Group #18075558 — subgroups

Subgroups — #18075558

Order 4864.

336 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14562391	C₂	1	1	yes	maximal, characteristic
3	#14562372	C₂	1	2	yes	maximal
4	C₁₉⋊#1309	C₂	1	2	yes	maximal
5	C₁₉×#1566	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926674	—	2	1	no	—
8	#11926674	—	2	1	no	—
9	C₈×Dic₃₈	—	2	1	no	—
10	C₈×Dic₃₈	—	2	1	no	—
11	#11926570	C₄	1	2	yes	—
12	#11926568	C₂²	1	2	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926499	C₄	1	2	yes	—
15	#11926295	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926291	—	2	2	no	—
18	#11926289	—	2	2	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#334	—	2	1	no	—
22	C₁₉×#334	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#10597372	C₂×C₄	1	2	yes	—
28	#10597370	—	2	1	no	—
29	#10597370	—	2	1	no	—
30	C₂×#64520	—	2	2	no	—
31	C₂×#64520	C₂×C₄	1	2	yes	—
32	#10597316	Q₈	1	2	yes	—
33	#10597315	D₄	1	1	yes	characteristic
34	#10597315	D₄	1	1	yes	characteristic
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	#10597272	—	2	2	no	—
44	Dic₁₉⋊C₈	—	2	2	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	C₈×Dic₁₉	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×Dic₃₈	—	2	1	no	—
56	M₁₆×C₁₉	—	8	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
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	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²⋊Dic₁₉	—	2	2	no	—
69	C₄⋊Dic₁₉	—	2	1	no	—
70	C₄⋊Dic₁₉	—	2	1	no	—
71	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
72	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
73	Dic₁₉⋊C₄	—	2	2	no	—
74	Dic₁₉⋊C₄	—	2	2	no	—
75	C₄×Dic₁₉	—	2	2	no	—
76	#64520	—	4	2	no	—
77	#64520	—	8	2	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#8637	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	#117	1	1	yes	characteristic
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	Dic₃₈	—	4	2	no	—
95	Dic₃₈	—	4	2	no	—
96	C₈×C₁₉	—	2	1	no	—
97	C₈×C₁₉	—	2	1	no	—
98	C₈×C₁₉	—	2	1	no	—
99	C₈×C₁₉	—	8	2	no	—
100	C₈×C₁₉	#101	1	2	yes	—
101	C₁₉⋊C₈	—	4	2	no	—
102	C₁₉⋊C₈	—	8	2	no	—
103	#2960	—	19	1	no	—
104	#1566	—	19	1	no	—
105	#1566	D₁₉	1	1	yes	characteristic
106	#1561	—	19	2	no	—
107	#1309	—	19	2	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	#380	1	1	yes	characteristic
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
116	C₄×C₁₉	#413	1	1	yes	characteristic
117	C₄×C₁₉	#471	1	2	yes	—
118	C₄×C₁₉	#471	1	2	yes	—
119	Dic₁₉	—	4	2	no	—
120	Dic₁₉	—	4	2	no	—
121	#533	—	19	1	no	—
122	#446	—	38	1	no	—
123	#446	—	38	1	no	—
124	C₈×Q₈	—	38	1	no	—
125	C₈×Q₈	—	38	1	no	—
126	#424	—	19	2	no	—
127	#423	—	19	1	no	—
128	#423	—	19	2	no	—
129	#423	C₂×D₁₉	1	2	yes	—
130	#405	—	19	2	no	—
131	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
132	#334	—	2	1	no	—
133	#334	—	2	1	no	—
134	#334	—	38	1	no	—
135	#334	—	38	1	no	—
136	#332	—	38	2	no	—
137	#332	—	38	2	no	—
138	C₂×C₁₉	—	4	1	no	—
139	C₂×C₁₉	#1801	1	1	yes	characteristic
140	C₂×C₁₉	#1815	1	1	yes	characteristic
141	C₂×C₁₉	#1815	1	1	yes	characteristic
142	C₂×M₁₆	—	2	2	no	—
143	C₂×M₁₆	—	19	2	no	—
144	C₂×M₁₆	—	38	2	no	—
145	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
146	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
147	C₄⋊Q₈	—	19	1	no	—
148	C₄⋊Q₈	—	19	1	no	—
149	#125	—	19	2	no	—
150	C₂²⋊Q₈	—	38	1	no	—
151	C₂²⋊Q₈	—	38	1	no	—
152	C₄×Q₈	—	38	1	no	—
153	C₄×Q₈	—	38	1	no	—
154	#117	—	19	2	no	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₄⋊C₈	—	38	2	no	—
160	C₄⋊C₈	—	38	1	no	—
161	C₄⋊C₈	—	38	2	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₄⋊C₈	—	38	1	no	—
164	#97	—	38	2	no	—
165	C₄×C₈	—	38	2	no	—
166	C₄×C₈	D₇₆	1	1	yes	characteristic
167	C₄×C₈	D₇₆	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
170	C₁₉	#8637	1	1	yes	characteristic, complemented, Sylow
171	C₂×Q₈	—	38	1	no	—
172	C₂×Q₈	—	38	1	no	—
173	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₂²×C₄	#64543	1	1	yes	characteristic
175	C₂²×C₄	#64545	1	1	yes	characteristic
176	M₁₆	—	8	2	no	—
177	M₁₆	—	76	2	no	—
178	M₁₆	—	152	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	—	76	2	no	—
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	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
188	C₄⋊C₄	—	19	2	no	—
189	C₄⋊C₄	—	19	2	no	—
190	C₄⋊C₄	—	38	1	no	—
191	C₄⋊C₄	—	38	2	no	—
192	C₄⋊C₄	—	38	1	no	—
193	C₄⋊C₄	—	38	2	no	—
194	C₂²⋊C₄	—	38	2	no	—
195	C₄²	—	38	2	no	—
196	C₄²	C₂×D₇₆	1	1	yes	characteristic
197	C₄²	D₄×D₁₉	1	1	yes	characteristic
198	C₄²	Q₈×D₁₉	1	1	yes	characteristic
199	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
200	C₂³	#10597338	1	1	yes	characteristic
201	Q₈	—	76	2	no	—
202	Q₈	—	76	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
210	C₂×C₄	#10597341	1	1	yes	characteristic
211	C₂×C₄	#10597343	1	1	yes	characteristic
212	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂×C₄	#10597384	1	1	yes	characteristic
214	C₂×C₄	#10597392	1	1	yes	characteristic
215	C₈	—	2	1	no	—
216	C₈	—	2	1	no	—
217	C₈	—	2	1	no	—
218	C₈	—	8	2	no	—
219	C₈	—	76	2	no	—
220	C₈	—	152	2	no	—
221	C₈	#10597281	1	2	yes	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#11926401	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	76	2	no	—
230	C₄	—	76	2	no	—
231	C₄	C₂×#10597281	1	1	yes	characteristic
232	C₄	#11926526	1	1	yes	characteristic
233	C₄	#11926804	1	2	yes	—
234	C₄	#11926808	1	2	yes	—
235	C₂	—	4	1	no	—
236	C₂	#14563628	1	1	yes	characteristic
237	C₂	#14563691	1	1	yes	characteristic
238	C₂	#14563695	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572569

C₂

yes

maximal, characteristic

#14562391

C₂

yes

maximal, characteristic

#14562372

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal

C₁₉×#1566

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926674

—

#11926674

—

C₈×Dic₃₈

—

C₈×Dic₃₈

—

#11926570

C₄

yes

—

#11926568

C₂²

yes

—

#11926568

C₂²

yes

characteristic

#11926499

C₄

yes

—

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#334

—

C₁₉×#334

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

#10597316

Q₈

yes

—

#10597315

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597272

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×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

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

100

C₈×C₁₉

#101

yes

—

101

C₁₉⋊C₈

—

102

C₁₉⋊C₈

—

103

#2960

—

104

#1566

—

105

#1566

D₁₉

yes

characteristic

106

#1561

—

107

#1309

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#380

yes

characteristic

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

C₂×#101

yes

characteristic

116

C₄×C₁₉

#413

yes

characteristic

117

C₄×C₁₉

#471

yes

—

118

C₄×C₁₉

#471

yes

—

119

Dic₁₉

—

120

Dic₁₉

—

121

#533

—

122

#446

—

123

#446

—

124

C₈×Q₈

—

125

C₈×Q₈

—

126

#424

—

127

#423

—

128

#423

—

129

#423

C₂×D₁₉

yes

—

130

#405

—

131

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

132

#334

—

133

#334

—

134

#334

—

135

#334

—

136

#332

—

137

#332

—

138

C₂×C₁₉

—

139

C₂×C₁₉

#1801

yes

characteristic

140

C₂×C₁₉

#1815

yes

characteristic

141

C₂×C₁₉

#1815

yes

characteristic

142

C₂×M₁₆

—

143

C₂×M₁₆

—

144

C₂×M₁₆

—

145

C₂²×C₈

C₄×D₁₉

yes

characteristic

146

C₂²×C₈

C₄×D₁₉

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

152

C₄×Q₈

—

153

C₄×Q₈

—

154

#117

—

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

#97

—

165

C₄×C₈

—

166

C₄×C₈

D₇₆

yes

characteristic

167

C₄×C₈

D₇₆

yes

characteristic

168

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

169

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

170

C₁₉

#8637

yes

characteristic, complemented, Sylow

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

174

C₂²×C₄

#64543

yes

characteristic

175

C₂²×C₄

#64545

yes

characteristic

176

M₁₆

—

177

M₁₆

—

178

M₁₆

—

152

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

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

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₂²⋊C₄

—

195

C₄²

—

196

C₄²

C₂×D₇₆

yes

characteristic

197

C₄²

D₄×D₁₉

yes

characteristic

198

C₄²

Q₈×D₁₉

yes

characteristic

199

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

200

C₂³

#10597338

yes

characteristic

201

Q₈

—

202

Q₈

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

210

C₂×C₄

#10597341

yes

characteristic

211

C₂×C₄

#10597343

yes

characteristic

212

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

213

C₂×C₄

#10597384

yes

characteristic

214

C₂×C₄

#10597392

yes

characteristic

215

C₈

—

216

C₈

—

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

152

—

221

C₈

#10597281

yes

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

#11926401

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₂×#10597281

yes

characteristic

232

C₄

#11926526

yes

characteristic

233

C₄

#11926804

yes

—

234

C₄

#11926808

yes

—

235

C₂

—

236

C₂

#14563628

yes

characteristic

237

C₂

#14563691

yes

characteristic

238

C₂

#14563695

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1566	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1566	D₁₉
hypocenter	C₁₉	#8637
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1566

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
170. C₁₉	#8637	semidirect

H ≅ G/N

type

170. C₁₉

#8637

semidirect

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

subgroup	index
#14572569	2
#14562391	2
#14562372	2
C₁₉⋊#1309	2
C₁₉×#1566	2
#8637	19

subgroup

index

#14572569

#14562391

#14562372

C₁₉⋊#1309

C₁₉×#1566

#8637

Subgroups — #18075558

Conjugacy classes of subgroups

Complements

Maximal subgroups