Group #18017608 — subgroups

Subgroups — C₁₉×#11649 #18017608

Order 4864.

348 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1331	C₂	1	4	yes	maximal, complemented
5	C₁₉×#532	—	2	1	no	—
6	C₁₉×#500	C₄	1	1	yes	characteristic
7	C₁₉×#493	C₄	1	1	yes	characteristic
8	C₁₉×#486	—	2	1	no	—
9	C₁₉×#466	—	2	1	no	—
10	C₁₉×#466	C₄	1	2	yes	—
11	C₄×D₈×C₁₉	—	2	1	no	—
12	C₄×D₈×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#431	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×C₄⋊C₁₆	—	2	1	no	—
16	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
17	C₄×C₁₆×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#335	C₂²	1	2	yes	—
19	C₁₉×#334	—	2	1	no	—
20	C₂×#41×C₁₉	—	4	1	no	—
21	C₂×D₈×C₁₉	—	2	1	no	—
22	C₂×D₈×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×#127	—	2	1	no	—
27	C₁₉×#124	—	4	1	no	—
28	C₁₉×#121	—	2	2	no	—
29	C₁₉×#121	—	4	1	no	—
30	C₄×D₄×C₁₉	—	2	2	no	—
31	C₄×D₄×C₁₉	—	4	1	no	—
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₁₆×C₁₉	—	2	2	no	—
34	C₁₉×#107	—	2	1	no	—
35	C₁₉×#107	C₂×C₄	1	2	yes	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×#102	—	2	2	no	—
38	C₁₉×#102	—	2	2	no	—
39	C₁₉×C₂²⋊C₈	—	4	1	no	—
40	C₄×C₈×C₁₉	—	4	1	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	#41×C₁₉	—	8	4	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	—	4	2	no	—
49	C₂×D₄×C₁₉	—	4	1	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
55	D₈×C₁₉	—	2	4	no	—
56	D₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	4	1	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₂²⋊C₄×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	#11649	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₁₉	—	4	2	no	—
75	C₂³×C₁₉	#102	1	1	yes	characteristic
76	Q₈×C₁₉	—	8	2	no	—
77	D₄×C₁₉	—	4	2	no	—
78	D₄×C₁₉	—	4	2	no	—
79	D₄×C₁₉	—	8	2	no	—
80	D₄×C₁₉	—	8	4	no	—
81	D₄×C₁₉	—	8	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	8	4	no	—
88	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
94	C₈×C₁₉	—	2	1	no	—
95	C₈×C₁₉	—	2	1	no	—
96	C₈×C₁₉	—	2	1	no	—
97	C₈×C₁₉	—	8	2	no	—
98	C₈×C₁₉	#131	1	2	yes	—
99	#3169	C₂×C₁₉	1	1	yes	characteristic
100	#2162	C₂×C₁₉	1	1	yes	characteristic, complemented
101	#1564	C₂×C₁₉	1	1	yes	characteristic, complemented
102	#1331	C₂×C₁₉	1	4	yes	complemented
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	8	2	no	—
107	C₂²×C₁₉	—	8	2	no	—
108	C₂²×C₁₉	—	8	2	no	—
109	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	8	2	no	—
114	C₄×C₁₉	#359	1	2	yes	—
115	C₄×C₁₉	#408	1	1	yes	characteristic
116	C₄×C₁₉	#421	1	1	yes	characteristic
117	C₄×C₁₉	#509	1	2	yes	—
118	#532	—	2	1	no	—
119	#500	C₄×C₁₉	1	1	yes	characteristic
120	#493	C₄×C₁₉	1	1	yes	characteristic
121	#486	—	2	1	no	—
122	#466	—	2	1	no	—
123	#466	C₄×C₁₉	1	2	yes	—
124	C₄×D₈	—	2	1	no	—
125	C₄×D₈	C₂²×C₁₉	1	2	yes	—
126	#431	—	2	1	no	—
127	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
128	C₄⋊C₁₆	—	2	1	no	—
129	C₂²⋊C₁₆	—	2	1	no	—
130	C₄×C₁₆	C₂²×C₁₉	1	2	yes	—
131	#335	C₂²×C₁₉	1	2	yes	—
132	#334	—	2	1	no	—
133	C₂×C₁₉	—	4	1	no	—
134	C₂×C₁₉	—	16	2	no	—
135	C₂×C₁₉	#1480	1	1	yes	characteristic
136	C₂×C₁₉	#2140	1	1	yes	characteristic
137	C₂×C₁₉	C₂×#359	1	1	yes	characteristic
138	C₂×#41	—	4	1	no	—
139	C₂×D₈	—	2	1	no	—
140	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
141	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
142	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
143	C₄⋊Q₈	—	2	1	no	—
144	#127	—	2	1	no	—
145	#124	—	4	1	no	—
146	#121	—	2	2	no	—
147	#121	—	4	1	no	—
148	C₄×D₄	—	2	2	no	—
149	C₄×D₄	—	4	1	no	—
150	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
151	C₂×C₁₆	—	2	2	no	—
152	#107	—	2	1	no	—
153	#107	C₂×C₄×C₁₉	1	2	yes	—
154	C₄⋊C₈	—	2	2	no	—
155	#102	—	2	2	no	—
156	#102	—	2	2	no	—
157	C₂²⋊C₈	—	4	1	no	—
158	C₄×C₈	—	4	1	no	—
159	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
160	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
161	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
162	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
163	C₁₉	#11649	1	1	yes	characteristic, direct product factor, Sylow
164	#41	—	8	4	no	—
165	C₂×Q₈	—	4	1	no	—
166	C₂×D₄	—	2	2	no	—
167	C₂×D₄	—	4	2	no	—
168	C₂×D₄	—	4	1	no	—
169	C₂×D₄	—	4	1	no	—
170	C₂²×C₄	—	4	2	no	—
171	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
172	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
173	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
174	D₈	—	2	4	no	—
175	D₈	—	4	2	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
180	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
181	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
182	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	4	1	no	—
185	C₂²⋊C₄	—	4	2	no	—
186	C₂²⋊C₄	—	4	2	no	—
187	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
188	C₄²	D₈×C₁₉	1	1	yes	characteristic
189	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
191	C₁₆	—	4	2	no	—
192	C₂³	—	4	2	no	—
193	C₂³	C₁₉×#102	1	1	yes	characteristic
194	Q₈	—	8	2	no	—
195	D₄	—	4	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	2	no	—
198	D₄	—	8	4	no	—
199	D₄	—	8	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	8	4	no	—
206	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
207	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
208	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
209	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
210	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
211	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
212	C₈	—	2	1	no	—
213	C₈	—	2	1	no	—
214	C₈	—	2	1	no	—
215	C₈	—	8	2	no	—
216	C₈	C₁₉×#131	1	2	yes	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	8	2	no	—
221	C₂²	—	8	2	no	—
222	C₂²	—	8	2	no	—
223	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	8	2	no	—
228	C₄	C₁₉×#359	1	2	yes	—
229	C₄	C₁₉×#408	1	1	yes	characteristic
230	C₄	C₁₉×#421	1	1	yes	characteristic
231	C₄	C₁₉×#509	1	2	yes	—
232	C₂	—	4	1	no	—
233	C₂	—	16	2	no	—
234	C₂	C₁₉×#1480	1	1	yes	characteristic
235	C₂	C₁₉×#2140	1	1	yes	characteristic
236	C₂	C₂×C₁₉×#359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3169

C₂

yes

maximal, characteristic

C₁₉×#2162

C₂

yes

maximal, characteristic, complemented

C₁₉×#1564

C₂

yes

maximal, characteristic, complemented

C₁₉×#1331

C₂

yes

maximal, complemented

C₁₉×#532

—

C₁₉×#500

C₄

yes

characteristic

C₁₉×#493

C₄

yes

characteristic

C₁₉×#486

—

C₁₉×#466

—

C₁₉×#466

C₄

yes

—

C₄×D₈×C₁₉

—

C₄×D₈×C₁₉

C₂²

yes

—

C₁₉×#431

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

—

C₄×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#335

C₂²

yes

—

C₁₉×#334

—

C₂×#41×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#127

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×#107

—

C₁₉×#107

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₁₉×#102

—

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

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

D₈×C₁₉

—

D₈×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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×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

—

#11649

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×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

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

#131

yes

—

#3169

C₂×C₁₉

yes

characteristic

100

#2162

C₂×C₁₉

yes

characteristic, complemented

101

#1564

C₂×C₁₉

yes

characteristic, complemented

102

#1331

C₂×C₁₉

yes

complemented

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

C₂×#102

yes

characteristic

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

#359

yes

—

115

C₄×C₁₉

#408

yes

characteristic

116

C₄×C₁₉

#421

yes

characteristic

117

C₄×C₁₉

#509

yes

—

118

#532

—

119

#500

C₄×C₁₉

yes

characteristic

120

#493

C₄×C₁₉

yes

characteristic

121

#486

—

122

#466

—

123

#466

C₄×C₁₉

yes

—

124

C₄×D₈

—

125

C₄×D₈

C₂²×C₁₉

yes

—

126

#431

—

127

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

128

C₄⋊C₁₆

—

129

C₂²⋊C₁₆

—

130

C₄×C₁₆

C₂²×C₁₉

yes

—

131

#335

C₂²×C₁₉

yes

—

132

#334

—

133

C₂×C₁₉

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#1480

yes

characteristic

136

C₂×C₁₉

#2140

yes

characteristic

137

C₂×C₁₉

C₂×#359

yes

characteristic

138

C₂×#41

—

139

C₂×D₈

—

140

C₂×D₈

C₂×C₄×C₁₉

yes

—

141

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

142

C₂²×C₈

D₄×C₁₉

yes

characteristic

143

C₄⋊Q₈

—

144

#127

—

145

#124

—

146

#121

—

147

#121

—

148

C₄×D₄

—

149

C₄×D₄

—

150

C₂×C₄²

D₄×C₁₉

yes

characteristic

151

C₂×C₁₆

—

152

#107

—

153

#107

C₂×C₄×C₁₉

yes

—

154

C₄⋊C₈

—

155

#102

—

156

#102

—

157

C₂²⋊C₈

—

158

C₄×C₈

—

159

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

160

C₄×C₈

D₄×C₁₉

yes

characteristic

161

C₄×C₈

D₄×C₁₉

yes

characteristic

162

C₄×C₈

C₂³×C₁₉

yes

characteristic

163

C₁₉

#11649

yes

characteristic, direct product factor, Sylow

164

#41

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

172

C₂²×C₄

D₈×C₁₉

yes

characteristic

173

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

174

D₈

—

175

D₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

180

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

181

C₂×C₈

C₂²×C₄×C₁₉

yes

characteristic

182

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

186

C₂²⋊C₄

—

187

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

188

C₄²

D₈×C₁₉

yes

characteristic

189

C₄²

SD₁₆×C₁₉

yes

characteristic

190

C₄²

C₂×D₄×C₁₉

yes

characteristic

191

C₁₆

—

192

C₂³

—

193

C₂³

C₁₉×#102

yes

characteristic

194

Q₈

—

195

D₄

—

196

D₄

—

197

D₄

—

198

D₄

—

199

D₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₁₉×#102

yes

characteristic

207

C₂×C₄

C₁₉×#102

yes

characteristic

208

C₂×C₄

C₁₉×#102

yes

characteristic

209

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

210

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

211

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

212

C₈

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

C₁₉×#131

yes

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

C₂×C₁₉×#102

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

C₁₉×#359

yes

—

229

C₄

C₁₉×#408

yes

characteristic

230

C₄

C₁₉×#421

yes

characteristic

231

C₄

C₁₉×#509

yes

—

232

C₂

—

233

C₂

—

234

C₂

C₁₉×#1480

yes

characteristic

235

C₂

C₁₉×#2140

yes

characteristic

236

C₂

C₂×C₁₉×#359

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#102
prime radical	C₁₉×#3169	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

C₂×D₈

commutator

C₂×C₈

C₂²×C₄×C₁₉

Frattini, cosocle

C₄×C₈

C₂³×C₁₉

socle

C₂²×C₁₉

C₂×#102

prime radical

C₁₉×#3169

C₂

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
2. C₁₉×#2162	C₂	semidirect
3. C₁₉×#1564	C₂	semidirect
4. C₁₉×#1331	C₂	semidirect
73. #11649	C₁₉	direct (N × H)
100. #2162	C₂×C₁₉	semidirect
101. #1564	C₂×C₁₉	semidirect
102. #1331	C₂×C₁₉	semidirect
163. C₁₉	#11649	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2162

C₂

semidirect

3. C₁₉×#1564

C₂

semidirect

4. C₁₉×#1331

C₂

semidirect

73. #11649

C₁₉

direct (N × H)

100. #2162

C₂×C₁₉

semidirect

101. #1564

C₂×C₁₉

semidirect

102. #1331

C₂×C₁₉

semidirect

163. C₁₉

#11649

direct (N × H)

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

subgroup	index
C₁₉×#3169	2
C₁₉×#2162	2
C₁₉×#1564	2
C₁₉×#1331	2
#11649	19

subgroup

index

C₁₉×#3169

C₁₉×#2162

C₁₉×#1564

C₁₉×#1331

#11649

Subgroups — C₁₉×#11649 #18017608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11649 #18017608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11649 #18017608