Group #18015990 — subgroups

Subgroups — C₁₉×#10031 #18015990

Order 4864.

468 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3249	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3113	C₂	1	2	yes	maximal
3	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1531	C₂	1	2	yes	maximal
5	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#533	C₂²	1	2	yes	—
7	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#483	—	2	2	no	—
9	C₁₉×#477	—	2	2	no	—
10	C₁₉×#475	—	2	2	no	—
11	C₁₉×#467	—	2	2	no	—
12	C₁₉×#462	—	2	2	no	—
13	C₁₉×#462	—	2	2	no	—
14	C₁₉×#451	—	2	2	no	—
15	C₁₉×#441	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	2	no	—
20	C₁₉×#330	—	2	4	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×Q₁₆×C₁₉	—	2	4	no	—
23	C₂×Q₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	2	yes	—
26	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×#125	—	2	2	no	—
29	C₁₉×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₄×Q₈×C₁₉	—	2	2	no	—
35	C₁₉×#117	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×#107	—	2	2	no	—
41	C₁₉×#106	—	2	4	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×#103	—	2	4	no	—
45	C₁₉×#103	—	2	4	no	—
46	C₁₉×#103	—	2	4	no	—
47	C₁₉×C₂²⋊C₈	—	2	2	no	—
48	C₁₉×#97	—	2	2	no	—
49	C₁₉×#97	D₄	1	4	yes	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	Q₁₆×C₁₉	—	4	8	no	—
60	Q₁₆×C₁₉	—	8	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	4	2	no	—
73	C₄⋊C₄×C₁₉	—	4	2	no	—
74	C₄⋊C₄×C₁₉	—	4	2	no	—
75	C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	—	4	2	no	—
78	C₄²×C₁₉	—	4	1	no	—
79	C₄²×C₁₉	C₂×D₄	1	2	yes	—
80	C₄²×C₁₉	C₂×D₄	1	2	yes	—
81	#10031	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂³×C₁₉	#121	1	1	yes	characteristic
83	Q₈×C₁₉	—	2	4	no	—
84	Q₈×C₁₉	—	4	2	no	—
85	Q₈×C₁₉	—	4	4	no	—
86	Q₈×C₁₉	—	4	2	no	—
87	Q₈×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	#120	1	2	yes	—
100	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#121	1	2	yes	—
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₈×C₁₉	—	4	2	no	—
104	C₈×C₁₉	—	4	4	no	—
105	C₈×C₁₉	—	4	2	no	—
106	#3249	C₂×C₁₉	1	1	yes	characteristic
107	#3113	C₂×C₁₉	1	2	yes	—
108	#1985	C₂×C₁₉	1	1	yes	characteristic
109	#1531	C₂×C₁₉	1	2	yes	—
110	#1290	C₂×C₁₉	1	1	yes	characteristic
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	#392	1	1	yes	characteristic
114	C₂²×C₁₉	#473	1	2	yes	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	2	no	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	—	8	2	no	—
120	C₄×C₁₉	—	8	2	no	—
121	C₄×C₁₉	—	8	1	no	—
122	C₄×C₁₉	#455	1	1	yes	characteristic
123	C₄×C₁₉	#456	1	1	yes	characteristic
124	#533	C₂²×C₁₉	1	2	yes	—
125	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
126	#483	—	2	2	no	—
127	#477	—	2	2	no	—
128	#475	—	2	2	no	—
129	#467	—	2	2	no	—
130	#462	—	2	2	no	—
131	#462	—	2	2	no	—
132	#451	—	2	2	no	—
133	#441	—	2	4	no	—
134	#432	C₂²×C₁₉	1	2	yes	—
135	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
136	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
137	#336	—	2	2	no	—
138	#330	—	2	4	no	—
139	C₂×C₁₉	—	2	2	no	—
140	C₂×C₁₉	#2007	1	1	yes	characteristic
141	C₂×C₁₉	#2010	1	1	yes	characteristic
142	C₂×C₁₉	#2020	1	1	yes	characteristic
143	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
144	C₂×Q₁₆	—	2	4	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	D₄×C₁₉	1	2	yes	—
148	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
149	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
150	#125	—	2	2	no	—
151	C₂²⋊Q₈	—	2	2	no	—
152	C₂²⋊Q₈	—	2	2	no	—
153	C₄×Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	#117	—	2	2	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
160	C₂×C₄²	—	2	1	no	—
161	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
162	#107	—	2	2	no	—
163	#106	—	2	4	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	#103	—	2	4	no	—
167	#103	—	2	4	no	—
168	#103	—	2	4	no	—
169	C₂²⋊C₈	—	2	2	no	—
170	#97	—	2	2	no	—
171	#97	D₄×C₁₉	1	4	yes	—
172	C₁₉	#10031	1	1	yes	characteristic, direct product factor, Sylow
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
181	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
182	Q₁₆	—	4	8	no	—
183	Q₁₆	—	8	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	4	1	no	—
188	C₂×C₈	—	4	1	no	—
189	C₂×C₈	—	4	2	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₂²⋊C₄	—	4	2	no	—
199	C₄²	—	4	1	no	—
200	C₄²	—	4	2	no	—
201	C₄²	—	4	1	no	—
202	C₄²	C₂×D₄×C₁₉	1	2	yes	—
203	C₄²	C₂×D₄×C₁₉	1	2	yes	—
204	C₂³	C₁₉×#121	1	1	yes	characteristic
205	Q₈	—	2	4	no	—
206	Q₈	—	4	2	no	—
207	Q₈	—	4	4	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	4	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	C₁₉×#120	1	2	yes	—
222	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
223	C₂×C₄	C₁₉×#121	1	2	yes	—
224	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
225	C₈	—	4	2	no	—
226	C₈	—	4	4	no	—
227	C₈	—	4	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	C₁₉×#392	1	1	yes	characteristic
231	C₂²	C₁₉×#473	1	2	yes	—
232	C₄	—	2	1	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	—	8	2	no	—
237	C₄	—	8	2	no	—
238	C₄	—	8	1	no	—
239	C₄	C₁₉×#455	1	1	yes	characteristic
240	C₄	C₁₉×#456	1	1	yes	characteristic
241	C₂	—	2	2	no	—
242	C₂	C₁₉×#2007	1	1	yes	characteristic
243	C₂	C₁₉×#2010	1	1	yes	characteristic
244	C₂	C₁₉×#2020	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3249

C₂

yes

maximal, characteristic

C₁₉×#3113

C₂

yes

maximal

C₁₉×#1985

C₂

yes

maximal, characteristic

C₁₉×#1531

C₂

yes

maximal

C₁₉×#1290

C₂

yes

maximal, characteristic

C₁₉×#533

C₂²

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#483

—

C₁₉×#477

—

C₁₉×#475

—

C₁₉×#467

—

C₁₉×#462

—

C₁₉×#462

—

C₁₉×#451

—

C₁₉×#441

—

C₁₉×#432

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#330

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

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

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#10031

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

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

—

100

C₂×C₄×C₁₉

#120

yes

characteristic

101

C₂×C₄×C₁₉

#121

yes

—

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

#3249

C₂×C₁₉

yes

characteristic

107

#3113

C₂×C₁₉

yes

—

108

#1985

C₂×C₁₉

yes

characteristic

109

#1531

C₂×C₁₉

yes

—

110

#1290

C₂×C₁₉

yes

characteristic

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#392

yes

characteristic

114

C₂²×C₁₉

#473

yes

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

#455

yes

characteristic

123

C₄×C₁₉

#456

yes

characteristic

124

#533

C₂²×C₁₉

yes

—

125

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

126

#483

—

127

#477

—

128

#475

—

129

#467

—

130

#462

—

131

#462

—

132

#451

—

133

#441

—

134

#432

C₂²×C₁₉

yes

—

135

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

136

C₂×#97

C₂²×C₁₉

yes

characteristic

137

#336

—

138

#330

—

139

C₂×C₁₉

—

140

C₂×C₁₉

#2007

yes

characteristic

141

C₂×C₁₉

#2010

yes

characteristic

142

C₂×C₁₉

#2020

yes

characteristic

143

C₂²×Q₈

D₄×C₁₉

yes

characteristic

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂²×C₈

—

147

C₂²×C₈

D₄×C₁₉

yes

—

148

C₄⋊Q₈

D₄×C₁₉

yes

—

149

C₄⋊Q₈

D₄×C₁₉

yes

—

150

#125

—

151

C₂²⋊Q₈

—

152

C₂²⋊Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

#117

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

160

C₂×C₄²

—

161

C₂×C₄²

C₂³×C₁₉

yes

characteristic

162

#107

—

163

#106

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#103

—

167

#103

—

168

#103

—

169

C₂²⋊C₈

—

170

#97

—

171

#97

D₄×C₁₉

yes

—

172

C₁₉

#10031

yes

characteristic, direct product factor, Sylow

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

180

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

181

C₂²×C₄

#41×C₁₉

yes

characteristic

182

Q₁₆

—

183

Q₁₆

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₂²⋊C₄

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

C₂×D₄×C₁₉

yes

—

203

C₄²

C₂×D₄×C₁₉

yes

—

204

C₂³

C₁₉×#121

yes

characteristic

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

C₁₉×#120

yes

—

222

C₂×C₄

C₁₉×#120

yes

characteristic

223

C₂×C₄

C₁₉×#121

yes

—

224

C₂×C₄

C₁₉×#127

yes

characteristic

225

C₈

—

226

C₈

—

227

C₈

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₁₉×#392

yes

characteristic

231

C₂²

C₁₉×#473

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

C₁₉×#455

yes

characteristic

240

C₄

C₁₉×#456

yes

characteristic

241

C₂

—

242

C₂

C₁₉×#2007

yes

characteristic

243

C₂

C₁₉×#2010

yes

characteristic

244

C₂

C₁₉×#2020

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂³×C₁₉

#121

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
81. #10031	C₁₉	direct (N × H)
172. C₁₉	#10031	direct (N × H)

H ≅ G/N

type

81. #10031

C₁₉

direct (N × H)

172. C₁₉

#10031

direct (N × H)

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

subgroup	index
C₁₉×#3249	2
C₁₉×#3113	2
C₁₉×#1985	2
C₁₉×#1531	2
C₁₉×#1290	2
#10031	19

subgroup

index

C₁₉×#3249

C₁₉×#3113

C₁₉×#1985

C₁₉×#1531

C₁₉×#1290

#10031

Subgroups — C₁₉×#10031 #18015990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10031 #18015990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10031 #18015990