Group #18014297 — subgroups

Subgroups — C₁₉×#8338 #18014297

Order 4864.

814 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 174 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×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1749	C₂	1	2	yes	maximal
3	C₂×C₁₉×#330	C₂	1	4	yes	maximal, complemented
4	C₁₉×#533	—	2	8	no	—
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	2	yes	—
6	C₂×C₁₉×#125	C₂²	1	2	yes	—
7	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
8	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
9	C₂×C₁₉×#117	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
12	C₂×C₁₉×#97	C₂²	1	4	yes	—
13	C₁₉×#336	—	2	2	no	—
14	C₁₉×#330	—	2	8	no	—
15	C₂²×Q₈×C₁₉	—	2	2	no	—
16	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	D₄	1	2	yes	—
18	C₂²×C₈×C₁₉	—	2	4	no	—
19	C₁₉×C₄⋊Q₈	—	2	8	no	—
20	C₁₉×#125	—	2	4	no	—
21	C₁₉×#125	D₄	1	8	yes	—
22	C₁₉×C₂²⋊Q₈	—	2	16	no	—
23	C₄×Q₈×C₁₉	—	2	16	no	—
24	C₁₉×#117	—	2	8	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	—	2	2	no	—
30	C₂×C₄²×C₁₉	—	2	4	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₁₉×C₂²⋊C₈	—	2	8	no	—
35	C₁₉×#97	—	2	8	no	—
36	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Q₈×C₁₉	—	2	8	no	—
38	C₂×Q₈×C₁₉	—	4	4	no	—
39	C₂×Q₈×C₁₉	—	4	4	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	4	no	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	—	2	4	no	—
46	C₂²×C₄×C₁₉	—	4	2	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	C₂×C₈×C₁₉	—	2	8	no	—
52	C₂×C₈×C₁₉	—	4	4	no	—
53	C₂×C₈×C₁₉	—	4	4	no	—
54	C₄⋊C₄×C₁₉	—	2	8	no	—
55	C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₄⋊C₄×C₁₉	—	2	16	no	—
57	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
58	C₂²⋊C₄×C₁₉	—	2	8	no	—
59	C₄²×C₁₉	—	2	8	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	4	no	—
62	C₄²×C₁₉	C₂×D₄	1	4	yes	—
63	#8338	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂³×C₁₉	—	2	1	no	—
65	C₂³×C₁₉	—	2	1	no	—
66	C₂³×C₁₉	—	2	2	no	—
67	C₂³×C₁₉	—	2	2	no	—
68	C₂³×C₁₉	#101	1	2	yes	—
69	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	16	no	—
71	C₂×C₄×C₁₉	—	2	8	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	8	no	—
81	C₂×C₄×C₁₉	—	4	8	no	—
82	C₂×C₄×C₁₉	—	4	4	no	—
83	C₂×C₄×C₁₉	—	4	4	no	—
84	C₂×C₄×C₁₉	#101	1	2	yes	—
85	C₂×C₄×C₁₉	#104	1	4	yes	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
87	C₂×C₄×C₁₉	#120	1	4	yes	—
88	C₈×C₁₉	—	4	8	no	—
89	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
90	#1749	C₂×C₁₉	1	2	yes	—
91	C₂×#330	C₂×C₁₉	1	4	yes	complemented
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	2	4	no	—
94	C₂²×C₁₉	—	4	1	no	—
95	C₂²×C₁₉	—	4	1	no	—
96	C₂²×C₁₉	—	4	2	no	—
97	C₂²×C₁₉	#379	1	1	yes	characteristic
98	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
100	C₂²×C₁₉	C₂×#104	1	2	yes	—
101	C₂²×C₁₉	#421	1	2	yes	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	2	4	no	—
105	C₄×C₁₉	—	2	4	no	—
106	C₄×C₁₉	—	4	8	no	—
107	#533	—	2	8	no	—
108	C₂×C₄⋊Q₈	C₄×C₁₉	1	2	yes	—
109	C₂×#125	C₂²×C₁₉	1	2	yes	—
110	C₂×C₂²⋊Q₈	—	2	2	no	—
111	C₂×C₄×Q₈	—	2	2	no	—
112	C₂×#117	C₄×C₁₉	1	2	yes	—
113	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
114	C₂×C₂²⋊C₈	—	2	2	no	—
115	C₂×#97	C₂²×C₁₉	1	4	yes	—
116	#336	—	2	2	no	—
117	#330	—	2	8	no	—
118	C₂×C₁₉	—	4	2	no	—
119	C₂×C₁₉	#1526	1	1	yes	characteristic
120	C₂×C₁₉	#1531	1	2	yes	—
121	C₂×C₁₉	#1537	1	1	yes	characteristic
122	C₂×C₁₉	#1784	1	1	yes	characteristic
123	C₂×C₁₉	#1789	1	2	yes	—
124	C₂²×Q₈	—	2	2	no	—
125	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
126	C₂³×C₄	D₄×C₁₉	1	2	yes	—
127	C₂²×C₈	—	2	4	no	—
128	C₄⋊Q₈	—	2	8	no	—
129	#125	—	2	4	no	—
130	#125	D₄×C₁₉	1	8	yes	—
131	C₂²⋊Q₈	—	2	16	no	—
132	C₄×Q₈	—	2	16	no	—
133	#117	—	2	8	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	2	4	no	—
136	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
137	C₂×C₂²⋊C₄	—	2	2	no	—
138	C₂×C₄²	—	2	2	no	—
139	C₂×C₄²	—	2	4	no	—
140	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
141	C₂×C₄²	D₄×C₁₉	1	2	yes	—
142	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
143	C₂²⋊C₈	—	2	8	no	—
144	#97	—	2	8	no	—
145	C₁₉	#8338	1	1	yes	characteristic, direct product factor, Sylow
146	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
147	C₂×Q₈	—	2	8	no	—
148	C₂×Q₈	—	4	4	no	—
149	C₂×Q₈	—	4	4	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	2	4	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
159	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
160	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
161	C₂×C₈	—	2	8	no	—
162	C₂×C₈	—	4	4	no	—
163	C₂×C₈	—	4	4	no	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	2	16	no	—
167	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
168	C₂²⋊C₄	—	2	8	no	—
169	C₄²	—	2	8	no	—
170	C₄²	—	2	2	no	—
171	C₄²	—	2	4	no	—
172	C₄²	C₂×D₄×C₁₉	1	4	yes	—
173	C₂³	—	2	1	no	—
174	C₂³	—	2	1	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	C₁₉×#101	1	2	yes	—
178	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
179	Q₈	—	4	16	no	—
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	8	no	—
190	C₂×C₄	—	4	8	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	C₁₉×#101	1	2	yes	—
194	C₂×C₄	C₁₉×#104	1	4	yes	—
195	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
196	C₂×C₄	C₁₉×#120	1	4	yes	—
197	C₈	—	4	8	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	4	no	—
200	C₂²	—	4	1	no	—
201	C₂²	—	4	2	no	—
202	C₂²	—	4	1	no	—
203	C₂²	C₁₉×#379	1	1	yes	characteristic
204	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
205	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
206	C₂²	C₂×C₁₉×#104	1	2	yes	—
207	C₂²	C₁₉×#421	1	2	yes	—
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	2	4	no	—
211	C₄	—	2	4	no	—
212	C₄	—	4	8	no	—
213	C₂	—	4	2	no	—
214	C₂	C₁₉×#1526	1	1	yes	characteristic
215	C₂	C₁₉×#1531	1	2	yes	—
216	C₂	C₁₉×#1537	1	1	yes	characteristic
217	C₂	C₁₉×#1784	1	1	yes	characteristic
218	C₂	C₁₉×#1789	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#533

C₂

yes

maximal, characteristic

C₁₉×#1749

C₂

yes

maximal

C₂×C₁₉×#330

C₂

yes

maximal, complemented

C₁₉×#533

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

—

C₂×C₁₉×#125

C₂²

yes

—

C₂×C₁₉×C₂²⋊Q₈

—

C₂×C₄×Q₈×C₁₉

—

C₂×C₁₉×#117

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

—

C₁₉×#336

—

C₁₉×#330

—

C₂²×Q₈×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

#8338

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#101

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₈×C₁₉

—

C₂×#533

C₂×C₁₉

yes

characteristic

#1749

C₂×C₁₉

yes

—

C₂×#330

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

100

C₂²×C₁₉

C₂×#104

yes

—

101

C₂²×C₁₉

#421

yes

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

#533

—

108

C₂×C₄⋊Q₈

C₄×C₁₉

yes

—

109

C₂×#125

C₂²×C₁₉

yes

—

110

C₂×C₂²⋊Q₈

—

111

C₂×C₄×Q₈

—

112

C₂×#117

C₄×C₁₉

yes

—

113

C₂²×C₄²

C₂²×C₁₉

yes

characteristic

114

C₂×C₂²⋊C₈

—

115

C₂×#97

C₂²×C₁₉

yes

—

116

#336

—

117

#330

—

118

C₂×C₁₉

—

119

C₂×C₁₉

#1526

yes

characteristic

120

C₂×C₁₉

#1531

yes

—

121

C₂×C₁₉

#1537

yes

characteristic

122

C₂×C₁₉

#1784

yes

characteristic

123

C₂×C₁₉

#1789

yes

—

124

C₂²×Q₈

—

125

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

126

C₂³×C₄

D₄×C₁₉

yes

—

127

C₂²×C₈

—

128

C₄⋊Q₈

—

129

#125

—

130

#125

D₄×C₁₉

yes

—

131

C₂²⋊Q₈

—

132

C₄×Q₈

—

133

#117

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

137

C₂×C₂²⋊C₄

—

138

C₂×C₄²

—

139

C₂×C₄²

—

140

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

141

C₂×C₄²

D₄×C₁₉

yes

—

142

C₂×C₄²

C₂³×C₁₉

yes

characteristic

143

C₂²⋊C₈

—

144

#97

—

145

C₁₉

#8338

yes

characteristic, direct product factor, Sylow

146

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

158

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

159

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

160

C₂²×C₄

C₂×D₄×C₁₉

yes

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

C₂²⋊C₄×C₁₉

yes

—

168

C₂²⋊C₄

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

172

C₄²

C₂×D₄×C₁₉

yes

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

C₁₉×#101

yes

—

178

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

179

Q₈

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

C₁₉×#101

yes

—

194

C₂×C₄

C₁₉×#104

yes

—

195

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

—

196

C₂×C₄

C₁₉×#120

yes

—

197

C₈

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

C₁₉×#379

yes

characteristic

204

C₂²

C₂×C₁₉×#101

yes

characteristic

205

C₂²

C₂×C₁₉×#101

yes

characteristic

206

C₂²

C₂×C₁₉×#104

yes

—

207

C₂²

C₁₉×#421

yes

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₂

—

214

C₂

C₁₉×#1526

yes

characteristic

215

C₂

C₁₉×#1531

yes

—

216

C₂

C₁₉×#1537

yes

characteristic

217

C₂

C₁₉×#1784

yes

characteristic

218

C₂

C₁₉×#1789

yes

—

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

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₂×C₁₉×#330	C₂	semidirect
63. #8338	C₁₉	direct (N × H)
91. C₂×#330	C₂×C₁₉	semidirect
145. C₁₉	#8338	direct (N × H)

H ≅ G/N

type

3. C₂×C₁₉×#330

C₂

semidirect

63. #8338

C₁₉

direct (N × H)

91. C₂×#330

C₂×C₁₉

semidirect

145. C₁₉

#8338

direct (N × H)

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

subgroup	index
C₂×C₁₉×#533	2
C₁₉×#1749	2
C₂×C₁₉×#330	2
#8338	19

subgroup

index

C₂×C₁₉×#533

C₁₉×#1749

C₂×C₁₉×#330

#8338

Subgroups — C₁₉×#8338 #18014297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8338 #18014297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8338 #18014297