Group #18019549 — subgroups

Subgroups — C₁₉×#13590 #18019549

Order 4864.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3152	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#356	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1411	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1410	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#137	—	2	2	no	—
6	C₁₉×#532	C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₉×#497	—	2	2	no	—
9	C₁₉×#494	C₄	1	1	yes	characteristic
10	C₁₉×#494	C₂²	1	1	yes	characteristic
11	C₁₉×#492	C₄	1	1	yes	characteristic
12	C₁₉×#492	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#101	—	2	2	no	—
14	C₄×M₁₆×C₁₉	C₄	1	1	yes	characteristic
15	C₁₉×#356	—	2	2	no	—
16	C₁₉×#356	C₂²	1	4	yes	—
17	C₂×#41×C₁₉	—	2	1	no	—
18	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
19	C₁₉×#137	—	4	4	no	—
20	C₁₉×#137	—	4	4	no	—
21	C₂×Q₁₆×C₁₉	—	2	2	no	—
22	C₂×Q₁₆×C₁₉	—	2	2	no	—
23	C₂×SD₁₆×C₁₉	—	2	2	no	—
24	C₂×SD₁₆×C₁₉	—	2	2	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	4	2	no	—
27	C₁₉×C₄⋊Q₈	—	4	1	no	—
28	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
29	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
30	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
31	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
32	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
33	C₁₉×#124	—	2	1	no	—
34	C₁₉×#121	—	4	1	no	—
35	C₄×D₄×C₁₉	—	4	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#101	—	2	4	no	—
39	C₁₉×#101	—	4	2	no	—
40	C₁₉×#97	—	2	1	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	#41×C₁₉	—	4	2	no	—
44	#41×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	1	no	—
47	C₂×Q₈×C₁₉	—	4	2	no	—
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	1	no	—
52	C₂×D₄×C₁₉	—	4	1	no	—
53	C₂×D₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	Q₁₆×C₁₉	—	4	4	no	—
59	Q₁₆×C₁₉	—	4	4	no	—
60	SD₁₆×C₁₉	—	4	4	no	—
61	SD₁₆×C₁₉	—	4	4	no	—
62	M₁₆×C₁₉	—	2	4	no	—
63	M₁₆×C₁₉	—	4	4	no	—
64	M₁₆×C₁₉	—	8	2	no	—
65	C₂×C₈×C₁₉	—	2	1	no	—
66	C₂×C₈×C₁₉	—	2	1	no	—
67	C₂×C₈×C₁₉	—	8	2	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	1	no	—
71	C₄⋊C₄×C₁₉	—	4	1	no	—
72	C₂²⋊C₄×C₁₉	—	4	2	no	—
73	C₄²×C₁₉	—	2	1	no	—
74	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	#13590	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₁₉	—	4	1	no	—
78	C₂³×C₁₉	#99	1	1	yes	characteristic
79	Q₈×C₁₉	—	4	2	no	—
80	Q₈×C₁₉	—	4	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	Q₈×C₁₉	—	8	2	no	—
83	D₄×C₁₉	—	4	2	no	—
84	D₄×C₁₉	—	8	2	no	—
85	D₄×C₁₉	—	8	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₈×C₁₉	—	2	2	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₈×C₁₉	—	8	4	no	—
102	#3152	C₂×C₁₉	1	1	yes	characteristic
103	C₂×#356	C₂×C₁₉	1	2	yes	complemented
104	#1411	C₂×C₁₉	1	2	yes	complemented
105	#1410	C₂×C₁₉	1	2	yes	complemented
106	C₂²×C₁₉	—	4	1	no	—
107	C₂²×C₁₉	—	8	2	no	—
108	C₂²×C₁₉	—	8	1	no	—
109	C₂²×C₁₉	#353	1	2	yes	—
110	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	4	1	no	—
115	C₄×C₁₉	—	4	2	no	—
116	C₄×C₁₉	—	4	2	no	—
117	C₄×C₁₉	—	8	1	no	—
118	C₂×#137	—	2	2	no	—
119	#532	C₄×C₁₉	1	1	yes	characteristic
120	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
121	#497	—	2	2	no	—
122	#494	C₄×C₁₉	1	1	yes	characteristic
123	#494	C₂²×C₁₉	1	1	yes	characteristic
124	#492	C₄×C₁₉	1	1	yes	characteristic
125	#492	C₂²×C₁₉	1	1	yes	characteristic
126	C₂×#101	—	2	2	no	—
127	C₄×M₁₆	C₄×C₁₉	1	1	yes	characteristic
128	#356	—	2	2	no	—
129	#356	C₂²×C₁₉	1	4	yes	—
130	C₂×C₁₉	—	2	1	no	—
131	C₂×C₁₉	—	2	2	no	—
132	C₂×C₁₉	—	16	1	no	—
133	C₂×C₁₉	C₂×#353	1	1	yes	characteristic
134	C₂×#41	—	2	1	no	—
135	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
136	#137	—	4	4	no	—
137	#137	—	4	4	no	—
138	C₂×Q₁₆	—	2	2	no	—
139	C₂×Q₁₆	—	2	2	no	—
140	C₂×SD₁₆	—	2	2	no	—
141	C₂×SD₁₆	—	2	2	no	—
142	C₂×M₁₆	—	2	1	no	—
143	C₂×M₁₆	—	4	2	no	—
144	C₄⋊Q₈	—	4	1	no	—
145	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
146	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
147	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
148	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
149	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
150	#124	—	2	1	no	—
151	#121	—	4	1	no	—
152	C₄×D₄	—	4	1	no	—
153	C₂×C₄⋊C₄	—	4	1	no	—
154	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
155	#101	—	2	4	no	—
156	#101	—	4	2	no	—
157	#97	—	2	1	no	—
158	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
159	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
160	C₁₉	#13590	1	1	yes	characteristic, direct product factor, Sylow
161	#41	—	4	2	no	—
162	#41	—	4	2	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	1	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
168	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
169	C₂×D₄	—	2	1	no	—
170	C₂×D₄	—	4	1	no	—
171	C₂×D₄	—	4	1	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	4	1	no	—
175	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
176	Q₁₆	—	4	4	no	—
177	Q₁₆	—	4	4	no	—
178	SD₁₆	—	4	4	no	—
179	SD₁₆	—	4	4	no	—
180	M₁₆	—	2	4	no	—
181	M₁₆	—	4	4	no	—
182	M₁₆	—	8	2	no	—
183	C₂×C₈	—	2	1	no	—
184	C₂×C₈	—	2	1	no	—
185	C₂×C₈	—	8	2	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	1	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₂²⋊C₄	—	4	2	no	—
191	C₄²	—	2	1	no	—
192	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
193	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
194	C₂³	—	4	1	no	—
195	C₂³	C₁₉×#99	1	1	yes	characteristic
196	Q₈	—	4	2	no	—
197	Q₈	—	4	2	no	—
198	Q₈	—	4	2	no	—
199	Q₈	—	8	2	no	—
200	D₄	—	4	2	no	—
201	D₄	—	8	2	no	—
202	D₄	—	8	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	8	1	no	—
213	C₂×C₄	—	8	1	no	—
214	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
215	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
216	C₈	—	2	2	no	—
217	C₈	—	2	2	no	—
218	C₈	—	8	4	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	8	2	no	—
221	C₂²	—	8	1	no	—
222	C₂²	C₁₉×#353	1	2	yes	—
223	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	4	1	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	1	no	—
231	C₂	—	2	1	no	—
232	C₂	—	2	2	no	—
233	C₂	—	16	1	no	—
234	C₂	C₂×C₁₉×#353	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3152

C₂

yes

maximal, characteristic

C₂×C₁₉×#356

C₂

yes

maximal, complemented

C₁₉×#1411

C₂

yes

maximal, complemented

C₁₉×#1410

C₂

yes

maximal, complemented

C₂×C₁₉×#137

—

C₁₉×#532

C₄

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#497

—

C₁₉×#494

C₄

yes

characteristic

C₁₉×#494

C₂²

yes

characteristic

C₁₉×#492

C₄

yes

characteristic

C₁₉×#492

C₂²

yes

characteristic

C₂×C₁₉×#101

—

C₄×M₁₆×C₁₉

C₄

yes

characteristic

C₁₉×#356

—

C₁₉×#356

C₂²

yes

—

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₁₉×#137

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂³

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#101

—

C₁₉×#101

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

C₂×D₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×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

C₂²×C₄

yes

characteristic

#13590

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

#99

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

#3152

C₂×C₁₉

yes

characteristic

103

C₂×#356

C₂×C₁₉

yes

complemented

104

#1411

C₂×C₁₉

yes

complemented

105

#1410

C₂×C₁₉

yes

complemented

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#353

yes

—

110

C₂²×C₁₉

C₂×#99

yes

characteristic

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₂×#137

—

119

#532

C₄×C₁₉

yes

characteristic

120

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

characteristic

121

#497

—

122

#494

C₄×C₁₉

yes

characteristic

123

#494

C₂²×C₁₉

yes

characteristic

124

#492

C₄×C₁₉

yes

characteristic

125

#492

C₂²×C₁₉

yes

characteristic

126

C₂×#101

—

127

C₄×M₁₆

C₄×C₁₉

yes

characteristic

128

#356

—

129

#356

C₂²×C₁₉

yes

—

130

C₂×C₁₉

—

131

C₂×C₁₉

—

132

C₂×C₁₉

—

133

C₂×C₁₉

C₂×#353

yes

characteristic

134

C₂×#41

—

135

C₂²×Q₈

D₄×C₁₉

yes

—

136

#137

—

137

#137

—

138

C₂×Q₁₆

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂×M₁₆

—

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

C₂×C₄×C₁₉

yes

characteristic

146

C₄⋊Q₈

C₂×C₄×C₁₉

yes

characteristic

147

C₄⋊Q₈

D₄×C₁₉

yes

—

148

C₄⋊Q₈

C₂³×C₁₉

yes

characteristic

149

#127

C₂×C₄×C₁₉

yes

characteristic

150

#124

—

151

#121

—

152

C₄×D₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

155

#101

—

156

#101

—

157

#97

—

158

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

159

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

160

C₁₉

#13590

yes

characteristic, direct product factor, Sylow

161

#41

—

162

#41

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

C₂²⋊C₄×C₁₉

yes

—

168

C₂×Q₈

C₂×D₄×C₁₉

yes

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

176

Q₁₆

—

177

Q₁₆

—

178

SD₁₆

—

179

SD₁₆

—

180

M₁₆

—

181

M₁₆

—

182

M₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

—

192

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

193

C₄²

C₂²×C₄×C₁₉

yes

characteristic

194

C₂³

—

195

C₂³

C₁₉×#99

yes

characteristic

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

D₄

—

201

D₄

—

202

D₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

C₁₉×#99

yes

characteristic

215

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

C₁₉×#353

yes

—

223

C₂²

C₂×C₁₉×#99

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₂

—

232

C₂

—

233

C₂

—

234

C₂

C₂×C₁₉×#353

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#353
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₉
prime radical	C₁₉×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊Q₈ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

C₂×#353

commutator

C₄²

C₂²×C₄×C₁₉

Frattini, cosocle

C₄⋊Q₈

C₂³×C₁₉

prime radical

C₁₉×#532

C₄

LCS

G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊Q₈ ◁ G

N	H ≅ G/N	type
2. C₂×C₁₉×#356	C₂	semidirect
3. C₁₉×#1411	C₂	semidirect
4. C₁₉×#1410	C₂	semidirect
76. #13590	C₁₉	direct (N × H)
103. C₂×#356	C₂×C₁₉	semidirect
104. #1411	C₂×C₁₉	semidirect
105. #1410	C₂×C₁₉	semidirect
160. C₁₉	#13590	direct (N × H)

H ≅ G/N

type

2. C₂×C₁₉×#356

C₂

semidirect

3. C₁₉×#1411

C₂

semidirect

4. C₁₉×#1410

C₂

semidirect

76. #13590

C₁₉

direct (N × H)

103. C₂×#356

C₂×C₁₉

semidirect

104. #1411

C₂×C₁₉

semidirect

105. #1410

C₂×C₁₉

semidirect

160. C₁₉

#13590

direct (N × H)

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

subgroup	index
C₁₉×#3152	2
C₂×C₁₉×#356	2
C₁₉×#1411	2
C₁₉×#1410	2
#13590	19

subgroup

index

C₁₉×#3152

C₂×C₁₉×#356

C₁₉×#1411

C₁₉×#1410

#13590

Subgroups — C₁₉×#13590 #18019549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13590 #18019549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13590 #18019549