉×#117

—

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

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

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

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

#8326

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₂×#540

C₂×C₁₉

yes

characteristic

#1478

C₂×C₁₉

yes

complemented

#1458

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

#379

yes

characteristic

107

C₂²×C₁₉

#408

yes

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

#408

yes

—

113

#540

—

114

C₂×#127

C₄×C₁₉

yes

characteristic

115

C₂×#125

C₄×C₁₉

yes

characteristic

116

C₂×#123

—

117

C₂×#121

—

118

C₂×#121

C₄×C₁₉

yes

—

119

C₂×C₄×D₄

C₂²×C₁₉

yes

—

120

C₂×#117

C₂²×C₁₉

yes

characteristic

121

#431

C₂²×C₁₉

yes

—

122

D₄⋊C₈

—

123

#324

—

124

#323

—

125

C₂×C₁₉

—

126

C₂×C₁₉

—

127

C₂×C₁₉

—

128

C₂×C₁₉

#1780

yes

characteristic

129

C₂×C₁₉

#1795

yes

—

130

C₂²×D₄

—

131

C₂²×D₄

—

132

C₂²×D₄

C₂×C₄×C₁₉

yes

—

133

C₂³×C₄

—

134

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

135

#127

—

136

#125

—

137

#123

—

138

#121

—

139

#121

—

140

#121

—

141

C₄×D₄

—

142

C₄×D₄

D₄×C₁₉

yes

—

143

#117

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

146

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

150

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

151

C₂×C₄²

C₂³×C₁₉

yes

characteristic

152

C₄⋊C₈

—

153

C₂²⋊C₈

—

154

C₄×C₈

—

155

C₁₉

#8326

yes

characteristic, direct product factor, Sylow

156

C₂⁴

—

157

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

C₂²⋊C₄×C₁₉

yes

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

171

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

172

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

173

C₂²×C₄

C₂×D₄×C₁₉

yes

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

C₂²⋊C₄×C₁₉

yes

—

179

C₂²⋊C₄

—

180

C₂²⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

C₂×D₄×C₁₉

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

192

D₄

—

193

D₄

—

194

D₄

—

195

D₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

—

206

C₂×C₄

C₁₉×#120

yes

—

207

C₂×C₄

C₁₉×#131

yes

—

208

C₈

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₁₉×#379

yes

characteristic

218

C₂²

C₁₉×#408

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

C₁₉×#408

yes

—

224

C₂

—

225

C₂

—

226

C₂

—

227

C₂

C₁₉×#1780

yes

characteristic

228

C₂

C₁₉×#1795

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#540	C₂
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

C₂×C₁₉×#540

C₂

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1478	C₂	semidirect
3. C₁₉×#1458	C₂	semidirect
69. #8326	C₁₉	direct (N × H)
96. #1478	C₂×C₁₉	semidirect
97. #1458	C₂×C₁₉	semidirect
155. C₁₉	#8326	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1478

C₂

semidirect

3. C₁₉×#1458

C₂

semidirect

69. #8326

C₁₉

direct (N × H)

96. #1478

C₂×C₁₉

semidirect

97. #1458

C₂×C₁₉

semidirect

155. C₁₉

#8326

direct (N × H)

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

subgroup	index
C₂×C₁₉×#540	2
C₁₉×#1478	2
C₁₉×#1458	2
#8326	19

subgroup

index

C₂×C₁₉×#540

C₁₉×#1478

C₁₉×#1458

#8326

Subgroups — C₁₉×#8326 #18014285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8326 #18014285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8326 #18014285