Group #18076418 — subgroups

Subgroups — #18076418

Order 4864.

386 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14572720	C₂	1	1	yes	maximal, characteristic
2	#14564572	C₂	1	1	yes	maximal, characteristic
3	#14562387	C₂	1	2	yes	maximal
4	#14561473	C₂	1	2	yes	maximal
5	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	2	no	—
7	#11926675	—	2	2	no	—
8	#11926601	—	2	2	no	—
9	#11926597	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	#11926299	—	2	2	no	—
13	#11926297	—	2	2	no	—
14	#11926295	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#101	C₄	1	2	yes	—
17	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#343	C₄	1	1	yes	characteristic
19	C₁₉×#343	C₄	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
27	C₂×C₄²×C₁₉	D₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₁₉×#101	—	2	4	no	—
32	C₁₉×#97	—	2	2	no	—
33	C₄×C₈×C₁₉	—	2	2	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
39	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
40	#10597260	—	2	4	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	M₁₆×C₁₉	—	2	2	no	—
53	M₁₆×C₁₉	—	2	2	no	—
54	M₁₆×C₁₉	—	2	2	no	—
55	M₁₆×C₁₉	M₁₆	1	4	yes	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	4	1	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	#8838	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	2	no	—
74	Q₈×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
88	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
90	C₈×C₁₉	—	2	4	no	—
91	C₈×C₁₉	—	4	2	no	—
92	C₁₉⋊C₈	—	4	2	no	—
93	C₁₉⋊C₈	—	4	2	no	—
94	C₁₉⋊C₈	—	4	2	no	—
95	C₁₉⋊C₈	—	8	1	no	—
96	#2983	—	19	1	no	—
97	#1984	—	19	1	no	—
98	C₄×#101	D₁₉	1	1	yes	characteristic
99	#1565	—	19	2	no	—
100	#1278	—	19	2	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	#385	1	1	yes	characteristic
104	C₂²×C₁₉	#423	1	1	yes	characteristic
105	C₂²×C₁₉	#424	1	1	yes	characteristic
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	4	2	no	—
109	C₄×C₁₉	—	4	2	no	—
110	C₄×C₁₉	#435	1	2	yes	—
111	C₄×C₁₉	#436	1	2	yes	—
112	C₄×C₁₉	#454	1	1	yes	characteristic
113	C₄×C₁₉	#456	1	1	yes	characteristic
114	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
115	#446	—	38	2	no	—
116	#446	—	38	2	no	—
117	#432	—	38	2	no	—
118	#431	—	19	2	no	—
119	C₂×C₄⋊C₈	—	19	1	no	—
120	C₂×#101	Dic₁₉	1	2	yes	—
121	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
122	C₂×C₄×C₈	—	19	1	no	—
123	#343	Dic₁₉	1	1	yes	characteristic
124	#343	Dic₁₉	1	1	yes	characteristic
125	#336	—	38	2	no	—
126	#335	—	38	2	no	—
127	#334	—	38	2	no	—
128	C₂×C₁₉	—	2	1	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	#1851	1	1	yes	characteristic
131	C₂×C₁₉	#1857	1	1	yes	characteristic
132	C₂×C₁₉	#1858	1	1	yes	characteristic
133	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
135	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
136	C₂²×C₈	—	38	1	no	—
137	C₂²×C₈	—	38	1	no	—
138	C₄×Q₈	—	2	2	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
141	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
142	C₂×C₄²	D₇₆	1	2	yes	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	19	2	no	—
145	C₄⋊C₈	—	19	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	38	2	no	—
149	#101	—	2	4	no	—
150	C₂²⋊C₈	—	38	2	no	—
151	#97	—	2	2	no	—
152	#97	—	38	4	no	—
153	C₄×C₈	—	2	2	no	—
154	C₄×C₈	—	38	2	no	—
155	C₄×C₈	—	38	2	no	—
156	C₁₉	#8838	1	1	yes	characteristic, complemented, Sylow
157	C₂×Q₈	—	2	2	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
162	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
163	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
164	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
165	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
166	M₁₆	—	2	2	no	—
167	M₁₆	—	2	2	no	—
168	M₁₆	—	2	2	no	—
169	M₁₆	#64520	1	4	yes	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	38	2	no	—
173	C₂×C₈	—	38	2	no	—
174	C₂×C₈	—	38	2	no	—
175	C₂×C₈	—	76	1	no	—
176	C₂×C₈	—	76	1	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	—	76	1	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	D₄×D₁₉	1	2	yes	—
184	C₄²	#64543	1	2	yes	—
185	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
186	Q₈	—	4	2	no	—
187	Q₈	—	4	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	#10597324	1	2	yes	—
197	C₂×C₄	#10597328	1	1	yes	characteristic
198	C₂×C₄	#10597332	1	1	yes	characteristic
199	C₂×C₄	C₂×#64520	1	2	yes	—
200	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
201	C₂×C₄	#10597394	1	1	yes	characteristic
202	C₂×C₄	#10597394	1	1	yes	characteristic
203	C₈	—	2	4	no	—
204	C₈	—	4	2	no	—
205	C₈	—	76	2	no	—
206	C₈	—	76	2	no	—
207	C₈	—	76	2	no	—
208	C₈	—	152	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	#11926419	1	1	yes	characteristic
212	C₂²	#11926568	1	1	yes	characteristic
213	C₂²	#11926571	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	2	no	—
216	C₄	—	4	2	no	—
217	C₄	—	4	2	no	—
218	C₄	#11926616	1	2	yes	—
219	C₄	#11926622	1	2	yes	—
220	C₄	#11926719	1	1	yes	characteristic
221	C₄	#11926729	1	1	yes	characteristic
222	C₂	—	2	1	no	—
223	C₂	—	2	1	no	—
224	C₂	#14563820	1	1	yes	characteristic
225	C₂	#14563852	1	1	yes	characteristic
226	C₂	#14563857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic

#14564572

C₂

yes

maximal, characteristic

#14562387

C₂

yes

maximal

#14561473

C₂

yes

maximal

C₄×C₁₉×#101

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#101

C₄

yes

—

C₄×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#343

C₄

yes

characteristic

C₁₉×#343

C₄

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#101

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

M₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8838

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₁₉

—

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

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2983

—

#1984

—

C₄×#101

D₁₉

yes

characteristic

#1565

—

100

#1278

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

#385

yes

characteristic

104

C₂²×C₁₉

#423

yes

characteristic

105

C₂²×C₁₉

#424

yes

characteristic

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

#435

yes

—

111

C₄×C₁₉

#436

yes

—

112

C₄×C₁₉

#454

yes

characteristic

113

C₄×C₁₉

#456

yes

characteristic

114

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

115

#446

—

116

#446

—

117

#432

—

118

#431

—

119

C₂×C₄⋊C₈

—

120

C₂×#101

Dic₁₉

yes

—

121

C₄×M₁₆

C₂×D₁₉

yes

—

122

C₂×C₄×C₈

—

123

#343

Dic₁₉

yes

characteristic

124

#343

Dic₁₉

yes

characteristic

125

#336

—

126

#335

—

127

#334

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#1851

yes

characteristic

131

C₂×C₁₉

#1857

yes

characteristic

132

C₂×C₁₉

#1858

yes

characteristic

133

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

134

C₂×M₁₆

C₂×Dic₁₉

yes

—

135

C₂×M₁₆

C₂×Dic₁₉

yes

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

140

C₂×C₄⋊C₄

Dic₃₈

yes

—

141

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

142

C₂×C₄²

D₇₆

yes

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#101

—

150

C₂²⋊C₈

—

151

#97

—

152

#97

—

153

C₄×C₈

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₁₉

#8838

yes

characteristic, complemented, Sylow

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

C₄⋊Dic₁₉

yes

—

162

C₂²×C₄

C₄⋊Dic₁₉

yes

—

163

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

164

C₂²×C₄

C₂×D₇₆

yes

characteristic

165

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

166

M₁₆

—

167

M₁₆

—

168

M₁₆

—

169

M₁₆

#64520

yes

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

D₄×D₁₉

yes

—

184

C₄²

#64543

yes

—

185

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

#10597324

yes

—

197

C₂×C₄

#10597328

yes

characteristic

198

C₂×C₄

#10597332

yes

characteristic

199

C₂×C₄

C₂×#64520

yes

—

200

C₂×C₄

D₄×Dic₁₉

yes

—

201

C₂×C₄

#10597394

yes

characteristic

202

C₂×C₄

#10597394

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

208

C₈

—

152

—

209

C₂²

—

210

C₂²

—

211

C₂²

#11926419

yes

characteristic

212

C₂²

#11926568

yes

characteristic

213

C₂²

#11926571

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

#11926616

yes

—

219

C₄

#11926622

yes

—

220

C₄

#11926719

yes

characteristic

221

C₄

#11926729

yes

characteristic

222

C₂

—

223

C₂

—

224

C₂

#14563820

yes

characteristic

225

C₂

#14563852

yes

characteristic

226

C₂

#14563857

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#101	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#101	D₁₉
hypocenter	C₁₉	#8838
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#101

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

N	H ≅ G/N	type
156. C₁₉	#8838	semidirect

H ≅ G/N

type

156. C₁₉

#8838

semidirect

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

subgroup	index
#14572720	2
#14564572	2
#14562387	2
#14561473	2
C₄×C₁₉×#101	2
#8838	19

subgroup

index

C₄×C₁₉×#101

Subgroups — #18076418

Conjugacy classes of subgroups

Complements

Maximal subgroups