Group #18013165 — subgroups

Subgroups — C₁₉×#7206 #18013165

Order 4864.

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

normal subgroups only

This group has 284 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×#1984	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×#431	—	2	1	no	—
6	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₉×#101	C₄	1	2	yes	—
8	C₄×M₁₆×C₁₉	—	2	1	no	—
9	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
10	C₁₉×#343	—	2	1	no	—
11	C₁₉×#336	—	2	1	no	—
12	C₁₉×#336	—	2	1	no	—
13	C₁₉×#324	—	2	1	no	—
14	C₁₉×#324	C₄	1	2	yes	—
15	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₂²×C₈×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	—	2	1	no	—
19	C₄×Q₈×C₁₉	—	4	1	no	—
20	C₄×Q₈×C₁₉	—	4	1	no	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₁₉×C₄⋊C₈	—	4	1	no	—
28	C₁₉×C₄⋊C₈	—	4	1	no	—
29	C₁₉×#101	—	2	2	no	—
30	C₁₉×#101	C₈	1	4	yes	complemented
31	C₁₉×C₂²⋊C₈	—	2	2	no	—
32	C₁₉×#97	—	4	1	no	—
33	C₄×C₈×C₁₉	—	4	1	no	—
34	C₄×C₈×C₁₉	—	4	1	no	—
35	C₄×C₈×C₁₉	—	4	1	no	—
36	C₂×Q₈×C₁₉	—	4	1	no	—
37	C₂×Q₈×C₁₉	—	4	1	no	—
38	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
39	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
40	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
47	M₁₆×C₁₉	—	2	4	no	—
48	M₁₆×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	—	2	2	no	—
50	C₂×C₈×C₁₉	—	4	1	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₂×C₈×C₁₉	—	4	1	no	—
56	C₄⋊C₄×C₁₉	—	4	1	no	—
57	C₄⋊C₄×C₁₉	—	4	1	no	—
58	C₄⋊C₄×C₁₉	—	4	1	no	—
59	C₄²×C₁₉	—	2	1	no	—
60	C₄²×C₁₉	—	2	1	no	—
61	C₄²×C₁₉	—	2	1	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	C₄²×C₁₉	—	2	1	no	—
65	#7206	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂³×C₁₉	#95	1	1	yes	characteristic
67	Q₈×C₁₉	—	4	2	no	—
68	Q₈×C₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	—	2	1	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	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
86	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
89	C₈×C₁₉	—	4	2	no	—
90	C₈×C₁₉	—	4	4	no	—
91	C₈×C₁₉	—	8	2	no	—
92	C₈×C₁₉	—	8	1	no	—
93	#1984	C₂×C₁₉	1	1	yes	characteristic
94	C₄×#101	C₂×C₁₉	1	1	yes	characteristic
95	#1461	C₂×C₁₉	1	1	yes	characteristic
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	#336	1	1	yes	characteristic
99	C₂²×C₁₉	#342	1	1	yes	characteristic
100	C₂²×C₁₉	#344	1	1	yes	characteristic
101	C₄×C₁₉	—	2	2	no	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	1	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	4	1	no	—
107	C₄×C₁₉	—	4	1	no	—
108	C₄×C₁₉	—	4	1	no	—
109	C₄×C₁₉	#355	1	1	yes	characteristic
110	C₄×C₁₉	#356	1	1	yes	characteristic
111	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
112	#431	—	2	1	no	—
113	C₂×C₄⋊C₈	C₄×C₁₉	1	1	yes	characteristic
114	C₂×#101	C₄×C₁₉	1	2	yes	—
115	C₄×M₁₆	—	2	1	no	—
116	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
117	#343	—	2	1	no	—
118	#336	—	2	1	no	—
119	#336	—	2	1	no	—
120	#324	—	2	1	no	—
121	#324	C₄×C₁₉	1	2	yes	—
122	C₂×C₁₉	—	2	1	no	—
123	C₂×C₁₉	—	2	1	no	—
124	C₂×C₁₉	#1282	1	1	yes	characteristic
125	C₂×C₁₉	#1394	1	1	yes	characteristic
126	C₂×C₁₉	#1395	1	1	yes	characteristic
127	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
128	C₂×M₁₆	—	2	2	no	—
129	C₂²×C₈	—	2	1	no	—
130	C₂²×C₈	—	2	1	no	—
131	C₄×Q₈	—	4	1	no	—
132	C₄×Q₈	—	4	1	no	—
133	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
134	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
135	C₂×C₄⋊C₄	Q₈×C₁₉	1	1	yes	characteristic
136	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
137	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
138	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
139	C₄⋊C₈	—	4	1	no	—
140	C₄⋊C₈	—	4	1	no	—
141	#101	—	2	2	no	—
142	#101	C₈×C₁₉	1	4	yes	complemented
143	C₂²⋊C₈	—	2	2	no	—
144	#97	—	4	1	no	—
145	C₄×C₈	—	4	1	no	—
146	C₄×C₈	—	4	1	no	—
147	C₄×C₈	—	4	1	no	—
148	C₁₉	#7206	1	1	yes	characteristic, direct product factor, Sylow
149	C₂×Q₈	—	4	1	no	—
150	C₂×Q₈	—	4	1	no	—
151	C₂×Q₈	C₂×C₈×C₁₉	1	2	yes	—
152	C₂×Q₈	M₁₆×C₁₉	1	2	yes	—
153	C₂²×C₄	C₄²×C₁₉	1	1	yes	characteristic
154	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
156	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
159	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
160	M₁₆	—	2	4	no	—
161	M₁₆	—	4	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	—	4	1	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	1	no	—
169	C₄⋊C₄	—	4	1	no	—
170	C₄⋊C₄	—	4	1	no	—
171	C₄⋊C₄	—	4	1	no	—
172	C₄²	—	2	1	no	—
173	C₄²	—	2	1	no	—
174	C₄²	—	2	1	no	—
175	C₄²	—	2	1	no	—
176	C₄²	—	2	1	no	—
177	C₄²	—	2	1	no	—
178	C₂³	C₁₉×#95	1	1	yes	characteristic
179	Q₈	—	4	2	no	—
180	Q₈	—	4	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	C₄×C₈×C₁₉	1	1	yes	characteristic
196	C₂×C₄	C₁₉×#97	1	1	yes	characteristic
197	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
198	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
199	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
200	C₂×C₄	C₁₉×C₄⋊C₈	1	2	yes	—
201	C₈	—	4	2	no	—
202	C₈	—	4	4	no	—
203	C₈	—	8	2	no	—
204	C₈	—	8	1	no	—
205	C₂²	—	2	1	no	—
206	C₂²	—	2	1	no	—
207	C₂²	C₁₉×#336	1	1	yes	characteristic
208	C₂²	C₁₉×#342	1	1	yes	characteristic
209	C₂²	C₁₉×#344	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	2	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	2	2	no	—
215	C₄	—	4	1	no	—
216	C₄	—	4	1	no	—
217	C₄	—	4	1	no	—
218	C₄	C₁₉×#355	1	1	yes	characteristic
219	C₄	C₁₉×#356	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	C₁₉×#1282	1	1	yes	characteristic
223	C₂	C₁₉×#1394	1	1	yes	characteristic
224	C₂	C₁₉×#1395	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1984

C₂

yes

maximal, characteristic

C₄×C₁₉×#101

C₂

yes

maximal, characteristic

C₁₉×#1461

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×#101

C₄

yes

—

C₄×M₁₆×C₁₉

—

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#343

—

C₁₉×#336

—

C₁₉×#336

—

C₁₉×#324

—

C₁₉×#324

C₄

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×#101

C₈

yes

complemented

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#7206

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#95

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1984

C₂×C₁₉

yes

characteristic

C₄×#101

C₂×C₁₉

yes

characteristic

#1461

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

100

C₂²×C₁₉

#344

yes

characteristic

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#355

yes

characteristic

110

C₄×C₁₉

#356

yes

characteristic

111

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

112

#431

—

113

C₂×C₄⋊C₈

C₄×C₁₉

yes

characteristic

114

C₂×#101

C₄×C₁₉

yes

—

115

C₄×M₁₆

—

116

C₂×C₄×C₈

C₄×C₁₉

yes

characteristic

117

#343

—

118

#336

—

119

#336

—

120

#324

—

121

#324

C₄×C₁₉

yes

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#1282

yes

characteristic

125

C₂×C₁₉

#1394

yes

characteristic

126

C₂×C₁₉

#1395

yes

characteristic

127

C₂²×Q₈

C₂×C₄×C₁₉

yes

characteristic

128

C₂×M₁₆

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₄×Q₈

—

132

C₄×Q₈

—

133

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

134

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

135

C₂×C₄⋊C₄

Q₈×C₁₉

yes

characteristic

136

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

137

C₂×C₄²

D₄×C₁₉

yes

characteristic

138

C₂×C₄²

D₄×C₁₉

yes

characteristic

139

C₄⋊C₈

—

140

C₄⋊C₈

—

141

#101

—

142

#101

C₈×C₁₉

yes

complemented

143

C₂²⋊C₈

—

144

#97

—

145

C₄×C₈

—

146

C₄×C₈

—

147

C₄×C₈

—

148

C₁₉

#7206

yes

characteristic, direct product factor, Sylow

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

C₂×C₈×C₁₉

yes

—

152

C₂×Q₈

M₁₆×C₁₉

yes

—

153

C₂²×C₄

C₄²×C₁₉

yes

characteristic

154

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

155

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

156

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

157

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

158

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

159

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

160

M₁₆

—

161

M₁₆

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄²

—

173

C₄²

—

174

C₄²

—

175

C₄²

—

176

C₄²

—

177

C₄²

—

178

C₂³

C₁₉×#95

yes

characteristic

179

Q₈

—

180

Q₈

—

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

C₄×C₈×C₁₉

yes

characteristic

196

C₂×C₄

C₁₉×#97

yes

characteristic

197

C₂×C₄

C₁₉×C₂²⋊C₈

yes

—

198

C₂×C₄

C₁₉×#99

yes

characteristic

199

C₂×C₄

C₁₉×#99

yes

characteristic

200

C₂×C₄

C₁₉×C₄⋊C₈

yes

—

201

C₈

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₂²

—

206

C₂²

—

207

C₂²

C₁₉×#336

yes

characteristic

208

C₂²

C₁₉×#342

yes

characteristic

209

C₂²

C₁₉×#344

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

C₁₉×#355

yes

characteristic

219

C₄

C₁₉×#356

yes

characteristic

220

C₂

—

221

C₂

—

222

C₂

C₁₉×#1282

yes

characteristic

223

C₂

C₁₉×#1394

yes

characteristic

224

C₂

C₁₉×#1395

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#99
commutator	C₂×C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₉
socle	C₂²×C₁₉	#342
prime radical	C₂³×C₁₉	#95
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#99

commutator

C₂×C₄

C₄×C₈×C₁₉

Frattini, cosocle

C₂×C₄×Q₈

C₂²×C₁₉

C₂²×C₁₉

C₂³×C₁₉

G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
30. C₁₉×#101	C₈	semidirect
65. #7206	C₁₉	direct (N × H)
142. #101	C₈×C₁₉	semidirect
148. C₁₉	#7206	direct (N × H)

H ≅ G/N

type

30. C₁₉×#101

C₈

semidirect

65. #7206

C₁₉

direct (N × H)

142. #101

C₈×C₁₉

semidirect

148. C₁₉

#7206

direct (N × H)

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

subgroup	index
C₁₉×#1984	2
C₄×C₁₉×#101	2
C₁₉×#1461	2
#7206	19

subgroup

index

C₁₉×#1984

C₄×C₁₉×#101

C₁₉×#1461

#7206

Subgroups — C₁₉×#7206 #18013165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7206 #18013165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7206 #18013165