Group #18019325 — subgroups

Subgroups — C₁₉×#13366 #18019325

Order 4864.

382 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 130 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×C₁₉×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#358	C₂	1	2	yes	maximal
3	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1380	C₂	1	2	yes	maximal
5	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#125	—	2	1	no	—
8	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#499	—	2	4	no	—
10	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#107	C₂²	1	2	yes	—
12	C₂×C₁₉×#106	—	2	1	no	—
13	C₂×C₁₉×#103	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#391	—	2	1	no	—
16	C₁₉×#358	—	2	4	no	—
17	C₂²×Q₈×C₁₉	—	2	1	no	—
18	C₂×Q₁₆×C₁₉	—	2	2	no	—
19	C₂×Q₁₆×C₁₉	—	2	2	no	—
20	C₂×Q₁₆×C₁₉	—	2	1	no	—
21	C₂×Q₁₆×C₁₉	Q₈	1	2	yes	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×#125	—	2	4	no	—
25	C₁₉×#125	—	4	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₁₆×C₁₉	—	2	2	no	—
31	C₂×C₁₆×C₁₉	—	2	2	no	—
32	C₂×C₁₆×C₁₉	—	2	2	no	—
33	C₁₉×#107	—	2	2	no	—
34	C₁₉×#107	—	2	2	no	—
35	C₁₉×#107	D₄	1	4	yes	—
36	C₁₉×#106	—	2	4	no	—
37	C₁₉×#103	—	4	2	no	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	C₁₉×#95	—	4	2	no	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂×Q₈×C₁₉	—	4	1	no	—
42	C₂×Q₈×C₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	—	4	1	no	—
44	C₂×Q₈×C₁₉	—	4	1	no	—
45	C₂×Q₈×C₁₉	—	4	1	no	—
46	C₂²×C₄×C₁₉	—	4	2	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	D₈	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	Q₁₆×C₁₉	—	2	4	no	—
52	Q₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	2	1	no	—
54	C₂×C₈×C₁₉	—	2	1	no	—
55	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
56	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₉	#41	1	2	yes	—
59	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄⋊C₄×C₁₉	—	4	8	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	—	2	1	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₁₆×C₁₉	—	4	2	no	—
68	#13366	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	2	no	—
71	Q₈×C₁₉	—	4	2	no	—
72	Q₈×C₁₉	—	8	1	no	—
73	Q₈×C₁₉	—	8	1	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	8	1	no	—
80	C₂×C₄×C₁₉	—	8	1	no	—
81	C₂×C₄×C₁₉	—	8	2	no	—
82	C₂×C₄×C₁₉	—	8	2	no	—
83	C₂×C₄×C₁₉	—	8	1	no	—
84	C₂×C₄×C₁₉	—	8	2	no	—
85	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	C₂²⋊Q₈	1	2	yes	—
93	C₈×C₁₉	#124	1	2	yes	—
94	C₂×#499	C₂×C₁₉	1	1	yes	characteristic
95	C₂×#358	C₂×C₁₉	1	2	yes	—
96	#1969	C₂×C₁₉	1	1	yes	characteristic
97	#1380	C₂×C₁₉	1	2	yes	—
98	#1374	C₂×C₁₉	1	1	yes	characteristic
99	C₂²×C₁₉	#447	1	1	yes	characteristic
100	C₂²×C₁₉	#474	1	1	yes	characteristic
101	C₂²×C₁₉	#486	1	1	yes	characteristic
102	C₂²×C₁₉	#508	1	2	yes	—
103	C₂²×C₁₉	#510	1	2	yes	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	—	8	4	no	—
106	C₄×C₁₉	—	8	2	no	—
107	C₄×C₁₉	—	16	1	no	—
108	C₄×C₁₉	#393	1	1	yes	characteristic
109	C₄×C₁₉	#448	1	1	yes	characteristic
110	C₄×C₁₉	#476	1	1	yes	characteristic
111	C₄×C₁₉	#489	1	1	yes	characteristic
112	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
113	C₂×#125	—	2	1	no	—
114	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
115	#499	—	2	4	no	—
116	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
117	C₂×#107	C₂²×C₁₉	1	2	yes	—
118	C₂×#106	—	2	1	no	—
119	C₂×#103	—	2	1	no	—
120	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
121	#391	—	2	1	no	—
122	#358	—	2	4	no	—
123	C₂×C₁₉	#2023	1	1	yes	characteristic
124	C₂×C₁₉	#2189	1	2	yes	—
125	C₂×C₁₉	#2229	1	2	yes	—
126	C₂×C₁₉	#2242	1	1	yes	characteristic
127	C₂×C₁₉	#2245	1	1	yes	characteristic
128	C₂²×Q₈	—	2	1	no	—
129	C₂×Q₁₆	—	2	2	no	—
130	C₂×Q₁₆	—	2	2	no	—
131	C₂×Q₁₆	—	2	1	no	—
132	C₂×Q₁₆	Q₈×C₁₉	1	2	yes	—
133	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
134	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
135	#125	—	2	4	no	—
136	#125	—	4	2	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	2	1	no	—
139	C₂×C₄⋊C₄	—	4	2	no	—
140	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
141	C₂×C₁₆	—	2	2	no	—
142	C₂×C₁₆	—	2	2	no	—
143	C₂×C₁₆	—	2	2	no	—
144	#107	—	2	2	no	—
145	#107	—	2	2	no	—
146	#107	D₄×C₁₉	1	4	yes	—
147	#106	—	2	4	no	—
148	#103	—	4	2	no	—
149	C₄×C₈	—	2	2	no	—
150	#95	—	4	2	no	—
151	C₁₉	#13366	1	1	yes	characteristic, direct product factor, Sylow
152	C₂×Q₈	—	2	2	no	—
153	C₂×Q₈	—	4	1	no	—
154	C₂×Q₈	—	4	1	no	—
155	C₂×Q₈	—	4	1	no	—
156	C₂×Q₈	—	4	1	no	—
157	C₂×Q₈	—	4	1	no	—
158	C₂²×C₄	—	4	1	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	D₈×C₁₉	1	2	yes	—
162	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
163	Q₁₆	—	2	4	no	—
164	Q₁₆	—	4	2	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
168	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
169	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
170	C₂×C₈	#41×C₁₉	1	2	yes	—
171	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
172	C₄⋊C₄	—	2	4	no	—
173	C₄⋊C₄	—	4	8	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	1	no	—
176	C₄⋊C₄	—	4	1	no	—
177	C₄²	—	2	1	no	—
178	C₄²	—	2	1	no	—
179	C₁₆	—	4	2	no	—
180	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
181	Q₈	—	4	2	no	—
182	Q₈	—	4	2	no	—
183	Q₈	—	8	1	no	—
184	Q₈	—	8	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	8	1	no	—
191	C₂×C₄	—	8	1	no	—
192	C₂×C₄	—	8	2	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	1	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
197	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
198	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
199	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
200	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	C₁₉×C₂²⋊Q₈	1	2	yes	—
204	C₈	C₁₉×#124	1	2	yes	—
205	C₂²	C₁₉×#447	1	1	yes	characteristic
206	C₂²	C₁₉×#474	1	1	yes	characteristic
207	C₂²	C₁₉×#486	1	1	yes	characteristic
208	C₂²	C₁₉×#508	1	2	yes	—
209	C₂²	C₁₉×#510	1	2	yes	—
210	C₄	—	4	2	no	—
211	C₄	—	8	4	no	—
212	C₄	—	8	2	no	—
213	C₄	—	16	1	no	—
214	C₄	C₁₉×#393	1	1	yes	characteristic
215	C₄	C₁₉×#448	1	1	yes	characteristic
216	C₄	C₁₉×#476	1	1	yes	characteristic
217	C₄	C₁₉×#489	1	1	yes	characteristic
218	C₂	C₁₉×#2023	1	1	yes	characteristic
219	C₂	C₁₉×#2189	1	2	yes	—
220	C₂	C₁₉×#2229	1	2	yes	—
221	C₂	C₁₉×#2242	1	1	yes	characteristic
222	C₂	C₁₉×#2245	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#499

C₂

yes

maximal, characteristic

C₂×C₁₉×#358

C₂

yes

maximal

C₁₉×#1969

C₂

yes

maximal, characteristic

C₁₉×#1380

C₂

yes

maximal

C₁₉×#1374

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#125

—

C₂²×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#499

—

C₂×C₁₉×#107

C₂²

yes

characteristic

C₂×C₁₉×#107

C₂²

yes

—

C₂×C₁₉×#106

—

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#358

—

C₂²×Q₈×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

Q₈

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×#125

—

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

D₄

yes

—

C₁₉×#106

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

#41

yes

—

C₂×C₈×C₁₉

#41

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#13366

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

#124

yes

—

C₂×#499

C₂×C₁₉

yes

characteristic

C₂×#358

C₂×C₁₉

yes

—

#1969

C₂×C₁₉

yes

characteristic

#1380

C₂×C₁₉

yes

—

#1374

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

#447

yes

characteristic

100

C₂²×C₁₉

#474

yes

characteristic

101

C₂²×C₁₉

#486

yes

characteristic

102

C₂²×C₁₉

#508

yes

—

103

C₂²×C₁₉

#510

yes

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

#393

yes

characteristic

109

C₄×C₁₉

#448

yes

characteristic

110

C₄×C₁₉

#476

yes

characteristic

111

C₄×C₁₉

#489

yes

characteristic

112

C₂²×Q₁₆

C₂²×C₁₉

yes

characteristic

113

C₂×#125

—

114

C₂²×C₁₆

C₂²×C₁₉

yes

—

115

#499

—

116

C₂×#107

C₂²×C₁₉

yes

characteristic

117

C₂×#107

C₂²×C₁₉

yes

—

118

C₂×#106

—

119

C₂×#103

—

120

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

121

#391

—

122

#358

—

123

C₂×C₁₉

#2023

yes

characteristic

124

C₂×C₁₉

#2189

yes

—

125

C₂×C₁₉

#2229

yes

—

126

C₂×C₁₉

#2242

yes

characteristic

127

C₂×C₁₉

#2245

yes

characteristic

128

C₂²×Q₈

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

Q₈×C₁₉

yes

—

133

C₂²×C₈

D₄×C₁₉

yes

characteristic

134

C₂²×C₈

C₂³×C₁₉

yes

characteristic

135

#125

—

136

#125

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄²

D₄×C₁₉

yes

characteristic

141

C₂×C₁₆

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

#107

—

145

#107

—

146

#107

D₄×C₁₉

yes

—

147

#106

—

148

#103

—

149

C₄×C₈

—

150

#95

—

151

C₁₉

#13366

yes

characteristic, direct product factor, Sylow

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

D₈×C₁₉

yes

—

162

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

163

Q₁₆

—

164

Q₁₆

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

SD₁₆×C₁₉

yes

—

168

C₂×C₈

C₂×D₄×C₁₉

yes

—

169

C₂×C₈

C₂×Q₈×C₁₉

yes

characteristic

170

C₂×C₈

#41×C₁₉

yes

—

171

C₂×C₈

#41×C₁₉

yes

characteristic

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄²

—

178

C₄²

—

179

C₁₆

—

180

C₂³

C₂×D₈×C₁₉

yes

characteristic

181

Q₈

—

182

Q₈

—

183

Q₈

—

184

Q₈

—

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

C₁₉×#120

yes

characteristic

197

C₂×C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

198

C₂×C₄

C₁₉×#124

yes

characteristic

199

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

200

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

201

C₂×C₄

C₁₉×#137

yes

characteristic

202

C₈

—

203

C₈

C₁₉×C₂²⋊Q₈

yes

—

204

C₈

C₁₉×#124

yes

—

205

C₂²

C₁₉×#447

yes

characteristic

206

C₂²

C₁₉×#474

yes

characteristic

207

C₂²

C₁₉×#486

yes

characteristic

208

C₂²

C₁₉×#508

yes

—

209

C₂²

C₁₉×#510

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

C₁₉×#393

yes

characteristic

215

C₄

C₁₉×#448

yes

characteristic

216

C₄

C₁₉×#476

yes

characteristic

217

C₄

C₁₉×#489

yes

characteristic

218

C₂

C₁₉×#2023

yes

characteristic

219

C₂

C₁₉×#2189

yes

—

220

C₂

C₁₉×#2229

yes

—

221

C₂

C₁₉×#2242

yes

characteristic

222

C₂

C₁₉×#2245

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
68. #13366	C₁₉	direct (N × H)
151. C₁₉	#13366	direct (N × H)

H ≅ G/N

type

68. #13366

C₁₉

direct (N × H)

151. C₁₉

#13366

direct (N × H)

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

subgroup	index
C₂×C₁₉×#499	2
C₂×C₁₉×#358	2
C₁₉×#1969	2
C₁₉×#1380	2
C₁₉×#1374	2
#13366	19

subgroup

index

C₂×C₁₉×#499

C₂×C₁₉×#358

C₁₉×#1969

C₁₉×#1380

C₁₉×#1374

#13366

Subgroups — C₁₉×#13366 #18019325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13366 #18019325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13366 #18019325