Group #18069069 — subgroups

Subgroups — #18069069

Order 4864.

474 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 175 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	C₄×C₂²⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
2	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	4	yes	—
4	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
5	#11926299	—	2	2	no	—
6	C₂³×C₈×C₁₉	C₄	1	2	yes	—
7	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#336	—	2	2	no	—
9	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
11	C₂²×C₈×C₁₉	—	2	2	no	—
12	C₂²×C₈×C₁₉	—	2	2	no	—
13	C₂²×C₈×C₁₉	—	4	2	no	—
14	C₂²×C₈×C₁₉	—	4	2	no	—
15	C₂²×C₈×C₁₉	C₈	1	4	yes	complemented
16	C₂×C₄²×C₁₉	—	4	2	no	—
17	C₂×C₄²×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
20	C₂²×C₁₉⋊C₈	—	2	4	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
22	C₂²⋊(C₁₉⋊C₈)	C₈	1	8	yes	complemented
23	C₄×C₁₉⋊C₈	—	4	4	no	—
24	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	—	4	2	no	—
29	C₂²×C₄×C₁₉	—	4	2	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
35	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
36	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
37	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
38	C₂×C₈×C₁₉	—	2	4	no	—
39	C₂×C₈×C₁₉	—	4	4	no	—
40	C₂×C₈×C₁₉	—	4	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	4	4	no	—
43	C₄²×C₁₉	—	2	4	no	—
44	C₄²×C₁₉	—	4	1	no	—
45	C₄²×C₁₉	—	4	1	no	—
46	C₂×C₁₉⋊C₈	—	2	8	no	—
47	C₂×C₁₉⋊C₈	—	4	4	no	—
48	C₂×C₁₉⋊C₈	—	4	4	no	—
49	#7016	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	—	2	1	no	—
51	C₂³×C₁₉	—	2	1	no	—
52	C₂³×C₁₉	—	2	2	no	—
53	C₂³×C₁₉	#95	1	1	yes	characteristic
54	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
55	C₂³×C₁₉	C₄×C₈	1	2	yes	—
56	C₂³×C₁₉	#97	1	1	yes	characteristic
57	C₂³×C₁₉	#97	1	2	yes	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	4	4	no	—
69	C₂×C₄×C₁₉	—	4	4	no	—
70	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
71	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
72	C₂×C₄×C₁₉	#99	1	2	yes	—
73	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
76	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
77	C₈×C₁₉	—	4	4	no	—
78	C₁₉⋊C₈	—	4	8	no	—
79	C₄×C₂²⋊C₈	—	19	2	no	—
80	C₂×#336	D₁₉	1	1	yes	characteristic
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	—	2	1	no	—
85	C₂²×C₁₉	—	2	2	no	—
86	C₂²×C₁₉	—	2	2	no	—
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	—	2	2	no	—
89	C₂²×C₁₉	C₈²	1	1	yes	characteristic
90	C₂²×C₁₉	#322	1	1	yes	characteristic
91	C₂²×C₁₉	#322	1	2	yes	—
92	C₂²×C₁₉	#336	1	2	yes	—
93	C₂²×C₁₉	#336	1	1	yes	characteristic
94	C₂²×C₁₉	#342	1	1	yes	characteristic
95	C₂²×C₁₉	#343	1	1	yes	characteristic
96	C₂²×C₁₉	#344	1	2	yes	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	2	4	no	—
99	C₄×C₁₉	—	2	4	no	—
100	C₄×C₁₉	#323	1	2	yes	—
101	C₄×C₁₉	#324	1	2	yes	—
102	C₂³×C₈	Dic₁₉	1	2	yes	—
103	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
104	C₂×C₂²⋊C₈	—	19	4	no	—
105	C₂×C₄×C₈	—	38	2	no	—
106	#336	—	2	2	no	—
107	#336	—	38	2	no	—
108	C₂×C₁₉	—	2	1	no	—
109	C₂×C₁₉	—	2	1	no	—
110	C₂×C₁₉	—	2	2	no	—
111	C₂×C₁₉	#1273	1	1	yes	characteristic
112	C₂×C₁₉	#1280	1	1	yes	characteristic
113	C₂×C₁₉	#1281	1	1	yes	characteristic
114	C₂×C₁₉	#1282	1	2	yes	—
115	C₂×C₁₉	#1283	1	2	yes	—
116	C₂³×C₄	C₄×D₁₉	1	2	yes	—
117	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
118	C₂²×C₈	—	2	2	no	—
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	4	2	no	—
121	C₂²×C₈	—	4	2	no	—
122	C₂²×C₈	—	38	4	no	—
123	C₂²×C₈	C₁₉⋊C₈	1	4	yes	complemented
124	C₂×C₄²	—	4	2	no	—
125	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
126	C₂×C₄²	D₇₆	1	1	yes	characteristic
127	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
128	C₂²⋊C₈	—	19	8	no	—
129	C₂²⋊C₈	—	38	4	no	—
130	C₄×C₈	—	76	4	no	—
131	C₁₉	#7016	1	1	yes	characteristic, complemented, Sylow
132	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
133	C₂²×C₄	—	2	1	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	—	4	2	no	—
137	C₂²×C₄	—	4	2	no	—
138	C₂²×C₄	C₈×D₁₉	1	4	yes	—
139	C₂²×C₄	#64515	1	4	yes	—
140	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
141	C₂²×C₄	#64520	1	2	yes	—
142	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
143	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
144	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
145	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	—	4	4	no	—
148	C₂×C₈	—	4	2	no	—
149	C₂×C₈	—	4	2	no	—
150	C₂×C₈	—	4	4	no	—
151	C₂×C₈	—	38	8	no	—
152	C₂×C₈	—	76	4	no	—
153	C₂×C₈	—	76	4	no	—
154	C₄²	—	2	4	no	—
155	C₄²	—	4	1	no	—
156	C₄²	—	4	1	no	—
157	C₂³	—	2	1	no	—
158	C₂³	—	2	1	no	—
159	C₂³	—	2	2	no	—
160	C₂³	C₄×C₁₉⋊C₈	1	1	yes	characteristic
161	C₂³	#10597260	1	1	yes	characteristic
162	C₂³	C₈×Dic₁₉	1	2	yes	—
163	C₂³	#10597272	1	2	yes	—
164	C₂³	C₁₉⋊#95	1	1	yes	characteristic
165	C₂×C₄	—	2	2	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	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
178	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
179	C₂×C₄	(C₂×D₁₉)⋊C₈	1	4	yes	—
180	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
181	C₂×C₄	#10597290	1	1	yes	characteristic
182	C₂×C₄	#10597291	1	2	yes	—
183	C₂×C₄	#10597293	1	1	yes	characteristic
184	C₈	—	4	4	no	—
185	C₈	—	76	8	no	—
186	C₂²	—	2	1	no	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	2	2	no	—
193	C₂²	—	2	2	no	—
194	C₂²	C₈×C₁₉⋊C₈	1	1	yes	characteristic
195	C₂²	#11926265	1	1	yes	characteristic
196	C₂²	#11926266	1	2	yes	—
197	C₂²	#11926298	1	2	yes	—
198	C₂²	#11926299	1	1	yes	characteristic
199	C₂²	#11926311	1	1	yes	characteristic
200	C₂²	#11926313	1	1	yes	characteristic
201	C₂²	#11926315	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	2	4	no	—
204	C₄	—	2	4	no	—
205	C₄	#11926268	1	2	yes	—
206	C₄	#11926270	1	2	yes	—
207	C₂	—	2	1	no	—
208	C₂	—	2	1	no	—
209	C₂	—	2	2	no	—
210	C₂	C₁₉⋊#1273	1	1	yes	characteristic
211	C₂	#14561478	1	1	yes	characteristic
212	C₂	#14561480	1	1	yes	characteristic
213	C₂	#14561482	1	2	yes	—
214	C₂	#14561485	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₂²⋊(C₁₉⋊C₈)

C₂

yes

maximal

C₂×C₁₉×#336

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

—

#11926299

—

C₂³×C₈×C₁₉

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₈

yes

complemented

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₈

yes

complemented

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₄²

yes

characteristic

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

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7016

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂³×C₁₉

C₄×C₈

yes

—

C₂³×C₁₉

#97

yes

characteristic

C₂³×C₁₉

#97

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

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₄×C₂²⋊C₈

—

C₂×#336

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₈²

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#336

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#323

yes

—

101

C₄×C₁₉

#324

yes

—

102

C₂³×C₈

Dic₁₉

yes

—

103

C₂²×C₄²

C₂×D₁₉

yes

characteristic

104

C₂×C₂²⋊C₈

—

105

C₂×C₄×C₈

—

106

#336

—

107

#336

—

108

C₂×C₁₉

—

109

C₂×C₁₉

—

110

C₂×C₁₉

—

111

C₂×C₁₉

#1273

yes

characteristic

112

C₂×C₁₉

#1280

yes

characteristic

113

C₂×C₁₉

#1281

yes

characteristic

114

C₂×C₁₉

#1282

yes

—

115

C₂×C₁₉

#1283

yes

—

116

C₂³×C₄

C₄×D₁₉

yes

—

117

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

118

C₂²×C₈

—

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

C₁₉⋊C₈

yes

complemented

124

C₂×C₄²

—

125

C₂×C₄²

Dic₃₈

yes

characteristic

126

C₂×C₄²

D₇₆

yes

characteristic

127

C₂×C₄²

C₂²⋊D₁₉

yes

—

128

C₂²⋊C₈

—

129

C₂²⋊C₈

—

130

C₄×C₈

—

131

C₁₉

#7016

yes

characteristic, complemented, Sylow

132

C₂⁴

C₄×Dic₁₉

yes

characteristic

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

C₈×D₁₉

yes

—

139

C₂²×C₄

#64515

yes

—

140

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

141

C₂²×C₄

#64520

yes

—

142

C₂²×C₄

Dic₁₉⋊C₄

yes

—

143

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

144

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

145

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

C₄×C₁₉⋊C₈

yes

characteristic

161

C₂³

#10597260

yes

characteristic

162

C₂³

C₈×Dic₁₉

yes

—

163

C₂³

#10597272

yes

—

164

C₂³

C₁₉⋊#95

yes

characteristic

165

C₂×C₄

—

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

—

176

C₂×C₄

—

177

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

178

C₂×C₄

Dic₁₉⋊C₈

yes

—

179

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

—

180

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

181

C₂×C₄

#10597290

yes

characteristic

182

C₂×C₄

#10597291

yes

—

183

C₂×C₄

#10597293

yes

characteristic

184

C₈

—

185

C₈

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

C₈×C₁₉⋊C₈

yes

characteristic

195

C₂²

#11926265

yes

characteristic

196

C₂²

#11926266

yes

—

197

C₂²

#11926298

yes

—

198

C₂²

#11926299

yes

characteristic

199

C₂²

#11926311

yes

characteristic

200

C₂²

#11926313

yes

characteristic

201

C₂²

#11926315

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

#11926268

yes

—

206

C₄

#11926270

yes

—

207

C₂

—

208

C₂

—

209

C₂

—

210

C₂

C₁₉⋊#1273

yes

characteristic

211

C₂

#14561478

yes

characteristic

212

C₂

#14561480

yes

characteristic

213

C₂

#14561482

yes

—

214

C₂

#14561485

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂²×C₁₉	C₈²
Frattini	C₂²×C₄²	C₂×D₁₉
Fitting	C₂×C₁₉×#336	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₄²
cosocle	C₂²×C₄²×C₁₉	C₂²
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#7016
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#336

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₁₉

commutator

C₂²×C₁₉

C₈²

Frattini

C₂²×C₄²

C₂×D₁₉

Fitting

C₂×C₁₉×#336

C₂

socle

C₂³×C₁₉

#95

prime radical

C₂⁴×C₁₉

C₄²

cosocle

C₂²×C₄²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#336

N	H ≅ G/N	type
15. C₂²×C₈×C₁₉	C₈	semidirect
22. C₂²⋊(C₁₉⋊C₈)	C₈	semidirect
123. C₂²×C₈	C₁₉⋊C₈	semidirect
131. C₁₉	#7016	semidirect

H ≅ G/N

type

15. C₂²×C₈×C₁₉

C₈

semidirect

22. C₂²⋊(C₁₉⋊C₈)

C₈

semidirect

123. C₂²×C₈

C₁₉⋊C₈

semidirect

131. C₁₉

#7016

semidirect

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

subgroup	index
C₄×C₂²⋊(C₁₉⋊C₈)	2
C₂×C₁₉×#336	2
#7016	19

subgroup

index

C₄×C₂²⋊(C₁₉⋊C₈)

C₂×C₁₉×#336

#7016

Subgroups — #18069069

Conjugacy classes of subgroups

Complements

Maximal subgroups