Group #18017912 — subgroups

Subgroups — C₁₉×#11953 #18017912

Order 4864.

296 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3170	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2163	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1365	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1362	C₂	1	2	yes	maximal, complemented
6	C₁₉×#533	—	2	1	no	—
7	C₁₉×#500	C₂²	1	1	yes	characteristic
8	C₁₉×#494	C₂²	1	1	yes	characteristic
9	C₁₉×#487	—	2	1	no	—
10	C₁₉×#467	—	2	1	no	—
11	C₁₉×#467	C₄	1	2	yes	—
12	C₄×Q₁₆×C₁₉	—	2	1	no	—
13	C₄×Q₁₆×C₁₉	C₄	1	2	yes	—
14	C₁₉×#431	—	2	1	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
18	C₁₉×#346	—	2	1	no	—
19	C₁₉×#335	C₂²	1	2	yes	—
20	C₁₉×#334	—	2	1	no	—
21	C₂×Q₁₆×C₁₉	—	2	1	no	—
22	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	—	2	1	no	—
27	C₁₉×#125	—	4	1	no	—
28	C₁₉×C₂²⋊Q₈	—	2	2	no	—
29	C₁₉×C₂²⋊Q₈	—	4	1	no	—
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	4	1	no	—
32	C₁₉×#117	—	4	1	no	—
33	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₁₆×C₁₉	—	2	2	no	—
35	C₁₉×#107	—	2	1	no	—
36	C₁₉×#107	C₂×C₄	1	2	yes	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×#103	—	2	2	no	—
39	C₁₉×#103	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	4	1	no	—
41	C₄×C₈×C₁₉	—	4	1	no	—
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
51	Q₁₆×C₁₉	—	4	2	no	—
52	Q₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	4	1	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	4	1	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₉	D₈	1	1	yes	characteristic
70	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₁₆×C₁₉	—	4	2	no	—
73	#11953	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₁₉	#102	1	1	yes	characteristic
75	Q₈×C₁₉	—	4	2	no	—
76	Q₈×C₁₉	—	4	2	no	—
77	Q₈×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	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	—	4	2	no	—
84	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₈×C₁₉	—	2	1	no	—
91	C₈×C₁₉	—	2	1	no	—
92	C₈×C₁₉	—	2	1	no	—
93	C₈×C₁₉	—	8	2	no	—
94	C₈×C₁₉	#135	1	2	yes	—
95	#3170	C₂×C₁₉	1	1	yes	characteristic
96	#2163	C₂×C₁₉	1	1	yes	characteristic
97	#1564	C₂×C₁₉	1	1	yes	characteristic
98	#1365	C₂×C₁₉	1	2	yes	complemented
99	#1362	C₂×C₁₉	1	2	yes	complemented
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	8	2	no	—
109	C₄×C₁₉	—	8	2	no	—
110	C₄×C₁₉	#413	1	1	yes	characteristic
111	C₄×C₁₉	#416	1	1	yes	characteristic
112	C₄×C₁₉	#510	1	2	yes	—
113	#533	—	2	1	no	—
114	#500	C₂²×C₁₉	1	1	yes	characteristic
115	#494	C₂²×C₁₉	1	1	yes	characteristic
116	#487	—	2	1	no	—
117	#467	—	2	1	no	—
118	#467	C₄×C₁₉	1	2	yes	—
119	C₄×Q₁₆	—	2	1	no	—
120	C₄×Q₁₆	C₄×C₁₉	1	2	yes	—
121	#431	—	2	1	no	—
122	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
123	C₄⋊C₁₆	C₂²×C₁₉	1	2	yes	—
124	C₂²⋊C₁₆	—	2	1	no	—
125	#346	—	2	1	no	—
126	#335	C₂²×C₁₉	1	2	yes	—
127	#334	—	2	1	no	—
128	C₂×C₁₉	—	4	1	no	—
129	C₂×C₁₉	#1540	1	1	yes	characteristic
130	C₂×C₁₉	#2141	1	1	yes	characteristic
131	C₂×C₁₉	#2148	1	1	yes	characteristic
132	C₂×Q₁₆	—	2	1	no	—
133	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
134	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
135	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
136	C₄⋊Q₈	—	2	1	no	—
137	C₄⋊Q₈	—	2	1	no	—
138	#125	—	4	1	no	—
139	C₂²⋊Q₈	—	2	2	no	—
140	C₂²⋊Q₈	—	4	1	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₄×Q₈	—	4	1	no	—
143	#117	—	4	1	no	—
144	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
145	C₂×C₁₆	—	2	2	no	—
146	#107	—	2	1	no	—
147	#107	C₂×C₄×C₁₉	1	2	yes	—
148	C₄⋊C₈	—	2	2	no	—
149	#103	—	2	2	no	—
150	#103	—	2	2	no	—
151	C₂²⋊C₈	—	4	1	no	—
152	C₄×C₈	—	4	1	no	—
153	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
154	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
155	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
156	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
157	C₁₉	#11953	1	1	yes	characteristic, direct product factor, Sylow
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	4	1	no	—
160	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
161	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
162	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
163	Q₁₆	—	4	2	no	—
164	Q₁₆	—	4	2	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
169	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
170	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
171	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	4	1	no	—
174	C₄⋊C₄	—	4	1	no	—
175	C₄⋊C₄	—	4	1	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₂²⋊C₄	—	4	2	no	—
179	C₄²	—	4	2	no	—
180	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
181	C₄²	D₈×C₁₉	1	1	yes	characteristic
182	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
183	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
184	C₁₆	—	4	2	no	—
185	C₂³	C₁₉×#102	1	1	yes	characteristic
186	Q₈	—	4	2	no	—
187	Q₈	—	4	2	no	—
188	Q₈	—	8	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
196	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
197	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
198	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
199	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
200	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
201	C₈	—	2	1	no	—
202	C₈	—	2	1	no	—
203	C₈	—	2	1	no	—
204	C₈	—	8	2	no	—
205	C₈	C₁₉×#135	1	2	yes	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	8	2	no	—
215	C₄	—	8	2	no	—
216	C₄	C₁₉×#413	1	1	yes	characteristic
217	C₄	C₁₉×#416	1	1	yes	characteristic
218	C₄	C₁₉×#510	1	2	yes	—
219	C₂	—	4	1	no	—
220	C₂	C₁₉×#1540	1	1	yes	characteristic
221	C₂	C₁₉×#2141	1	1	yes	characteristic
222	C₂	C₁₉×#2148	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3170

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, characteristic

C₁₉×#1564

C₂

yes

maximal, characteristic

C₁₉×#1365

C₂

yes

maximal, complemented

C₁₉×#1362

C₂

yes

maximal, complemented

C₁₉×#533

—

C₁₉×#500

C₂²

yes

characteristic

C₁₉×#494

C₂²

yes

characteristic

C₁₉×#487

—

C₁₉×#467

—

C₁₉×#467

C₄

yes

—

C₄×Q₁₆×C₁₉

—

C₄×Q₁₆×C₁₉

C₄

yes

—

C₁₉×#431

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

C₂²

yes

—

C₁₉×C₂²⋊C₁₆

—

C₁₉×#346

—

C₁₉×#335

C₂²

yes

—

C₁₉×#334

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×#107

—

C₁₉×#107

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×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

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₁₆×C₁₉

—

#11953

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#102

yes

characteristic

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

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#135

yes

—

#3170

C₂×C₁₉

yes

characteristic

#2163

C₂×C₁₉

yes

characteristic

#1564

C₂×C₁₉

yes

characteristic

#1365

C₂×C₁₉

yes

complemented

#1362

C₂×C₁₉

yes

complemented

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

C₂×#102

yes

characteristic

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

#413

yes

characteristic

111

C₄×C₁₉

#416

yes

characteristic

112

C₄×C₁₉

#510

yes

—

113

#533

—

114

#500

C₂²×C₁₉

yes

characteristic

115

#494

C₂²×C₁₉

yes

characteristic

116

#487

—

117

#467

—

118

#467

C₄×C₁₉

yes

—

119

C₄×Q₁₆

—

120

C₄×Q₁₆

C₄×C₁₉

yes

—

121

#431

—

122

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

123

C₄⋊C₁₆

C₂²×C₁₉

yes

—

124

C₂²⋊C₁₆

—

125

#346

—

126

#335

C₂²×C₁₉

yes

—

127

#334

—

128

C₂×C₁₉

—

129

C₂×C₁₉

#1540

yes

characteristic

130

C₂×C₁₉

#2141

yes

characteristic

131

C₂×C₁₉

#2148

yes

characteristic

132

C₂×Q₁₆

—

133

C₂×Q₁₆

C₂×C₄×C₁₉

yes

—

134

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

135

C₂²×C₈

D₄×C₁₉

yes

characteristic

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

#125

—

139

C₂²⋊Q₈

—

140

C₂²⋊Q₈

—

141

C₄×Q₈

—

142

C₄×Q₈

—

143

#117

—

144

C₂×C₄²

D₄×C₁₉

yes

characteristic

145

C₂×C₁₆

—

146

#107

—

147

#107

C₂×C₄×C₁₉

yes

—

148

C₄⋊C₈

—

149

#103

—

150

#103

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

154

C₄×C₈

D₄×C₁₉

yes

characteristic

155

C₄×C₈

D₄×C₁₉

yes

characteristic

156

C₄×C₈

C₂³×C₁₉

yes

characteristic

157

C₁₉

#11953

yes

characteristic, direct product factor, Sylow

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

161

C₂²×C₄

D₈×C₁₉

yes

characteristic

162

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

163

Q₁₆

—

164

Q₁₆

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

169

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

170

C₂×C₈

C₂²×C₄×C₁₉

yes

characteristic

171

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

—

180

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

181

C₄²

D₈×C₁₉

yes

characteristic

182

C₄²

SD₁₆×C₁₉

yes

characteristic

183

C₄²

C₂×D₄×C₁₉

yes

characteristic

184

C₁₆

—

185

C₂³

C₁₉×#102

yes

characteristic

186

Q₈

—

187

Q₈

—

188

Q₈

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

C₁₉×#102

yes

characteristic

196

C₂×C₄

C₁₉×#102

yes

characteristic

197

C₂×C₄

C₁₉×#102

yes

characteristic

198

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

199

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

200

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

201

C₈

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

C₁₉×#135

yes

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

C₂×C₁₉×#102

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

C₁₉×#413

yes

characteristic

217

C₄

C₁₉×#416

yes

characteristic

218

C₄

C₁₉×#510

yes

—

219

C₂

—

220

C₂

C₁₉×#1540

yes

characteristic

221

C₂

C₁₉×#2141

yes

characteristic

222

C₂

C₁₉×#2148

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#102

commutator

C₂×C₈

C₂²×C₄×C₁₉

Frattini, cosocle

C₄×C₈

C₂³×C₁₉

prime radical

C₂³×C₁₉

#102

LCS

G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
4. C₁₉×#1365	C₂	semidirect
5. C₁₉×#1362	C₂	semidirect
73. #11953	C₁₉	direct (N × H)
98. #1365	C₂×C₁₉	semidirect
99. #1362	C₂×C₁₉	semidirect
157. C₁₉	#11953	direct (N × H)

H ≅ G/N

type

4. C₁₉×#1365

C₂

semidirect

5. C₁₉×#1362

C₂

semidirect

73. #11953

C₁₉

direct (N × H)

98. #1365

C₂×C₁₉

semidirect

99. #1362

C₂×C₁₉

semidirect

157. C₁₉

#11953

direct (N × H)

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

subgroup	index
C₁₉×#3170	2
C₁₉×#2163	2
C₁₉×#1564	2
C₁₉×#1365	2
C₁₉×#1362	2
#11953	19

subgroup

index

C₁₉×#3170

C₁₉×#2163

C₁₉×#1564

C₁₉×#1365

C₁₉×#1362

#11953

Subgroups — C₁₉×#11953 #18017912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11953 #18017912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11953 #18017912