Group #18014486 — subgroups

Subgroups — C₁₉×#8527 #18014486

Order 4864.

656 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 142 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	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1558	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1534	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1464	C₂	1	2	yes	maximal
5	C₁₉×#541	—	2	4	no	—
6	C₁₉×#541	—	2	4	no	—
7	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#126	—	2	2	no	—
9	C₂×C₁₉×#125	—	2	2	no	—
10	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
12	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₁₉×#432	C₂²	1	4	yes	—
15	C₁₉×#333	—	2	4	no	—
16	C₁₉×#330	—	2	4	no	—
17	C₁₉×#324	—	2	2	no	—
18	C₁₉×#323	—	2	2	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
23	C₁₉×#126	—	2	16	no	—
24	C₁₉×#125	—	2	16	no	—
25	C₁₉×#125	—	2	2	no	—
26	C₁₉×#125	D₄	1	4	yes	—
27	C₁₉×C₂²⋊Q₈	—	2	4	no	—
28	C₁₉×C₂²⋊Q₈	—	2	4	no	—
29	C₄×Q₈×C₁₉	—	2	4	no	—
30	C₄×Q₈×C₁₉	—	2	4	no	—
31	C₁₉×#117	—	2	2	no	—
32	C₁₉×#117	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
41	C₂×C₄²×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×C₄⋊C₈	—	2	4	no	—
45	C₁₉×C₂²⋊C₈	—	2	4	no	—
46	C₁₉×#97	—	2	4	no	—
47	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	4	4	no	—
50	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₉	—	4	4	no	—
61	C₄⋊C₄×C₁₉	—	2	8	no	—
62	C₄⋊C₄×C₁₉	—	2	8	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	2	8	no	—
65	C₄⋊C₄×C₁₉	—	2	8	no	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
68	C₂²⋊C₄×C₁₉	—	2	8	no	—
69	C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₄²×C₁₉	—	2	8	no	—
71	C₄²×C₁₉	—	2	1	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	C₂×D₄	1	2	yes	—
74	C₄²×C₁₉	C₂×D₄	1	2	yes	—
75	#8527	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂³×C₁₉	—	2	1	no	—
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	—	4	2	no	—
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	Q₈×C₁₉	—	4	4	no	—
81	Q₈×C₁₉	—	4	4	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	—	4	4	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#120	1	4	yes	—
97	C₈×C₁₉	—	8	4	no	—
98	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
99	#1558	C₂×C₁₉	1	2	yes	complemented
100	#1534	C₂×C₁₉	1	2	yes	complemented
101	#1464	C₂×C₁₉	1	2	yes	—
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	—	4	1	no	—
105	C₂²×C₁₉	—	8	2	no	—
106	C₂²×C₁₉	#379	1	1	yes	characteristic
107	C₂²×C₁₉	#413	1	2	yes	—
108	C₄×C₁₉	—	2	4	no	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	—	4	4	no	—
113	C₄×C₁₉	—	4	1	no	—
114	C₄×C₁₉	—	4	4	no	—
115	#541	—	2	4	no	—
116	#541	—	2	4	no	—
117	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
118	C₂×#126	—	2	2	no	—
119	C₂×#125	—	2	2	no	—
120	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
121	C₂×C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
122	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
123	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
124	#432	C₂²×C₁₉	1	4	yes	—
125	#333	—	2	4	no	—
126	#330	—	2	4	no	—
127	#324	—	2	2	no	—
128	#323	—	2	2	no	—
129	C₂×C₁₉	—	2	2	no	—
130	C₂×C₁₉	—	8	1	no	—
131	C₂×C₁₉	#1785	1	1	yes	characteristic
132	C₂×C₁₉	#1796	1	2	yes	—
133	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
134	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	D₄×C₁₉	1	4	yes	—
137	#126	—	2	16	no	—
138	#125	—	2	16	no	—
139	#125	—	2	2	no	—
140	#125	D₄×C₁₉	1	4	yes	—
141	C₂²⋊Q₈	—	2	4	no	—
142	C₂²⋊Q₈	—	2	4	no	—
143	C₄×Q₈	—	2	4	no	—
144	C₄×Q₈	—	2	4	no	—
145	#117	—	2	2	no	—
146	#117	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
152	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
153	C₂×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
155	C₂×C₄²	—	2	2	no	—
156	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
157	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
158	C₄⋊C₈	—	2	4	no	—
159	C₂²⋊C₈	—	2	4	no	—
160	#97	—	2	4	no	—
161	C₁₉	#8527	1	1	yes	characteristic, direct product factor, Sylow
162	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	4	2	no	—
171	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
173	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
174	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
175	C₂×C₈	—	4	4	no	—
176	C₄⋊C₄	—	2	8	no	—
177	C₄⋊C₄	—	2	8	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	8	no	—
180	C₄⋊C₄	—	2	8	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
183	C₂²⋊C₄	—	2	8	no	—
184	C₂²⋊C₄	—	2	4	no	—
185	C₄²	—	2	8	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	C₂×D₄×C₁₉	1	2	yes	—
189	C₄²	C₂×D₄×C₁₉	1	2	yes	—
190	C₂³	—	2	1	no	—
191	C₂³	—	2	2	no	—
192	C₂³	—	4	2	no	—
193	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	4	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
209	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
210	C₂×C₄	C₁₉×#120	1	4	yes	—
211	C₈	—	8	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	8	2	no	—
216	C₂²	C₁₉×#379	1	1	yes	characteristic
217	C₂²	C₁₉×#413	1	2	yes	—
218	C₄	—	2	1	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	4	no	—
221	C₄	—	4	1	no	—
222	C₄	—	4	4	no	—
223	C₄	—	4	4	no	—
224	C₄	—	4	2	no	—
225	C₂	—	2	2	no	—
226	C₂	—	8	1	no	—
227	C₂	C₁₉×#1785	1	1	yes	characteristic
228	C₂	C₁₉×#1796	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#541

C₂

yes

maximal, characteristic

C₁₉×#1558

C₂

yes

maximal, complemented

C₁₉×#1534

C₂

yes

maximal, complemented

C₁₉×#1464

C₂

yes

maximal

C₁₉×#541

—

C₁₉×#541

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#126

—

C₂×C₁₉×#125

—

C₂×C₁₉×#125

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊Q₈

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₄

yes

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#432

C₂²

yes

—

C₁₉×#333

—

C₁₉×#330

—

C₁₉×#324

—

C₁₉×#323

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#126

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#8527

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₈×C₁₉

—

C₂×#541

C₂×C₁₉

yes

characteristic

#1558

C₂×C₁₉

yes

complemented

100

#1534

C₂×C₁₉

yes

complemented

101

#1464

C₂×C₁₉

yes

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

#379

yes

characteristic

107

C₂²×C₁₉

#413

yes

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

#541

—

116

#541

—

117

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

characteristic

118

C₂×#126

—

119

C₂×#125

—

120

C₂×#125

C₂²×C₁₉

yes

characteristic

121

C₂×C₂²⋊Q₈

C₄×C₁₉

yes

—

122

C₂×C₄×Q₈

C₄×C₁₉

yes

—

123

C₂×#117

C₂²×C₁₉

yes

characteristic

124

#432

C₂²×C₁₉

yes

—

125

#333

—

126

#330

—

127

#324

—

128

#323

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1785

yes

characteristic

132

C₂×C₁₉

#1796

yes

—

133

C₂²×Q₈

C₂×C₄×C₁₉

yes

—

134

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

135

C₄⋊Q₈

—

136

C₄⋊Q₈

D₄×C₁₉

yes

—

137

#126

—

138

#125

—

139

#125

—

140

#125

D₄×C₁₉

yes

—

141

C₂²⋊Q₈

—

142

C₂²⋊Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

#117

—

146

#117

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

152

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

153

C₂×C₂²⋊C₄

—

154

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

157

C₂×C₄²

C₂³×C₁₉

yes

characteristic

158

C₄⋊C₈

—

159

C₂²⋊C₈

—

160

#97

—

161

C₁₉

#8527

yes

characteristic, direct product factor, Sylow

162

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

C₂²⋊C₄×C₁₉

yes

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

172

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

173

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

174

C₂²×C₄

C₂×D₄×C₁₉

yes

—

175

C₂×C₈

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

C₂²⋊C₄×C₁₉

yes

—

183

C₂²⋊C₄

—

184

C₂²⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

C₂×D₄×C₁₉

yes

—

189

C₄²

C₂×D₄×C₁₉

yes

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

194

Q₈

—

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

209

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

210

C₂×C₄

C₁₉×#120

yes

—

211

C₈

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

C₁₉×#379

yes

characteristic

217

C₂²

C₁₉×#413

yes

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₂

—

226

C₂

—

227

C₂

C₁₉×#1785

yes

characteristic

228

C₂

C₁₉×#1796

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#379

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1558	C₂	semidirect
3. C₁₉×#1534	C₂	semidirect
75. #8527	C₁₉	direct (N × H)
99. #1558	C₂×C₁₉	semidirect
100. #1534	C₂×C₁₉	semidirect
161. C₁₉	#8527	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1558

C₂

semidirect

3. C₁₉×#1534

C₂

semidirect

75. #8527

C₁₉

direct (N × H)

99. #1558

C₂×C₁₉

semidirect

100. #1534

C₂×C₁₉

semidirect

161. C₁₉

#8527

direct (N × H)

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

subgroup	index
C₂×C₁₉×#541	2
C₁₉×#1558	2
C₁₉×#1534	2
C₁₉×#1464	2
#8527	19

subgroup

index

C₂×C₁₉×#541

C₁₉×#1558

C₁₉×#1534

C₁₉×#1464

#8527

Subgroups — C₁₉×#8527 #18014486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8527 #18014486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8527 #18014486