Group #18069512 — subgroups

Subgroups — #18069512

Order 4864.

310 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 103 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×#11926326	C₂	1	2	yes	maximal
2	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597269	—	2	2	no	—
4	#11926326	—	2	2	no	—
5	#11926326	C₄	1	4	yes	complemented
6	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
9	C₁₉×#336	—	2	2	no	—
10	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂×M₁₆×C₁₉	—	4	1	no	—
12	C₂×M₁₆×C₁₉	—	4	1	no	—
13	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
14	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	Q₈	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	1	no	—
17	C₂²×C₈×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	—	4	1	no	—
19	C₂²×C₈×C₁₉	—	4	1	no	—
20	C₂²×C₈×C₁₉	C₈	1	2	yes	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₁₉×#117	—	4	1	no	—
23	C₁₉×#117	—	4	1	no	—
24	C₂×C₄⋊C₄×C₁₉	C₈	1	2	yes	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	—	2	1	no	—
27	#10597269	—	2	4	no	—
28	#10597269	—	4	2	no	—
29	C₂×C₁₉⋊C₁₆	—	4	2	no	—
30	C₂⁴×C₁₉	M₁₆	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	—	2	1	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
42	M₁₆×C₁₉	—	4	2	no	—
43	M₁₆×C₁₉	—	4	1	no	—
44	M₁₆×C₁₉	—	4	1	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	—	4	1	no	—
50	C₂×C₈×C₁₉	—	4	1	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₄⋊C₄×C₁₉	—	4	2	no	—
55	C₂²⋊C₄×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	4	1	no	—
57	C₄²×C₁₉	—	4	1	no	—
58	C₁₉⋊C₁₆	—	4	4	no	—
59	#7194	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	—	2	1	no	—
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	4	2	no	—
63	C₂³×C₁₉	#97	1	1	yes	characteristic
64	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
65	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
86	C₈×C₁₉	—	2	2	no	—
87	C₈×C₁₉	—	2	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₂×#349	—	19	2	no	—
90	#1729	D₁₉	1	1	yes	characteristic
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	—	2	1	no	—
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	4	1	no	—
95	C₂²×C₁₉	—	4	1	no	—
96	C₂²×C₁₉	—	4	2	no	—
97	C₂²×C₁₉	—	4	2	no	—
98	C₂²×C₁₉	#323	1	1	yes	characteristic
99	C₂²×C₁₉	#324	1	1	yes	characteristic
100	C₂²×C₁₉	#336	1	1	yes	characteristic
101	C₄×C₁₉	—	2	1	no	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	8	2	no	—
104	C₄×C₁₉	#323	1	1	yes	characteristic
105	C₄×C₁₉	#324	1	1	yes	characteristic
106	C₄×C₁₉	#342	1	1	yes	characteristic
107	C₄×C₁₉	#343	1	1	yes	characteristic
108	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
109	C₂³×C₈	Dic₁₉	1	1	yes	characteristic
110	C₂×#117	Dic₁₉	1	1	yes	characteristic
111	C₂×M₃₂	—	38	2	no	—
112	#349	—	19	4	no	—
113	#349	—	38	2	no	—
114	#336	—	2	2	no	—
115	C₂×C₁₉	—	2	1	no	—
116	C₂×C₁₉	—	2	1	no	—
117	C₂×C₁₉	—	4	1	no	—
118	C₂×C₁₉	—	4	1	no	—
119	C₂×C₁₉	#1280	1	1	yes	characteristic
120	C₂×C₁₉	#1321	1	2	yes	—
121	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
122	C₂×M₁₆	—	4	1	no	—
123	C₂×M₁₆	—	4	1	no	—
124	C₂×M₁₆	Dic₃₈	1	1	yes	characteristic
125	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
126	C₂×M₁₆	D₇₆	1	1	yes	characteristic
127	C₂²×C₈	—	2	1	no	—
128	C₂²×C₈	—	2	1	no	—
129	C₂²×C₈	—	4	1	no	—
130	C₂²×C₈	—	4	1	no	—
131	C₂²×C₈	C₁₉⋊C₈	1	2	yes	—
132	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
133	#117	—	4	1	no	—
134	#117	—	4	1	no	—
135	C₂×C₄⋊C₄	C₁₉⋊C₈	1	2	yes	—
136	C₂×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₄²	—	2	1	no	—
138	M₃₂	—	38	4	no	—
139	M₃₂	—	76	2	no	—
140	C₂×C₁₆	—	76	2	no	—
141	C₁₉	#7194	1	1	yes	characteristic, complemented, Sylow
142	C₂⁴	#64520	1	1	yes	characteristic
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	2	1	no	—
146	C₂²×C₄	—	2	1	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
149	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
150	C₂²×C₄	#64520	1	1	yes	characteristic
151	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
152	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
153	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
154	M₁₆	—	4	1	no	—
155	M₁₆	—	4	2	no	—
156	M₁₆	—	4	1	no	—
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	4	1	no	—
162	C₂×C₈	—	4	1	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
165	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
166	C₄⋊C₄	—	4	2	no	—
167	C₂²⋊C₄	—	4	2	no	—
168	C₄²	—	4	1	no	—
169	C₄²	—	4	1	no	—
170	C₁₆	—	76	4	no	—
171	C₂³	—	2	1	no	—
172	C₂³	—	2	1	no	—
173	C₂³	—	4	2	no	—
174	C₂³	#10597260	1	1	yes	characteristic
175	C₂³	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
176	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
190	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
191	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
192	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
193	C₂×C₄	#10597290	1	1	yes	characteristic
194	C₂×C₄	#10597291	1	1	yes	characteristic
195	C₂×C₄	#10597291	1	1	yes	characteristic
196	C₂×C₄	#10597293	1	1	yes	characteristic
197	C₈	—	2	2	no	—
198	C₈	—	2	2	no	—
199	C₈	—	4	2	no	—
200	C₂²	—	2	2	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	—	4	1	no	—
204	C₂²	—	4	1	no	—
205	C₂²	—	4	2	no	—
206	C₂²	—	4	2	no	—
207	C₂²	#11926268	1	1	yes	characteristic
208	C₂²	#11926270	1	1	yes	characteristic
209	C₂²	#11926299	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	8	2	no	—
213	C₄	#11926268	1	1	yes	characteristic
214	C₄	#11926270	1	1	yes	characteristic
215	C₄	#11926311	1	1	yes	characteristic
216	C₄	#11926313	1	1	yes	characteristic
217	C₂	—	2	1	no	—
218	C₂	—	2	1	no	—
219	C₂	—	4	1	no	—
220	C₂	—	4	1	no	—
221	C₂	#14561478	1	1	yes	characteristic
222	C₂	#14561573	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926326

C₂

yes

maximal

C₁₉×#1729

C₂

yes

maximal, characteristic

C₂×#10597269

—

#11926326

—

#11926326

C₄

yes

complemented

C₂²×M₁₆×C₁₉

C₂²

yes

characteristic

C₂³×C₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#117

C₄

yes

characteristic

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₈

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₈

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₉⋊C₁₆

—

#7194

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#97

yes

characteristic

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂³×C₁₉

C₄⋊C₈

yes

characteristic

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

#95

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₂×#349

—

#1729

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

100

C₂²×C₁₉

#336

yes

characteristic

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

#323

yes

characteristic

105

C₄×C₁₉

#324

yes

characteristic

106

C₄×C₁₉

#342

yes

characteristic

107

C₄×C₁₉

#343

yes

characteristic

108

C₂²×M₁₆

C₂×D₁₉

yes

characteristic

109

C₂³×C₈

Dic₁₉

yes

characteristic

110

C₂×#117

Dic₁₉

yes

characteristic

111

C₂×M₃₂

—

112

#349

—

113

#349

—

114

#336

—

115

C₂×C₁₉

—

116

C₂×C₁₉

—

117

C₂×C₁₉

—

118

C₂×C₁₉

—

119

C₂×C₁₉

#1280

yes

characteristic

120

C₂×C₁₉

#1321

yes

—

121

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

122

C₂×M₁₆

—

123

C₂×M₁₆

—

124

C₂×M₁₆

Dic₃₈

yes

characteristic

125

C₂×M₁₆

C₄×D₁₉

yes

—

126

C₂×M₁₆

D₇₆

yes

characteristic

127

C₂²×C₈

—

128

C₂²×C₈

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₂²×C₈

C₁₉⋊C₈

yes

—

132

C₂²×C₈

C₂²⋊D₁₉

yes

—

133

#117

—

134

#117

—

135

C₂×C₄⋊C₄

C₁₉⋊C₈

yes

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

—

138

M₃₂

—

139

M₃₂

—

140

C₂×C₁₆

—

141

C₁₉

#7194

yes

characteristic, complemented, Sylow

142

C₂⁴

#64520

yes

characteristic

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

149

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

150

C₂²×C₄

#64520

yes

characteristic

151

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

152

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

153

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

154

M₁₆

—

155

M₁₆

—

156

M₁₆

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

Dic₁₉⋊C₄

yes

—

165

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

166

C₄⋊C₄

—

167

C₂²⋊C₄

—

168

C₄²

—

169

C₄²

—

170

C₁₆

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

#10597260

yes

characteristic

175

C₂³

C₄⋊(C₁₉⋊C₈)

yes

characteristic

176

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

190

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

191

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

192

C₂×C₄

C₁₉⋊#95

yes

characteristic

193

C₂×C₄

#10597290

yes

characteristic

194

C₂×C₄

#10597291

yes

characteristic

195

C₂×C₄

#10597291

yes

characteristic

196

C₂×C₄

#10597293

yes

characteristic

197

C₈

—

198

C₈

—

199

C₈

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

#11926268

yes

characteristic

208

C₂²

#11926270

yes

characteristic

209

C₂²

#11926299

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

#11926268

yes

characteristic

214

C₄

#11926270

yes

characteristic

215

C₄

#11926311

yes

characteristic

216

C₄

#11926313

yes

characteristic

217

C₂

—

218

C₂

—

219

C₂

—

220

C₂

—

221

C₂

#14561478

yes

characteristic

222

C₂

#14561573

yes

—

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂²×M₁₆	C₂×D₁₉
Fitting	C₁₉×#1729	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂⁴×C₁₉	M₁₆
cosocle	C₂²×M₁₆×C₁₉	C₂²
hypercenter	#1729	D₁₉
hypocenter	C₁₉	#7194
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ #1729

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₂²×M₁₆

C₂×D₁₉

Fitting

C₁₉×#1729

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂⁴×C₁₉

M₁₆

cosocle

C₂²×M₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ #1729

N	H ≅ G/N	type
5. #11926326	C₄	semidirect
141. C₁₉	#7194	semidirect

H ≅ G/N

type

5. #11926326

C₄

semidirect

141. C₁₉

#7194

semidirect

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

subgroup	index
C₂×#11926326	2
C₁₉×#1729	2
#7194	19

subgroup

index

C₂×#11926326

C₁₉×#1729

#7194

Subgroups — #18069512

Conjugacy classes of subgroups

Complements

Maximal subgroups