Group #18017910 — subgroups

Subgroups — C₁₉×#11951 #18017910

Order 4864.

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

normal subgroups only

This group has 340 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×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1364	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1361	C₂	1	2	yes	maximal, complemented
6	C₁₉×#532	—	2	1	no	—
7	C₁₉×#500	C₂²	1	1	yes	characteristic
8	C₁₉×#493	C₂²	1	1	yes	characteristic
9	C₁₉×#486	—	2	1	no	—
10	C₁₉×#466	—	2	1	no	—
11	C₁₉×#466	C₄	1	2	yes	—
12	C₄×D₈×C₁₉	—	2	1	no	—
13	C₄×D₈×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×#41×C₁₉	—	4	1	no	—
22	C₂×D₈×C₁₉	—	2	1	no	—
23	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₁₉×C₄⋊Q₈	—	2	1	no	—
27	C₁₉×#127	—	2	1	no	—
28	C₁₉×#124	—	4	1	no	—
29	C₁₉×#121	—	2	2	no	—
30	C₁₉×#121	—	4	1	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₄×D₄×C₁₉	—	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×#102	—	2	2	no	—
39	C₁₉×#102	—	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	#41×C₁₉	—	8	4	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	—	4	2	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
56	D₈×C₁₉	—	4	2	no	—
57	D₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	4	1	no	—
67	C₂²⋊C₄×C₁₉	—	4	2	no	—
68	C₂²⋊C₄×C₁₉	—	4	2	no	—
69	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₉	D₈	1	1	yes	characteristic
71	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₁₆×C₁₉	—	4	2	no	—
74	#11951	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₁₉	—	4	2	no	—
76	C₂³×C₁₉	#102	1	1	yes	characteristic
77	Q₈×C₁₉	—	8	2	no	—
78	D₄×C₁₉	—	4	2	no	—
79	D₄×C₁₉	—	4	2	no	—
80	D₄×C₁₉	—	8	2	no	—
81	D₄×C₁₉	—	8	4	no	—
82	D₄×C₁₉	—	8	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	1	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	8	4	no	—
89	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
95	C₈×C₁₉	—	2	1	no	—
96	C₈×C₁₉	—	2	1	no	—
97	C₈×C₁₉	—	2	1	no	—
98	C₈×C₁₉	—	8	2	no	—
99	C₈×C₁₉	#135	1	2	yes	—
100	#3169	C₂×C₁₉	1	1	yes	characteristic
101	#2163	C₂×C₁₉	1	1	yes	characteristic, complemented
102	#1564	C₂×C₁₉	1	1	yes	characteristic, complemented
103	#1364	C₂×C₁₉	1	2	yes	complemented
104	#1361	C₂×C₁₉	1	2	yes	complemented
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	8	2	no	—
109	C₂²×C₁₉	—	8	2	no	—
110	C₂²×C₁₉	—	8	2	no	—
111	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	8	2	no	—
117	C₄×C₁₉	#413	1	1	yes	characteristic
118	C₄×C₁₉	#416	1	1	yes	characteristic
119	C₄×C₁₉	#509	1	2	yes	—
120	#532	—	2	1	no	—
121	#500	C₂²×C₁₉	1	1	yes	characteristic
122	#493	C₂²×C₁₉	1	1	yes	characteristic
123	#486	—	2	1	no	—
124	#466	—	2	1	no	—
125	#466	C₄×C₁₉	1	2	yes	—
126	C₄×D₈	—	2	1	no	—
127	C₄×D₈	C₄×C₁₉	1	2	yes	—
128	#431	—	2	1	no	—
129	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
130	C₄⋊C₁₆	C₂²×C₁₉	1	2	yes	—
131	C₂²⋊C₁₆	—	2	1	no	—
132	#346	—	2	1	no	—
133	#335	C₂²×C₁₉	1	2	yes	—
134	#334	—	2	1	no	—
135	C₂×C₁₉	—	4	1	no	—
136	C₂×C₁₉	—	16	2	no	—
137	C₂×C₁₉	#1540	1	1	yes	characteristic
138	C₂×C₁₉	#2140	1	1	yes	characteristic
139	C₂×C₁₉	#2148	1	1	yes	characteristic
140	C₂×#41	—	4	1	no	—
141	C₂×D₈	—	2	1	no	—
142	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
143	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
144	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
145	C₄⋊Q₈	—	2	1	no	—
146	#127	—	2	1	no	—
147	#124	—	4	1	no	—
148	#121	—	2	2	no	—
149	#121	—	4	1	no	—
150	C₄×D₄	—	2	2	no	—
151	C₄×D₄	—	4	1	no	—
152	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
153	C₂×C₁₆	—	2	2	no	—
154	#107	—	2	1	no	—
155	#107	C₂×C₄×C₁₉	1	2	yes	—
156	C₄⋊C₈	—	2	2	no	—
157	#102	—	2	2	no	—
158	#102	—	2	2	no	—
159	C₂²⋊C₈	—	4	1	no	—
160	C₄×C₈	—	4	1	no	—
161	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
162	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
163	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
164	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
165	C₁₉	#11951	1	1	yes	characteristic, direct product factor, Sylow
166	#41	—	8	4	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	4	2	no	—
170	C₂×D₄	—	4	1	no	—
171	C₂×D₄	—	4	1	no	—
172	C₂²×C₄	—	4	2	no	—
173	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
174	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
175	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
176	D₈	—	4	2	no	—
177	D₈	—	4	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
182	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
183	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
184	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₂²⋊C₄	—	4	2	no	—
188	C₂²⋊C₄	—	4	2	no	—
189	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
190	C₄²	D₈×C₁₉	1	1	yes	characteristic
191	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
192	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
193	C₁₆	—	4	2	no	—
194	C₂³	—	4	2	no	—
195	C₂³	C₁₉×#102	1	1	yes	characteristic
196	Q₈	—	8	2	no	—
197	D₄	—	4	2	no	—
198	D₄	—	4	2	no	—
199	D₄	—	8	2	no	—
200	D₄	—	8	4	no	—
201	D₄	—	8	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	8	4	no	—
208	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
209	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
210	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
211	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
212	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
213	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
214	C₈	—	2	1	no	—
215	C₈	—	2	1	no	—
216	C₈	—	2	1	no	—
217	C₈	—	8	2	no	—
218	C₈	C₁₉×#135	1	2	yes	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	8	2	no	—
223	C₂²	—	8	2	no	—
224	C₂²	—	8	2	no	—
225	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	8	2	no	—
231	C₄	C₁₉×#413	1	1	yes	characteristic
232	C₄	C₁₉×#416	1	1	yes	characteristic
233	C₄	C₁₉×#509	1	2	yes	—
234	C₂	—	4	1	no	—
235	C₂	—	16	2	no	—
236	C₂	C₁₉×#1540	1	1	yes	characteristic
237	C₂	C₁₉×#2140	1	1	yes	characteristic
238	C₂	C₁₉×#2148	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3169

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, characteristic, complemented

C₁₉×#1564

C₂

yes

maximal, characteristic, complemented

C₁₉×#1364

C₂

yes

maximal, complemented

C₁₉×#1361

C₂

yes

maximal, complemented

C₁₉×#532

—

C₁₉×#500

C₂²

yes

characteristic

C₁₉×#493

C₂²

yes

characteristic

C₁₉×#486

—

C₁₉×#466

—

C₁₉×#466

C₄

yes

—

C₄×D₈×C₁₉

—

C₄×D₈×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×#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

—

#11951

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

#135

yes

—

100

#3169

C₂×C₁₉

yes

characteristic

101

#2163

C₂×C₁₉

yes

characteristic, complemented

102

#1564

C₂×C₁₉

yes

characteristic, complemented

103

#1364

C₂×C₁₉

yes

complemented

104

#1361

C₂×C₁₉

yes

complemented

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

C₂×#102

yes

characteristic

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#413

yes

characteristic

118

C₄×C₁₉

#416

yes

characteristic

119

C₄×C₁₉

#509

yes

—

120

#532

—

121

#500

C₂²×C₁₉

yes

characteristic

122

#493

C₂²×C₁₉

yes

characteristic

123

#486

—

124

#466

—

125

#466

C₄×C₁₉

yes

—

126

C₄×D₈

—

127

C₄×D₈

C₄×C₁₉

yes

—

128

#431

—

129

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

130

C₄⋊C₁₆

C₂²×C₁₉

yes

—

131

C₂²⋊C₁₆

—

132

#346

—

133

#335

C₂²×C₁₉

yes

—

134

#334

—

135

C₂×C₁₉

—

136

C₂×C₁₉

—

137

C₂×C₁₉

#1540

yes

characteristic

138

C₂×C₁₉

#2140

yes

characteristic

139

C₂×C₁₉

#2148

yes

characteristic

140

C₂×#41

—

141

C₂×D₈

—

142

C₂×D₈

C₂×C₄×C₁₉

yes

—

143

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

144

C₂²×C₈

D₄×C₁₉

yes

characteristic

145

C₄⋊Q₈

—

146

#127

—

147

#124

—

148

#121

—

149

#121

—

150

C₄×D₄

—

151

C₄×D₄

—

152

C₂×C₄²

D₄×C₁₉

yes

characteristic

153

C₂×C₁₆

—

154

#107

—

155

#107

C₂×C₄×C₁₉

yes

—

156

C₄⋊C₈

—

157

#102

—

158

#102

—

159

C₂²⋊C₈

—

160

C₄×C₈

—

161

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

162

C₄×C₈

D₄×C₁₉

yes

characteristic

163

C₄×C₈

D₄×C₁₉

yes

characteristic

164

C₄×C₈

C₂³×C₁₉

yes

characteristic

165

C₁₉

#11951

yes

characteristic, direct product factor, Sylow

166

#41

—

167

C₂×Q₈

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

174

C₂²×C₄

D₈×C₁₉

yes

characteristic

175

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

176

D₈

—

177

D₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

182

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

183

C₂×C₈

C₂²×C₄×C₁₉

yes

characteristic

184

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

190

C₄²

D₈×C₁₉

yes

characteristic

191

C₄²

SD₁₆×C₁₉

yes

characteristic

192

C₄²

C₂×D₄×C₁₉

yes

characteristic

193

C₁₆

—

194

C₂³

—

195

C₂³

C₁₉×#102

yes

characteristic

196

Q₈

—

197

D₄

—

198

D₄

—

199

D₄

—

200

D₄

—

201

D₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

C₁₉×#102

yes

characteristic

209

C₂×C₄

C₁₉×#102

yes

characteristic

210

C₂×C₄

C₁₉×#102

yes

characteristic

211

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

212

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

213

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

—

218

C₈

C₁₉×#135

yes

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₂×C₁₉×#102

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₁₉×#413

yes

characteristic

232

C₄

C₁₉×#416

yes

characteristic

233

C₄

C₁₉×#509

yes

—

234

C₂

—

235

C₂

—

236

C₂

C₁₉×#1540

yes

characteristic

237

C₂

C₁₉×#2140

yes

characteristic

238

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	C₁₉×#3169	C₂
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

C₁₉×#3169

C₂

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
2. C₁₉×#2163	C₂	semidirect
3. C₁₉×#1564	C₂	semidirect
4. C₁₉×#1364	C₂	semidirect
5. C₁₉×#1361	C₂	semidirect
74. #11951	C₁₉	direct (N × H)
101. #2163	C₂×C₁₉	semidirect
102. #1564	C₂×C₁₉	semidirect
103. #1364	C₂×C₁₉	semidirect
104. #1361	C₂×C₁₉	semidirect
165. C₁₉	#11951	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2163

C₂

semidirect

3. C₁₉×#1564

C₂

semidirect

4. C₁₉×#1364

C₂

semidirect

5. C₁₉×#1361

C₂

semidirect

74. #11951

C₁₉

direct (N × H)

101. #2163

C₂×C₁₉

semidirect

102. #1564

C₂×C₁₉

semidirect

103. #1364

C₂×C₁₉

semidirect

104. #1361

C₂×C₁₉

semidirect

165. C₁₉

#11951

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×#2163	2
C₁₉×#1564	2
C₁₉×#1364	2
C₁₉×#1361	2
#11951	19

subgroup

index

C₁₉×#3169

C₁₉×#2163

C₁₉×#1564

C₁₉×#1364

C₁₉×#1361

#11951

Subgroups — C₁₉×#11951 #18017910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11951 #18017910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11951 #18017910