Group #18075769 — subgroups

Subgroups — #18075769

Order 4864.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14572569	C₂	1	1	yes	maximal, characteristic
2	#14563766	C₂	1	1	yes	maximal, characteristic
3	#14562200	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926674	—	2	1	no	—
8	#11926674	C₄	1	2	yes	complemented
9	C₈×Dic₃₈	—	2	1	no	—
10	C₈×Dic₃₈	C₄	1	2	yes	complemented
11	#11926570	—	2	1	no	—
12	#11926568	C₂²	1	1	yes	characteristic
13	#11926499	—	2	1	no	—
14	#11926410	C₂²	1	2	yes	—
15	#11926307	—	2	1	no	—
16	#11926307	—	2	1	no	—
17	#11926282	—	2	4	no	—
18	C₁₉×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	#10597372	—	2	1	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	#10597370	—	2	1	no	—
28	#10597370	D₄	1	2	yes	—
29	C₂×#64520	—	2	1	no	—
30	#10597316	—	2	1	no	—
31	#10597315	Q₈	1	1	yes	characteristic
32	#10597315	Q₈	1	1	yes	characteristic
33	C₄×Dic₃₈	—	2	1	no	—
34	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₂²⋊C₈	—	2	2	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	#10597272	—	2	2	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	Dic₁₉⋊C₈	—	2	2	no	—
47	C₈×Dic₁₉	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	4	2	no	—
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₂²⋊Dic₁₉	—	2	2	no	—
68	C₄⋊Dic₁₉	—	2	1	no	—
69	C₄⋊Dic₁₉	—	2	1	no	—
70	C₄⋊Dic₁₉	—	2	1	no	—
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
74	Dic₁₉⋊C₄	—	2	2	no	—
75	Dic₁₉⋊C₄	—	2	2	no	—
76	C₄×Dic₁₉	—	2	2	no	—
77	#64520	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	#8679	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	#121	1	1	yes	characteristic
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#135	1	2	yes	—
90	C₂×C₄×C₁₉	#137	1	2	yes	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	8	2	no	—
94	C₂×Dic₁₉	—	8	2	no	—
95	C₂×Dic₁₉	—	8	2	no	—
96	Dic₃₈	—	4	2	no	—
97	Dic₃₈	—	4	2	no	—
98	C₈×C₁₉	—	2	1	no	—
99	C₈×C₁₉	—	2	1	no	—
100	C₈×C₁₉	—	2	1	no	—
101	C₈×C₁₉	—	2	1	no	—
102	C₈×C₁₉	—	8	2	no	—
103	C₁₉⋊C₈	—	4	2	no	—
104	#2960	—	19	1	no	—
105	#1835	—	19	1	no	—
106	#1564	D₁₉	1	1	yes	characteristic
107	#1518	—	19	2	no	—
108	#1286	—	19	2	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	#380	1	1	yes	characteristic
112	C₂²×C₁₉	#464	1	2	yes	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	#416	1	1	yes	characteristic
118	C₄×C₁₉	#419	1	1	yes	characteristic
119	C₄×C₁₉	#479	1	2	yes	—
120	Dic₁₉	—	4	2	no	—
121	Dic₁₉	—	4	2	no	—
122	Dic₁₉	—	16	2	no	—
123	#533	—	19	1	no	—
124	#446	—	19	2	no	—
125	#446	—	38	1	no	—
126	C₈×Q₈	—	19	2	no	—
127	C₈×Q₈	—	38	1	no	—
128	#431	C₂×D₁₉	1	2	yes	—
129	#424	—	38	1	no	—
130	#423	—	19	1	no	—
131	#405	—	38	1	no	—
132	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
133	#382	—	19	2	no	—
134	#340	—	38	1	no	—
135	#340	—	38	1	no	—
136	#335	—	2	1	no	—
137	#334	—	2	1	no	—
138	#328	—	38	4	no	—
139	C₂×C₁₉	—	2	2	no	—
140	C₂×C₁₉	#1805	1	1	yes	characteristic
141	C₂×C₁₉	#1812	1	1	yes	characteristic
142	C₂×C₁₉	#1814	1	1	yes	characteristic
143	C₂×M₁₆	—	38	1	no	—
144	C₂²×C₈	D₇₆	1	1	yes	characteristic
145	C₂²×C₈	D₇₆	1	1	yes	characteristic
146	C₄⋊Q₈	—	19	1	no	—
147	C₄⋊Q₈	—	19	1	no	—
148	#125	—	38	1	no	—
149	C₂²⋊Q₈	—	19	2	no	—
150	C₂²⋊Q₈	—	38	1	no	—
151	C₄×Q₈	—	19	2	no	—
152	C₄×Q₈	—	38	1	no	—
153	#117	—	38	1	no	—
154	C₂×C₄⋊C₄	—	38	2	no	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	19	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₄⋊C₈	—	38	2	no	—
160	C₄⋊C₈	—	38	1	no	—
161	C₂²⋊C₈	—	2	2	no	—
162	#97	—	38	2	no	—
163	C₄×C₈	—	2	2	no	—
164	C₄×C₈	—	38	2	no	—
165	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
166	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
167	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
169	#95	—	38	2	no	—
170	#95	—	38	2	no	—
171	C₁₉	#8679	1	1	yes	characteristic, complemented, Sylow
172	C₂×Q₈	—	19	2	no	—
173	C₂×Q₈	—	38	1	no	—
174	C₂²×C₄	—	76	2	no	—
175	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
177	C₂²×C₄	#64545	1	1	yes	characteristic
178	M₁₆	—	76	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
184	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
185	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄	—	19	2	no	—
188	C₄⋊C₄	—	38	2	no	—
189	C₄⋊C₄	—	38	1	no	—
190	C₄⋊C₄	—	38	2	no	—
191	C₄⋊C₄	—	38	1	no	—
192	C₄⋊C₄	—	38	1	no	—
193	C₄⋊C₄	—	76	2	no	—
194	C₄⋊C₄	—	76	2	no	—
195	C₂²⋊C₄	—	38	2	no	—
196	C₄²	—	38	2	no	—
197	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
198	C₄²	#64543	1	1	yes	characteristic
199	C₄²	Q₈×D₁₉	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂³	#10597341	1	1	yes	characteristic
202	Q₈	—	76	2	no	—
203	Q₈	—	76	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	38	2	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	152	2	no	—
209	C₂×C₄	—	152	2	no	—
210	C₂×C₄	—	152	2	no	—
211	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
212	C₂×C₄	#10597338	1	1	yes	characteristic
213	C₂×C₄	#10597343	1	1	yes	characteristic
214	C₂×C₄	#10597350	1	2	yes	—
215	C₂×C₄	#10597355	1	2	yes	—
216	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
217	C₂×C₄	#10597384	1	1	yes	characteristic
218	C₂×C₄	#10597392	1	1	yes	characteristic
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	76	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#11926401	1	1	yes	characteristic
228	C₂²	#11926767	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	304	2	no	—
234	C₄	—	76	2	no	—
235	C₄	—	76	2	no	—
236	C₄	#11926541	1	1	yes	characteristic
237	C₄	#11926554	1	1	yes	characteristic
238	C₄	#11926852	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#14563651	1	1	yes	characteristic
241	C₂	#14563678	1	1	yes	characteristic
242	C₂	#14563690	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572569

C₂

yes

maximal, characteristic

#14563766

C₂

yes

maximal, characteristic

#14562200

C₂

yes

maximal

#14561494

C₂

yes

maximal

C₁₉×#1564

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926674

—

#11926674

C₄

yes

complemented

C₈×Dic₃₈

—

C₈×Dic₃₈

C₄

yes

complemented

#11926570

—

#11926568

C₂²

yes

characteristic

#11926499

—

#11926410

C₂²

yes

—

#11926307

—

#11926307

—

#11926282

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597370

D₄

yes

—

C₂×#64520

—

#10597316

—

#10597315

Q₈

yes

characteristic

#10597315

Q₈

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597272

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

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

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

#2960

—

105

#1835

—

106

#1564

D₁₉

yes

characteristic

107

#1518

—

108

#1286

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#380

yes

characteristic

112

C₂²×C₁₉

#464

yes

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#416

yes

characteristic

118

C₄×C₁₉

#419

yes

characteristic

119

C₄×C₁₉

#479

yes

—

120

Dic₁₉

—

121

Dic₁₉

—

122

Dic₁₉

—

123

#533

—

124

#446

—

125

#446

—

126

C₈×Q₈

—

127

C₈×Q₈

—

128

#431

C₂×D₁₉

yes

—

129

#424

—

130

#423

—

131

#405

—

132

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

133

#382

—

134

#340

—

135

#340

—

136

#335

—

137

#334

—

138

#328

—

139

C₂×C₁₉

—

140

C₂×C₁₉

#1805

yes

characteristic

141

C₂×C₁₉

#1812

yes

characteristic

142

C₂×C₁₉

#1814

yes

characteristic

143

C₂×M₁₆

—

144

C₂²×C₈

D₇₆

yes

characteristic

145

C₂²×C₈

D₇₆

yes

characteristic

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

#125

—

149

C₂²⋊Q₈

—

150

C₂²⋊Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

#117

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

C₄×D₁₉

yes

characteristic

166

C₄×C₈

C₄×D₁₉

yes

characteristic

167

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

168

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

169

#95

—

170

#95

—

171

C₁₉

#8679

yes

characteristic, complemented, Sylow

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×D₇₆

yes

characteristic

176

C₂²×C₄

D₄×D₁₉

yes

characteristic

177

C₂²×C₄

#64545

yes

characteristic

178

M₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

184

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

185

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₄²

—

197

C₄²

C₂×C₄×D₁₉

yes

characteristic

198

C₄²

#64543

yes

characteristic

199

C₄²

Q₈×D₁₉

yes

characteristic

200

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

201

C₂³

#10597341

yes

characteristic

202

Q₈

—

203

Q₈

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

152

—

209

C₂×C₄

—

152

—

210

C₂×C₄

—

152

—

211

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

212

C₂×C₄

#10597338

yes

characteristic

213

C₂×C₄

#10597343

yes

characteristic

214

C₂×C₄

#10597350

yes

—

215

C₂×C₄

#10597355

yes

—

216

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

217

C₂×C₄

#10597384

yes

characteristic

218

C₂×C₄

#10597392

yes

characteristic

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₂²

—

226

C₂²

—

227

C₂²

#11926401

yes

characteristic

228

C₂²

#11926767

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

304

—

234

C₄

—

235

C₄

—

236

C₄

#11926541

yes

characteristic

237

C₄

#11926554

yes

characteristic

238

C₄

#11926852

yes

—

239

C₂

—

240

C₂

#14563651

yes

characteristic

241

C₂

#14563678

yes

characteristic

242

C₂

#14563690

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8679
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂²

#11926401

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1564

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
8. #11926674	C₄	semidirect
10. C₈×Dic₃₈	C₄	semidirect
171. C₁₉	#8679	semidirect

H ≅ G/N

type

8. #11926674

C₄

semidirect

10. C₈×Dic₃₈

C₄

semidirect

171. C₁₉

#8679

semidirect

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

subgroup	index
#14572569	2
#14563766	2
#14562200	2
#14561494	2
C₁₉×#1564	2
#8679	19

subgroup

index

C₁₉×#1564

Subgroups — #18075769

Conjugacy classes of subgroups

Complements

Maximal subgroups