Group #18013605 — subgroups

Subgroups — C₁₉×#7646 #18013605

Order 4864.

490 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 134 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	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1817	C₂	1	2	yes	maximal
3	C₁₉×#1271	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
6	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
8	C₁₉×#389	C₄	1	2	yes	—
9	C₁₉×#389	C₂²	1	2	yes	—
10	C₁₉×#385	—	2	2	no	—
11	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
12	C₁₉×#336	—	2	2	no	—
13	C₁₉×#336	C₂²	1	4	yes	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂²×C₈×C₁₉	—	2	4	no	—
17	C₁₉×#117	—	2	4	no	—
18	C₁₉×#117	—	4	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	—	2	1	no	—
27	C₂×C₄²×C₁₉	—	4	2	no	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₁₉×C₂²⋊C₈	—	4	4	no	—
32	C₁₉×#95	—	2	2	no	—
33	C₁₉×#95	—	2	2	no	—
34	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	4	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	4	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂×C₈×C₁₉	—	4	4	no	—
48	C₂×C₈×C₁₉	—	4	4	no	—
49	C₂×C₈×C₁₉	—	4	4	no	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	4	4	no	—
53	C₄⋊C₄×C₁₉	—	4	4	no	—
54	C₄⋊C₄×C₁₉	M₁₆	1	4	yes	—
55	C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂²⋊C₄×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	—	2	4	no	—
58	C₄²×C₁₉	—	4	1	no	—
59	C₄²×C₁₉	—	4	2	no	—
60	C₄²×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	—	4	2	no	—
62	#7646	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂³×C₁₉	—	2	1	no	—
64	C₂³×C₁₉	—	2	1	no	—
65	C₂³×C₁₉	—	2	2	no	—
66	C₂³×C₁₉	—	2	2	no	—
67	C₂³×C₁₉	#99	1	2	yes	—
68	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	8	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	2	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	4	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	—	4	8	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	#101	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
88	C₂×C₄×C₁₉	#135	1	4	yes	—
89	C₈×C₁₉	—	8	4	no	—
90	#2296	C₂×C₁₉	1	1	yes	characteristic
91	#1817	C₂×C₁₉	1	2	yes	—
92	#1271	C₂×C₁₉	1	4	yes	complemented
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	2	4	no	—
95	C₂²×C₁₉	—	4	1	no	—
96	C₂²×C₁₉	—	4	1	no	—
97	C₂²×C₁₉	—	4	2	no	—
98	C₂²×C₁₉	#407	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
100	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
101	C₂²×C₁₉	#416	1	2	yes	—
102	C₂²×C₁₉	#421	1	2	yes	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	—	2	4	no	—
106	C₄×C₁₉	—	4	4	no	—
107	C₄×C₁₉	—	4	2	no	—
108	C₄×C₁₉	—	8	2	no	—
109	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
110	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
111	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
112	C₂×C₂²⋊C₈	—	2	2	no	—
113	#389	C₄×C₁₉	1	2	yes	—
114	#389	C₂²×C₁₉	1	2	yes	—
115	#385	—	2	2	no	—
116	C₄×C₄⋊C₄	—	2	2	no	—
117	#336	—	2	2	no	—
118	#336	C₂²×C₁₉	1	4	yes	—
119	C₂×C₁₉	—	4	2	no	—
120	C₂×C₁₉	#1463	1	1	yes	characteristic
121	C₂×C₁₉	#1488	1	2	yes	—
122	C₂×C₁₉	#1516	1	2	yes	—
123	C₂×C₁₉	#1537	1	1	yes	characteristic
124	C₂×C₁₉	#1544	1	1	yes	characteristic
125	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
126	C₂³×C₄	D₄×C₁₉	1	2	yes	—
127	C₂²×C₈	—	2	4	no	—
128	#117	—	2	4	no	—
129	#117	—	4	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
133	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
134	C₂×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₄²	—	2	1	no	—
137	C₂×C₄²	—	2	1	no	—
138	C₂×C₄²	—	4	2	no	—
139	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄²	D₄×C₁₉	1	2	yes	—
141	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
142	C₂²⋊C₈	—	4	4	no	—
143	#95	—	2	2	no	—
144	#95	—	2	2	no	—
145	C₁₉	#7646	1	1	yes	characteristic, direct product factor, Sylow
146	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	4	no	—
152	C₂²×C₄	—	2	4	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
156	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
159	C₂×C₈	—	4	4	no	—
160	C₂×C₈	—	4	4	no	—
161	C₂×C₈	—	4	4	no	—
162	C₄⋊C₄	—	2	2	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₄⋊C₄	M₁₆×C₁₉	1	4	yes	—
167	C₂²⋊C₄	—	2	4	no	—
168	C₂²⋊C₄	—	4	2	no	—
169	C₄²	—	2	4	no	—
170	C₄²	—	4	1	no	—
171	C₄²	—	4	2	no	—
172	C₄²	—	4	1	no	—
173	C₄²	—	4	2	no	—
174	C₂³	—	2	1	no	—
175	C₂³	—	2	1	no	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	2	no	—
178	C₂³	C₁₉×#99	1	2	yes	—
179	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	4	8	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	C₁₉×#101	1	2	yes	—
198	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
199	C₂×C₄	C₁₉×#135	1	4	yes	—
200	C₈	—	8	4	no	—
201	C₂²	—	2	2	no	—
202	C₂²	—	2	4	no	—
203	C₂²	—	4	2	no	—
204	C₂²	—	4	1	no	—
205	C₂²	—	4	1	no	—
206	C₂²	C₁₉×#407	1	1	yes	characteristic
207	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
208	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
209	C₂²	C₁₉×#416	1	2	yes	—
210	C₂²	C₁₉×#421	1	2	yes	—
211	C₄	—	2	2	no	—
212	C₄	—	2	2	no	—
213	C₄	—	2	4	no	—
214	C₄	—	4	4	no	—
215	C₄	—	4	2	no	—
216	C₄	—	8	2	no	—
217	C₂	—	4	2	no	—
218	C₂	C₁₉×#1463	1	1	yes	characteristic
219	C₂	C₁₉×#1488	1	2	yes	—
220	C₂	C₁₉×#1516	1	2	yes	—
221	C₂	C₁₉×#1537	1	1	yes	characteristic
222	C₂	C₁₉×#1544	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2296

C₂

yes

maximal, characteristic

C₁₉×#1817

C₂

yes

maximal

C₁₉×#1271

C₂

yes

maximal, complemented

C₂×C₁₉×#117

C₄

yes

characteristic

C₂×C₁₉×#117

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₁₉×#389

C₄

yes

—

C₁₉×#389

C₂²

yes

—

C₁₉×#385

—

C₄×C₄⋊C₄×C₁₉

—

C₁₉×#336

—

C₁₉×#336

C₂²

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

M₁₆

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#7646

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

#2296

C₂×C₁₉

yes

characteristic

#1817

C₂×C₁₉

yes

—

#1271

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#407

yes

characteristic

C₂²×C₁₉

C₂×#99

yes

characteristic

100

C₂²×C₁₉

C₂×#101

yes

characteristic

101

C₂²×C₁₉

#416

yes

—

102

C₂²×C₁₉

#421

yes

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₂×#117

C₄×C₁₉

yes

characteristic

110

C₂×#117

C₄×C₁₉

yes

characteristic

111

C₂²×C₄²

C₂²×C₁₉

yes

characteristic

112

C₂×C₂²⋊C₈

—

113

#389

C₄×C₁₉

yes

—

114

#389

C₂²×C₁₉

yes

—

115

#385

—

116

C₄×C₄⋊C₄

—

117

#336

—

118

#336

C₂²×C₁₉

yes

—

119

C₂×C₁₉

—

120

C₂×C₁₉

#1463

yes

characteristic

121

C₂×C₁₉

#1488

yes

—

122

C₂×C₁₉

#1516

yes

—

123

C₂×C₁₉

#1537

yes

characteristic

124

C₂×C₁₉

#1544

yes

characteristic

125

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

126

C₂³×C₄

D₄×C₁₉

yes

—

127

C₂²×C₈

—

128

#117

—

129

#117

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

133

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

134

C₂×C₂²⋊C₄

—

135

C₂×C₂²⋊C₄

—

136

C₂×C₄²

—

137

C₂×C₄²

—

138

C₂×C₄²

—

139

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

140

C₂×C₄²

D₄×C₁₉

yes

—

141

C₂×C₄²

C₂³×C₁₉

yes

characteristic

142

C₂²⋊C₈

—

143

#95

—

144

#95

—

145

C₁₉

#7646

yes

characteristic, direct product factor, Sylow

146

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

156

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

157

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

158

C₂²×C₄

C₂×D₄×C₁₉

yes

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

M₁₆×C₁₉

yes

—

167

C₂²⋊C₄

—

168

C₂²⋊C₄

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

172

C₄²

—

173

C₄²

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

C₁₉×#99

yes

—

179

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

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

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

C₁₉×#101

yes

—

198

C₂×C₄

C₂×M₁₆×C₁₉

yes

—

199

C₂×C₄

C₁₉×#135

yes

—

200

C₈

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

C₁₉×#407

yes

characteristic

207

C₂²

C₂×C₁₉×#99

yes

characteristic

208

C₂²

C₂×C₁₉×#101

yes

characteristic

209

C₂²

C₁₉×#416

yes

—

210

C₂²

C₁₉×#421

yes

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₂

—

218

C₂

C₁₉×#1463

yes

characteristic

219

C₂

C₁₉×#1488

yes

—

220

C₂

C₁₉×#1516

yes

—

221

C₂

C₁₉×#1537

yes

characteristic

222

C₂

C₁₉×#1544

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1271	C₂	semidirect
62. #7646	C₁₉	direct (N × H)
92. #1271	C₂×C₁₉	semidirect
145. C₁₉	#7646	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1271

C₂

semidirect

62. #7646

C₁₉

direct (N × H)

92. #1271

C₂×C₁₉

semidirect

145. C₁₉

#7646

direct (N × H)

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

subgroup	index
C₁₉×#2296	2
C₁₉×#1817	2
C₁₉×#1271	2
#7646	19

subgroup

index

C₁₉×#2296

C₁₉×#1817

C₁₉×#1271

#7646

Subgroups — C₁₉×#7646 #18013605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7646 #18013605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7646 #18013605