Group #18017447 — subgroups

Subgroups — C₁₉×#11488 #18017447

Order 4864.

418 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 142 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×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2163	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1314	C₂	1	4	yes	maximal, complemented
4	C₂³×C₈×C₁₉	C₄	1	2	yes	—
5	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
6	C₈×D₄×C₁₉	—	2	2	no	—
7	C₈×D₄×C₁₉	—	2	2	no	—
8	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×C₄⋊C₁₆	—	2	2	no	—
12	C₁₉×C₂²⋊C₁₆	C₂²	1	4	yes	—
13	C₁₉×#346	—	2	2	no	—
14	C₂²×D₄×C₁₉	C₈	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	—	4	4	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄×D₄×C₁₉	—	2	2	no	—
23	C₄×D₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	C₈	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₉	C₈	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₆×C₁₉	—	2	4	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₂²⋊C₈	—	2	4	no	—
30	C₄×C₈×C₁₉	D₄	1	2	yes	—
31	C₄×C₈×C₁₉	D₄	1	2	yes	—
32	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
33	C₂×D₄×C₁₉	—	2	4	no	—
34	C₂×D₄×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	—	4	2	no	—
39	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	4	1	no	—
46	C₂×C₈×C₁₉	—	4	4	no	—
47	C₂×C₈×C₁₉	—	4	4	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂²⋊C₄×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₄²×C₁₉	M₁₆	1	2	yes	—
56	C₁₆×C₁₉	—	4	4	no	—
57	#11488	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂³×C₁₉	—	2	2	no	—
59	C₂³×C₁₉	—	2	2	no	—
60	C₂³×C₁₉	—	4	2	no	—
61	C₂³×C₁₉	—	4	2	no	—
62	C₂³×C₁₉	M₃₂	1	4	yes	—
63	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
64	D₄×C₁₉	—	2	8	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	4	1	no	—
70	C₂×C₄×C₁₉	—	4	4	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
75	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
78	C₈×C₁₉	—	2	2	no	—
79	C₈×C₁₉	—	2	1	no	—
80	C₈×C₁₉	—	4	2	no	—
81	C₈×C₁₉	#100	1	2	yes	—
82	C₂×C₈×D₄	C₂×C₁₉	1	1	yes	characteristic
83	#2163	C₂×C₁₉	1	2	yes	complemented
84	#1314	C₂×C₁₉	1	4	yes	complemented
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	4	no	—
88	C₂²×C₁₉	—	4	4	no	—
89	C₂²×C₁₉	—	4	4	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
93	C₂²×C₁₉	C₂×M₃₂	1	2	yes	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	#410	1	1	yes	characteristic
99	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
100	C₂³×C₈	C₄×C₁₉	1	2	yes	—
101	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
102	C₈×D₄	—	2	2	no	—
103	C₈×D₄	—	2	2	no	—
104	C₂×C₄⋊C₈	C₄×C₁₉	1	1	yes	characteristic
105	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
106	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
107	C₄⋊C₁₆	—	2	2	no	—
108	C₂²⋊C₁₆	C₂²×C₁₉	1	4	yes	—
109	#346	—	2	2	no	—
110	C₂×C₁₉	—	2	2	no	—
111	C₂×C₁₉	—	4	4	no	—
112	C₂×C₁₉	#1460	1	1	yes	characteristic
113	C₂×C₁₉	#2112	1	1	yes	characteristic
114	C₂×C₁₉	#2115	1	1	yes	characteristic
115	C₂²×D₄	C₈×C₁₉	1	1	yes	characteristic
116	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
117	C₂²×C₈	—	2	2	no	—
118	C₂²×C₈	—	2	2	no	—
119	C₂²×C₈	—	4	4	no	—
120	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
121	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
122	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
123	C₄×D₄	—	2	2	no	—
124	C₄×D₄	—	2	2	no	—
125	C₂×C₄⋊C₄	C₈×C₁₉	1	1	yes	characteristic
126	C₂×C₂²⋊C₄	C₈×C₁₉	1	2	yes	—
127	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
128	C₂×C₁₆	—	2	4	no	—
129	C₄⋊C₈	—	2	2	no	—
130	C₂²⋊C₈	—	2	4	no	—
131	C₄×C₈	D₄×C₁₉	1	2	yes	—
132	C₄×C₈	D₄×C₁₉	1	2	yes	—
133	C₁₉	#11488	1	1	yes	characteristic, direct product factor, Sylow
134	C₂⁴	C₂×C₈×C₁₉	1	2	yes	—
135	C₂×D₄	—	2	4	no	—
136	C₂×D₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
142	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
143	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
144	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	4	1	no	—
148	C₂×C₈	—	4	4	no	—
149	C₂×C₈	—	4	4	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
152	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
153	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
154	C₄⋊C₄	—	2	2	no	—
155	C₂²⋊C₄	—	2	4	no	—
156	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
157	C₄²	M₁₆×C₁₉	1	2	yes	—
158	C₁₆	—	4	4	no	—
159	C₂³	—	2	2	no	—
160	C₂³	—	2	2	no	—
161	C₂³	—	4	2	no	—
162	C₂³	—	4	2	no	—
163	C₂³	C₁₉×M₃₂	1	4	yes	—
164	C₂³	C₂²×C₈×C₁₉	1	1	yes	characteristic
165	D₄	—	2	8	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
176	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
177	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
178	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
179	C₈	—	2	2	no	—
180	C₈	—	2	1	no	—
181	C₈	—	4	2	no	—
182	C₈	C₁₉×#100	1	2	yes	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	1	no	—
185	C₂²	—	2	4	no	—
186	C₂²	—	4	4	no	—
187	C₂²	—	4	4	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
191	C₂²	C₂×C₁₉×M₃₂	1	2	yes	—
192	C₄	—	2	1	no	—
193	C₄	—	2	2	no	—
194	C₄	—	2	2	no	—
195	C₄	—	4	2	no	—
196	C₄	C₁₉×#410	1	1	yes	characteristic
197	C₄	C₂×C₁₉×#100	1	1	yes	characteristic
198	C₂	—	2	2	no	—
199	C₂	—	4	4	no	—
200	C₂	C₁₉×#1460	1	1	yes	characteristic
201	C₂	C₁₉×#2112	1	1	yes	characteristic
202	C₂	C₁₉×#2115	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₄×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, complemented

C₁₉×#1314

C₂

yes

maximal, complemented

C₂³×C₈×C₁₉

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₈×D₄×C₁₉

—

C₈×D₄×C₁₉

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

C₂²

yes

—

C₁₉×#346

—

C₂²×D₄×C₁₉

C₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₈

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂⁴×C₁₉

C₂×C₈

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

M₁₆

yes

—

C₁₆×C₁₉

—

#11488

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

M₃₂

yes

—

C₂³×C₁₉

C₂²×C₈

yes

characteristic

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

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#100

yes

—

C₂×C₈×D₄

C₂×C₁₉

yes

characteristic

#2163

C₂×C₁₉

yes

complemented

#1314

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₁₉

C₂×M₃₂

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

100

C₂³×C₈

C₄×C₁₉

yes

—

101

C₂×C₄×D₄

C₄×C₁₉

yes

characteristic

102

C₈×D₄

—

103

C₈×D₄

—

104

C₂×C₄⋊C₈

C₄×C₁₉

yes

characteristic

105

C₂×C₂²⋊C₈

C₂²×C₁₉

yes

—

106

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

107

C₄⋊C₁₆

—

108

C₂²⋊C₁₆

C₂²×C₁₉

yes

—

109

#346

—

110

C₂×C₁₉

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#1460

yes

characteristic

113

C₂×C₁₉

#2112

yes

characteristic

114

C₂×C₁₉

#2115

yes

characteristic

115

C₂²×D₄

C₈×C₁₉

yes

characteristic

116

C₂³×C₄

C₂×C₄×C₁₉

yes

—

117

C₂²×C₈

—

118

C₂²×C₈

—

119

C₂²×C₈

—

120

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

121

C₂²×C₈

C₂×C₄×C₁₉

yes

—

122

C₂²×C₈

C₂³×C₁₉

yes

characteristic

123

C₄×D₄

—

124

C₄×D₄

—

125

C₂×C₄⋊C₄

C₈×C₁₉

yes

characteristic

126

C₂×C₂²⋊C₄

C₈×C₁₉

yes

—

127

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

128

C₂×C₁₆

—

129

C₄⋊C₈

—

130

C₂²⋊C₈

—

131

C₄×C₈

D₄×C₁₉

yes

—

132

C₄×C₈

D₄×C₁₉

yes

—

133

C₁₉

#11488

yes

characteristic, direct product factor, Sylow

134

C₂⁴

C₂×C₈×C₁₉

yes

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

142

C₂²×C₄

C₂×C₈×C₁₉

yes

—

143

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

144

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

152

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

153

C₂×C₈

C₂×D₄×C₁₉

yes

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₄²

C₂²⋊C₄×C₁₉

yes

—

157

C₄²

M₁₆×C₁₉

yes

—

158

C₁₆

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

C₁₉×M₃₂

yes

—

164

C₂³

C₂²×C₈×C₁₉

yes

characteristic

165

D₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₁₉×C₂²⋊C₈

yes

—

176

C₂×C₄

C₁₉×C₂²⋊C₈

yes

—

177

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

178

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

C₁₉×#100

yes

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

C₂×C₁₉×C₂²⋊C₈

yes

characteristic

191

C₂²

C₂×C₁₉×M₃₂

yes

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

C₁₉×#410

yes

characteristic

197

C₄

C₂×C₁₉×#100

yes

characteristic

198

C₂

—

199

C₂

—

200

C₂

C₁₉×#1460

yes

characteristic

201

C₂

C₁₉×#2112

yes

characteristic

202

C₂

C₁₉×#2115

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₈
prime radical	C₂²×D₄×C₁₉	C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₈×C₁₉

Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

socle

C₂²×C₁₉

C₂×C₂²⋊C₈

prime radical

C₂²×D₄×C₁₉

C₈

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2163	C₂	semidirect
3. C₁₉×#1314	C₂	semidirect
57. #11488	C₁₉	direct (N × H)
83. #2163	C₂×C₁₉	semidirect
84. #1314	C₂×C₁₉	semidirect
133. C₁₉	#11488	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2163

C₂

semidirect

3. C₁₉×#1314

C₂

semidirect

57. #11488

C₁₉

direct (N × H)

83. #2163

C₂×C₁₉

semidirect

84. #1314

C₂×C₁₉

semidirect

133. C₁₉

#11488

direct (N × H)

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

subgroup	index
C₂×C₈×D₄×C₁₉	2
C₁₉×#2163	2
C₁₉×#1314	2
#11488	19

subgroup

index

C₂×C₈×D₄×C₁₉

C₁₉×#2163

C₁₉×#1314

#11488

Subgroups — C₁₉×#11488 #18017447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11488 #18017447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11488 #18017447