Group #18016623 — subgroups

Subgroups — C₁₉×#10664 #18016623

Order 4864.

304 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 106 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×#1985	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1838	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1571	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1570	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1487	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1487	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1275	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#431	C₂²	1	1	yes	characteristic
10	C₁₉×#431	C₂²	1	1	yes	characteristic
11	C₁₉×#423	C₂²	1	1	yes	characteristic
12	C₁₉×#423	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
15	C₁₉×#341	—	2	2	no	—
16	C₁₉×#336	—	2	2	no	—
17	C₁₉×#335	—	2	2	no	—
18	C₁₉×#334	—	2	2	no	—
19	C₁₉×Q₈⋊C₈	—	2	2	no	—
20	C₁₉×Q₈⋊C₈	—	2	2	no	—
21	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	2	yes	—
26	C₄×Q₈×C₁₉	—	2	1	no	—
27	C₄×Q₈×C₁₉	—	2	1	no	—
28	C₄×Q₈×C₁₉	—	2	1	no	—
29	C₄×Q₈×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×C₂²⋊C₈	—	2	1	no	—
43	C₁₉×C₂²⋊C₈	—	2	1	no	—
44	C₁₉×#97	—	2	1	no	—
45	C₁₉×#97	—	2	1	no	—
46	C₄×C₈×C₁₉	D₄	1	2	yes	—
47	C₄×C₈×C₁₉	D₄	1	2	yes	—
48	C₂×Q₈×C₁₉	—	2	1	no	—
49	C₂×Q₈×C₁₉	—	2	1	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
56	M₁₆×C₁₉	—	4	2	no	—
57	M₁₆×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	4	1	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	1	no	—
68	C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	1	no	—
71	C₄²×C₁₉	—	4	1	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₉	#41	1	1	yes	characteristic
76	C₄²×C₁₉	#41	1	1	yes	characteristic
77	#10664	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
79	Q₈×C₁₉	—	2	2	no	—
80	Q₈×C₁₉	—	2	2	no	—
81	Q₈×C₁₉	—	4	1	no	—
82	Q₈×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#135	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₈×C₁₉	—	4	2	no	—
99	C₈×C₁₉	—	4	2	no	—
100	C₈×C₁₉	—	4	2	no	—
101	C₈×C₁₉	—	8	1	no	—
102	C₈×C₁₉	—	8	1	no	—
103	C₈×C₁₉	—	8	1	no	—
104	#1985	C₂×C₁₉	1	1	yes	characteristic
105	#1838	C₂×C₁₉	1	1	yes	characteristic
106	#1571	C₂×C₁₉	1	1	yes	characteristic
107	#1570	C₂×C₁₉	1	1	yes	characteristic
108	#1487	C₂×C₁₉	1	1	yes	characteristic
109	#1487	C₂×C₁₉	1	1	yes	characteristic
110	#1275	C₂×C₁₉	1	1	yes	characteristic
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	#399	1	1	yes	characteristic
114	C₂²×C₁₉	#479	1	2	yes	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	4	2	no	—
120	C₄×C₁₉	—	8	1	no	—
121	C₄×C₁₉	#485	1	2	yes	—
122	C₄×C₁₉	#495	1	1	yes	characteristic
123	C₄×C₁₉	#497	1	1	yes	characteristic
124	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
125	#431	C₂²×C₁₉	1	1	yes	characteristic
126	#431	C₂²×C₁₉	1	1	yes	characteristic
127	#423	C₂²×C₁₉	1	1	yes	characteristic
128	#423	C₂²×C₁₉	1	1	yes	characteristic
129	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
130	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
131	#341	—	2	2	no	—
132	#336	—	2	2	no	—
133	#335	—	2	2	no	—
134	#334	—	2	2	no	—
135	Q₈⋊C₈	—	2	2	no	—
136	Q₈⋊C₈	—	2	2	no	—
137	C₂×C₁₉	—	2	2	no	—
138	C₂×C₁₉	#2091	1	1	yes	characteristic
139	C₂×C₁₉	#2097	1	1	yes	characteristic
140	C₂×C₁₉	#2098	1	1	yes	characteristic
141	C₂²×Q₈	Q₈×C₁₉	1	1	yes	characteristic
142	C₂×M₁₆	—	2	1	no	—
143	C₂×M₁₆	—	2	1	no	—
144	C₂²×C₈	—	2	1	no	—
145	C₂²×C₈	D₄×C₁₉	1	2	yes	—
146	C₄×Q₈	—	2	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	Q₈×C₁₉	1	1	yes	characteristic
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	2	1	no	—
160	C₄⋊C₈	—	2	1	no	—
161	C₄⋊C₈	—	2	1	no	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	2	1	no	—
164	#97	—	2	1	no	—
165	#97	—	2	1	no	—
166	C₄×C₈	D₄×C₁₉	1	2	yes	—
167	C₄×C₈	D₄×C₁₉	1	2	yes	—
168	C₁₉	#10664	1	1	yes	characteristic, direct product factor, Sylow
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
175	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
176	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
177	M₁₆	—	4	2	no	—
178	M₁₆	—	4	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	1	no	—
185	C₂×C₈	—	4	1	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	4	1	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄²	—	4	1	no	—
193	C₄²	—	4	1	no	—
194	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
195	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
196	C₄²	#41×C₁₉	1	1	yes	characteristic
197	C₄²	#41×C₁₉	1	1	yes	characteristic
198	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
199	Q₈	—	2	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	4	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
211	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
213	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
214	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
215	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
216	C₂×C₄	C₁₉×#135	1	2	yes	—
217	C₂×C₄	C₁₉×#137	1	2	yes	—
218	C₈	—	4	2	no	—
219	C₈	—	4	2	no	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	8	1	no	—
223	C₈	—	8	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	C₁₉×#399	1	1	yes	characteristic
227	C₂²	C₁₉×#479	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	4	2	no	—
233	C₄	—	8	1	no	—
234	C₄	C₁₉×#485	1	2	yes	—
235	C₄	C₁₉×#495	1	1	yes	characteristic
236	C₄	C₁₉×#497	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	C₁₉×#2091	1	1	yes	characteristic
239	C₂	C₁₉×#2097	1	1	yes	characteristic
240	C₂	C₁₉×#2098	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1985

C₂

yes

maximal, characteristic

C₁₉×#1838

C₂

yes

maximal, characteristic

C₁₉×#1571

C₂

yes

maximal, characteristic

C₁₉×#1570

C₂

yes

maximal, characteristic

C₁₉×#1487

C₂

yes

maximal, characteristic

C₁₉×#1487

C₂

yes

maximal, characteristic

C₁₉×#1275

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#341

—

C₁₉×#336

—

C₁₉×#335

—

C₁₉×#334

—

C₁₉×Q₈⋊C₈

—

C₁₉×Q₈⋊C₈

—

C₂²×Q₈×C₁₉

Q₈

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

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×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

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

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

#1985

C₂×C₁₉

yes

characteristic

105

#1838

C₂×C₁₉

yes

characteristic

106

#1571

C₂×C₁₉

yes

characteristic

107

#1570

C₂×C₁₉

yes

characteristic

108

#1487

C₂×C₁₉

yes

characteristic

109

#1487

C₂×C₁₉

yes

characteristic

110

#1275

C₂×C₁₉

yes

characteristic

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#399

yes

characteristic

114

C₂²×C₁₉

#479

yes

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#485

yes

—

122

C₄×C₁₉

#495

yes

characteristic

123

C₄×C₁₉

#497

yes

characteristic

124

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

125

#431

C₂²×C₁₉

yes

characteristic

126

#431

C₂²×C₁₉

yes

characteristic

127

#423

C₂²×C₁₉

yes

characteristic

128

#423

C₂²×C₁₉

yes

characteristic

129

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

130

C₂×#97

C₂²×C₁₉

yes

characteristic

131

#341

—

132

#336

—

133

#335

—

134

#334

—

135

Q₈⋊C₈

—

136

Q₈⋊C₈

—

137

C₂×C₁₉

—

138

C₂×C₁₉

#2091

yes

characteristic

139

C₂×C₁₉

#2097

yes

characteristic

140

C₂×C₁₉

#2098

yes

characteristic

141

C₂²×Q₈

Q₈×C₁₉

yes

characteristic

142

C₂×M₁₆

—

143

C₂×M₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

D₄×C₁₉

yes

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

Q₈×C₁₉

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

C₂³×C₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

#97

—

165

#97

—

166

C₄×C₈

D₄×C₁₉

yes

—

167

C₄×C₈

D₄×C₁₉

yes

—

168

C₁₉

#10664

yes

characteristic, direct product factor, Sylow

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

175

C₂²×C₄

C₂×Q₈×C₁₉

yes

characteristic

176

C₂²×C₄

#41×C₁₉

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄²

—

193

C₄²

—

194

C₄²

C₂×D₄×C₁₉

yes

characteristic

195

C₄²

C₂×D₄×C₁₉

yes

characteristic

196

C₄²

#41×C₁₉

yes

characteristic

197

C₄²

#41×C₁₉

yes

characteristic

198

C₂³

C₁₉×C₂²⋊Q₈

yes

characteristic

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

211

C₂×C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

212

C₂×C₄

C₁₉×#123

yes

characteristic

213

C₂×C₄

C₁₉×#123

yes

characteristic

214

C₂×C₄

C₁₉×#123

yes

characteristic

215

C₂×C₄

C₁₉×#127

yes

characteristic

216

C₂×C₄

C₁₉×#135

yes

—

217

C₂×C₄

C₁₉×#137

yes

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₂²

—

225

C₂²

—

226

C₂²

C₁₉×#399

yes

characteristic

227

C₂²

C₁₉×#479

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

C₁₉×#485

yes

—

235

C₄

C₁₉×#495

yes

characteristic

236

C₄

C₁₉×#497

yes

characteristic

237

C₂

—

238

C₂

C₁₉×#2091

yes

characteristic

239

C₂

C₁₉×#2097

yes

characteristic

240

C₂

C₁₉×#2098

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#399
prime radical	C₂³×C₁₉	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

socle

C₂²×C₁₉

#399

prime radical

C₂³×C₁₉

C₂²⋊Q₈

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
77. #10664	C₁₉	direct (N × H)
168. C₁₉	#10664	direct (N × H)

H ≅ G/N

type

77. #10664

C₁₉

direct (N × H)

168. C₁₉

#10664

direct (N × H)

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

subgroup	index
C₁₉×#1985	2
C₁₉×#1838	2
C₁₉×#1571	2
C₁₉×#1570	2
C₁₉×#1487	2
C₁₉×#1275	2
#10664	19

subgroup

index

C₁₉×#1985

C₁₉×#1838

C₁₉×#1571

C₁₉×#1570

C₁₉×#1487

C₁₉×#1275

#10664

Subgroups — C₁₉×#10664 #18016623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10664 #18016623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10664 #18016623