Group #18073115 — subgroups

Subgroups — #18073115

Order 4864.

430 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 161 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×Q₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597293	C₂	1	1	yes	maximal, characteristic
3	#14561925	C₂	1	2	yes	maximal
4	#14561484	C₂	1	2	yes	maximal
5	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₉⋊C₈	—	2	2	no	—
7	Q₈×C₁₉⋊C₈	—	2	2	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#10597293	C₄	1	2	yes	—
11	C₄×#64520	C₂²	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926313	C₄	1	2	yes	—
15	#11926266	—	2	2	no	—
16	#11926265	—	2	2	no	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	2	yes	—
19	C₁₉×#324	C₄	1	4	yes	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×#64520	C₂×C₄	1	4	yes	—
28	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
30	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
33	C₄×C₈×C₁₉	—	2	2	no	—
34	#10597293	—	2	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
37	#10597260	—	2	2	no	—
38	C₄×C₁₉⋊C₈	—	2	2	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
46	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
47	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄²×C₁₉	—	2	2	no	—
55	C₄²×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	C₂×D₄	1	2	yes	—
57	C₄²×C₁₉	#41	1	2	yes	—
58	#64520	—	2	4	no	—
59	#64520	—	2	4	no	—
60	C₂×C₁₉⋊C₈	—	2	2	no	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	C₂×C₁₉⋊C₈	—	4	1	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
67	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
68	#8165	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	Q₈×C₁₉	—	2	8	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	#97	1	4	yes	—
79	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
84	C₂×C₄×C₁₉	#131	1	2	yes	—
85	C₈×C₁₉	—	4	4	no	—
86	C₁₉⋊C₈	—	2	1	no	—
87	C₁₉⋊C₈	—	2	2	no	—
88	C₁₉⋊C₈	—	4	2	no	—
89	C₁₉⋊C₈	—	4	4	no	—
90	C₁₉⋊C₈	#101	1	2	yes	complemented
91	C₂×C₈×Q₈	—	19	1	no	—
92	C₄×#101	—	19	1	no	—
93	#1461	D₁₉	1	1	yes	characteristic
94	#1451	—	19	2	no	—
95	#1283	—	19	2	no	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
100	C₂²×C₁₉	#405	1	1	yes	characteristic
101	C₄×C₁₉	—	2	4	no	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
106	C₄×C₁₉	#413	1	1	yes	characteristic
107	C₄×C₁₉	#435	1	4	yes	—
108	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
109	C₈×Q₈	—	38	2	no	—
110	C₈×Q₈	—	38	2	no	—
111	#431	C₂×D₁₉	1	2	yes	—
112	C₂×C₄⋊C₈	—	19	2	no	—
113	C₂×C₄⋊C₈	—	19	1	no	—
114	C₂×#101	—	19	2	no	—
115	C₄×M₁₆	—	19	2	no	—
116	C₂×C₄×C₈	—	19	1	no	—
117	C₂×C₄×C₈	—	19	2	no	—
118	#343	—	19	2	no	—
119	#324	Dic₁₉	1	4	yes	—
120	#322	—	38	2	no	—
121	#322	—	38	2	no	—
122	C₂×C₁₉	—	2	1	no	—
123	C₂×C₁₉	—	2	1	no	—
124	C₂×C₁₉	#1752	1	1	yes	characteristic
125	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
126	C₂×C₁₉	#1757	1	1	yes	characteristic
127	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
128	C₂×M₁₆	—	19	4	no	—
129	C₂²×C₈	—	19	1	no	—
130	C₂²×C₈	—	19	1	no	—
131	C₂²×C₈	—	19	2	no	—
132	C₄×Q₈	—	2	2	no	—
133	C₄×Q₈	—	2	2	no	—
134	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
135	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
136	C₂×C₄²	C₄×D₁₉	1	2	yes	—
137	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
138	C₄⋊C₈	—	2	2	no	—
139	C₄⋊C₈	—	38	4	no	—
140	C₄⋊C₈	—	38	2	no	—
141	#101	—	38	4	no	—
142	C₂²⋊C₈	C₂×Dic₁₉	1	4	yes	—
143	#97	—	38	2	no	—
144	C₄×C₈	—	2	2	no	—
145	C₄×C₈	—	19	2	no	—
146	C₄×C₈	—	19	2	no	—
147	C₄×C₈	—	38	2	no	—
148	C₄×C₈	—	38	2	no	—
149	C₄×C₈	—	38	2	no	—
150	C₁₉	#8165	1	1	yes	characteristic, complemented, Sylow
151	C₂×Q₈	—	2	2	no	—
152	C₂×Q₈	—	2	2	no	—
153	C₂×Q₈	#64515	1	4	yes	—
154	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
155	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
156	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
159	M₁₆	—	38	4	no	—
160	M₁₆	—	38	4	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	19	1	no	—
163	C₂×C₈	—	19	1	no	—
164	C₂×C₈	—	19	2	no	—
165	C₂×C₈	—	38	2	no	—
166	C₂×C₈	—	38	2	no	—
167	C₂×C₈	—	38	4	no	—
168	C₂×C₈	—	76	1	no	—
169	C₂×C₈	—	76	2	no	—
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	2	2	no	—
174	C₄²	D₄×D₁₉	1	2	yes	—
175	C₄²	#64543	1	2	yes	—
176	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
177	Q₈	—	2	8	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	1	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	#10597272	1	4	yes	—
186	C₂×C₄	#10597323	1	1	yes	characteristic
187	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
188	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
189	C₂×C₄	C₂×#64515	1	2	yes	—
190	C₂×C₄	#10597353	1	2	yes	—
191	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
192	C₈	—	4	4	no	—
193	C₈	—	19	2	no	—
194	C₈	—	38	1	no	—
195	C₈	—	38	2	no	—
196	C₈	—	76	4	no	—
197	C₈	—	76	2	no	—
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
201	C₂²	C₂×#10597272	1	1	yes	characteristic
202	C₂²	#11926502	1	1	yes	characteristic
203	C₄	—	2	4	no	—
204	C₄	—	2	1	no	—
205	C₄	—	2	2	no	—
206	C₄	—	4	2	no	—
207	C₄	#101×D₁₉	1	1	yes	characteristic
208	C₄	#11926527	1	1	yes	characteristic
209	C₄	#11926612	1	4	yes	—
210	C₂	—	2	1	no	—
211	C₂	—	2	1	no	—
212	C₂	#14563414	1	1	yes	characteristic
213	C₂	#101×Dic₁₉	1	1	yes	characteristic
214	C₂	#14563437	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₄×#10597293

C₂

yes

maximal, characteristic

#14561925

C₂

yes

maximal

#14561484

C₂

yes

maximal

C₁₉×#1461

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

Q₈×C₁₉⋊C₈

—

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597293

C₄

yes

—

C₄×#64520

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926313

C₄

yes

—

#11926266

—

#11926265

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

—

C₁₉×#324

C₄

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8165

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

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

#97

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#101

yes

complemented

C₂×C₈×Q₈

—

C₄×#101

—

#1461

D₁₉

yes

characteristic

#1451

—

#1283

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×#97

yes

characteristic

100

C₂²×C₁₉

#405

yes

characteristic

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

C₂×#101

yes

characteristic

106

C₄×C₁₉

#413

yes

characteristic

107

C₄×C₁₉

#435

yes

—

108

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

109

C₈×Q₈

—

110

C₈×Q₈

—

111

#431

C₂×D₁₉

yes

—

112

C₂×C₄⋊C₈

—

113

C₂×C₄⋊C₈

—

114

C₂×#101

—

115

C₄×M₁₆

—

116

C₂×C₄×C₈

—

117

C₂×C₄×C₈

—

118

#343

—

119

#324

Dic₁₉

yes

—

120

#322

—

121

#322

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#1752

yes

characteristic

125

C₂×C₁₉

C₄×#101

yes

characteristic

126

C₂×C₁₉

#1757

yes

characteristic

127

C₂²×Q₈

C₄×D₁₉

yes

characteristic

128

C₂×M₁₆

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₂²×C₈

—

132

C₄×Q₈

—

133

C₄×Q₈

—

134

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

135

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

136

C₂×C₄²

C₄×D₁₉

yes

—

137

C₂×C₄²

C₂²×D₁₉

yes

characteristic

138

C₄⋊C₈

—

139

C₄⋊C₈

—

140

C₄⋊C₈

—

141

#101

—

142

C₂²⋊C₈

C₂×Dic₁₉

yes

—

143

#97

—

144

C₄×C₈

—

145

C₄×C₈

—

146

C₄×C₈

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₁₉

#8165

yes

characteristic, complemented, Sylow

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

#64515

yes

—

154

C₂²×C₄

C₄×Dic₁₉

yes

—

155

C₂²×C₄

C₄×Dic₁₉

yes

—

156

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

157

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

158

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

159

M₁₆

—

160

M₁₆

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄²

—

173

C₄²

—

174

C₄²

D₄×D₁₉

yes

—

175

C₄²

#64543

yes

—

176

C₂³

C₂×C₄×Dic₁₉

yes

characteristic

177

Q₈

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

#10597272

yes

—

186

C₂×C₄

#10597323

yes

characteristic

187

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

188

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

189

C₂×C₄

C₂×#64515

yes

—

190

C₂×C₄

#10597353

yes

—

191

C₂×C₄

D₄×Dic₁₉

yes

—

192

C₈

—

193

C₈

—

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

—

198

C₂²

—

199

C₂²

—

200

C₂²

C₂²⋊C₄×Dic₁₉

yes

characteristic

201

C₂²

C₂×#10597272

yes

characteristic

202

C₂²

#11926502

yes

characteristic

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

#101×D₁₉

yes

characteristic

208

C₄

#11926527

yes

characteristic

209

C₄

#11926612

yes

—

210

C₂

—

211

C₂

—

212

C₂

#14563414

yes

characteristic

213

C₂

#101×Dic₁₉

yes

characteristic

214

C₂

#14563437

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator, prime radical	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1461	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1461	D₁₉
hypocenter	C₁₉	#8165
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1461

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₁₉

commutator, prime radical

C₂³×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1461

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1461

N	H ≅ G/N	type
90. C₁₉⋊C₈	#101	semidirect
150. C₁₉	#8165	semidirect

H ≅ G/N

type

90. C₁₉⋊C₈

#101

semidirect

150. C₁₉

#8165

semidirect

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

subgroup	index
C₂×Q₈×C₁₉⋊C₈	2
C₄×#10597293	2
#14561925	2
#14561484	2
C₁₉×#1461	2
#8165	19

subgroup

index

C₂×Q₈×C₁₉⋊C₈

C₁₉×#1461

Subgroups — #18073115

Conjugacy classes of subgroups

Complements

Maximal subgroups