Group #18017480 — subgroups

Subgroups — C₁₉×#11521 #18017480

Order 4864.

330 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2920	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2165	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1327	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1320	C₂	1	2	yes	maximal
5	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×#432	—	2	2	no	—
7	C₁₉×#431	—	2	2	no	—
8	C₁₉×#423	C₄	1	1	yes	characteristic
9	C₁₉×#423	C₂²	1	1	yes	characteristic
10	C₁₉×#407	C₄	1	1	yes	characteristic
11	C₁₉×#407	C₂²	1	1	yes	characteristic
12	C₄×M₁₆×C₁₉	C₄	1	1	yes	characteristic
13	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#364	—	2	2	no	—
15	C₁₉×#349	C₂²	1	4	yes	—
16	C₁₉×#347	—	2	2	no	—
17	C₂³×C₄×C₁₉	—	2	1	no	—
18	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	—	2	1	no	—
24	C₂×C₄²×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	—	2	1	no	—
27	C₂×C₄²×C₁₉	—	2	1	no	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₁₉×M₃₂	—	2	4	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×C₂²⋊C₈	—	2	2	no	—
35	C₁₉×#97	—	2	1	no	—
36	C₁₉×#97	D₄	1	2	yes	—
37	C₄×C₈×C₁₉	—	2	1	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₂⁴×C₁₉	M₁₆	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	—	2	1	no	—
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	—	4	4	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	M₁₆×C₁₉	—	4	1	no	—
54	M₁₆×C₁₉	—	4	1	no	—
55	M₁₆×C₁₉	—	4	1	no	—
56	M₁₆×C₁₉	—	4	1	no	—
57	C₂×C₈×C₁₉	—	2	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	C₄²×C₁₉	—	2	1	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
70	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
71	C₁₆×C₁₉	—	4	4	no	—
72	#11521	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂³×C₁₉	—	2	1	no	—
74	C₂³×C₁₉	—	4	2	no	—
75	C₂³×C₁₉	—	4	1	no	—
76	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	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	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
96	C₈×C₁₉	—	2	2	no	—
97	C₈×C₁₉	—	2	2	no	—
98	C₈×C₁₉	—	4	1	no	—
99	C₈×C₁₉	—	4	1	no	—
100	#2920	C₂×C₁₉	1	1	yes	characteristic
101	#2165	C₂×C₁₉	1	2	yes	complemented
102	#1327	C₂×C₁₉	1	2	yes	complemented
103	#1320	C₂×C₁₉	1	2	yes	—
104	C₂²×C₁₉	—	2	2	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	4	1	no	—
107	C₂²×C₁₉	—	4	1	no	—
108	C₂²×C₁₉	—	4	2	no	—
109	C₂²×C₁₉	—	4	2	no	—
110	C₂²×C₁₉	—	4	1	no	—
111	C₂²×C₁₉	#407	1	1	yes	characteristic
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	4	1	no	—
116	C₄×C₁₉	—	4	1	no	—
117	C₄×C₁₉	—	4	1	no	—
118	C₄×C₁₉	#410	1	1	yes	characteristic
119	C₄×C₁₉	#413	1	1	yes	characteristic
120	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic
121	#432	—	2	2	no	—
122	#431	—	2	2	no	—
123	#423	C₄×C₁₉	1	1	yes	characteristic
124	#423	C₂²×C₁₉	1	1	yes	characteristic
125	#407	C₄×C₁₉	1	1	yes	characteristic
126	#407	C₂²×C₁₉	1	1	yes	characteristic
127	C₄×M₁₆	C₄×C₁₉	1	1	yes	characteristic
128	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
129	#364	—	2	2	no	—
130	#349	C₂²×C₁₉	1	4	yes	—
131	#347	—	2	2	no	—
132	C₂×C₁₉	—	2	1	no	—
133	C₂×C₁₉	—	4	2	no	—
134	C₂×C₁₉	—	4	1	no	—
135	C₂×C₁₉	#1464	1	1	yes	characteristic
136	C₂³×C₄	—	2	1	no	—
137	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
138	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
139	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
140	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
141	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
142	C₂×C₄²	—	2	1	no	—
143	C₂×C₄²	—	2	1	no	—
144	C₂×C₄²	—	2	1	no	—
145	C₂×C₄²	—	2	1	no	—
146	C₂×C₄²	—	2	1	no	—
147	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
148	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
149	M₃₂	—	2	4	no	—
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₂²⋊C₈	—	2	2	no	—
153	C₂²⋊C₈	—	2	2	no	—
154	#97	—	2	1	no	—
155	#97	D₄×C₁₉	1	2	yes	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	D₄×C₁₉	1	2	yes	—
158	C₁₉	#11521	1	1	yes	characteristic, direct product factor, Sylow
159	C₂⁴	M₁₆×C₁₉	1	1	yes	characteristic
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	2	1	no	—
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	4	4	no	—
169	C₂²×C₄	—	4	1	no	—
170	C₂²×C₄	—	4	1	no	—
171	C₂²×C₄	M₁₆×C₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
173	M₁₆	—	4	1	no	—
174	M₁₆	—	4	1	no	—
175	M₁₆	—	4	1	no	—
176	M₁₆	—	4	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
180	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
181	C₄²	—	2	1	no	—
182	C₄²	—	2	1	no	—
183	C₄²	—	2	1	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	2	1	no	—
187	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
188	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
189	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
190	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
191	C₁₆	—	4	4	no	—
192	C₂³	—	2	1	no	—
193	C₂³	—	4	2	no	—
194	C₂³	—	4	1	no	—
195	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
214	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
215	C₈	—	2	2	no	—
216	C₈	—	2	2	no	—
217	C₈	—	4	1	no	—
218	C₈	—	4	1	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	4	1	no	—
223	C₂²	—	4	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	1	no	—
226	C₂²	C₁₉×#407	1	1	yes	characteristic
227	C₄	—	2	2	no	—
228	C₄	—	2	2	no	—
229	C₄	—	2	1	no	—
230	C₄	—	4	1	no	—
231	C₄	—	4	1	no	—
232	C₄	—	4	1	no	—
233	C₄	C₁₉×#410	1	1	yes	characteristic
234	C₄	C₁₉×#413	1	1	yes	characteristic
235	C₂	—	2	1	no	—
236	C₂	—	4	2	no	—
237	C₂	—	4	1	no	—
238	C₂	C₁₉×#1464	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2920

C₂

yes

maximal, characteristic

C₁₉×#2165

C₂

yes

maximal, complemented

C₁₉×#1327

C₂

yes

maximal, complemented

C₁₉×#1320

C₂

yes

maximal

C₂²×C₄²×C₁₉

C₄

yes

characteristic

C₁₉×#432

—

C₁₉×#431

—

C₁₉×#423

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#407

C₄

yes

characteristic

C₁₉×#407

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₄

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#364

—

C₁₉×#349

C₂²

yes

—

C₁₉×#347

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂³

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×M₃₂

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₂⁴×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₆×C₁₉

—

#11521

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×M₁₆

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

100

#2920

C₂×C₁₉

yes

characteristic

101

#2165

C₂×C₁₉

yes

complemented

102

#1327

C₂×C₁₉

yes

complemented

103

#1320

C₂×C₁₉

yes

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#407

yes

characteristic

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

#410

yes

characteristic

119

C₄×C₁₉

#413

yes

characteristic

120

C₂²×C₄²

C₄×C₁₉

yes

characteristic

121

#432

—

122

#431

—

123

#423

C₄×C₁₉

yes

characteristic

124

#423

C₂²×C₁₉

yes

characteristic

125

#407

C₄×C₁₉

yes

characteristic

126

#407

C₂²×C₁₉

yes

characteristic

127

C₄×M₁₆

C₄×C₁₉

yes

characteristic

128

C₄×M₁₆

C₂²×C₁₉

yes

characteristic

129

#364

—

130

#349

C₂²×C₁₉

yes

—

131

#347

—

132

C₂×C₁₉

—

133

C₂×C₁₉

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#1464

yes

characteristic

136

C₂³×C₄

—

137

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

138

C₂×M₁₆

C₂×C₄×C₁₉

yes

characteristic

139

C₂×M₁₆

C₂×C₄×C₁₉

yes

characteristic

140

C₂×M₁₆

C₂×C₄×C₁₉

yes

characteristic

141

C₂×M₁₆

C₂³×C₁₉

yes

characteristic

142

C₂×C₄²

—

143

C₂×C₄²

—

144

C₂×C₄²

—

145

C₂×C₄²

—

146

C₂×C₄²

—

147

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

148

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

149

M₃₂

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₂²⋊C₈

—

153

C₂²⋊C₈

—

154

#97

—

155

#97

D₄×C₁₉

yes

—

156

C₄×C₈

—

157

C₄×C₈

D₄×C₁₉

yes

—

158

C₁₉

#11521

yes

characteristic, direct product factor, Sylow

159

C₂⁴

M₁₆×C₁₉

yes

characteristic

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

M₁₆×C₁₉

yes

characteristic

172

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

176

M₁₆

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

C₂²⋊C₄×C₁₉

yes

—

180

C₂×C₈

C₂×D₄×C₁₉

yes

—

181

C₄²

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

188

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

189

C₄²

M₁₆×C₁₉

yes

characteristic

190

C₄²

M₁₆×C₁₉

yes

characteristic

191

C₁₆

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

C₂×M₁₆×C₁₉

yes

characteristic

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

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

214

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

215

C₈

—

216

C₈

—

217

C₈

—

218

C₈

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

C₁₉×#407

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

C₁₉×#410

yes

characteristic

234

C₄

C₁₉×#413

yes

characteristic

235

C₂

—

236

C₂

—

237

C₂

—

238

C₂

C₁₉×#1464

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#1464
prime radical	C₂⁴×C₁₉	M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

subgroup

G/H

center

C₄×C₁₉

#410

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×M₁₆

C₂³×C₁₉

socle

C₂×C₁₉

#1464

prime radical

C₂⁴×C₁₉

M₁₆

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2165	C₂	semidirect
3. C₁₉×#1327	C₂	semidirect
72. #11521	C₁₉	direct (N × H)
101. #2165	C₂×C₁₉	semidirect
102. #1327	C₂×C₁₉	semidirect
158. C₁₉	#11521	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2165

C₂

semidirect

3. C₁₉×#1327

C₂

semidirect

72. #11521

C₁₉

direct (N × H)

101. #2165

C₂×C₁₉

semidirect

102. #1327

C₂×C₁₉

semidirect

158. C₁₉

#11521

direct (N × H)

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

subgroup	index
C₁₉×#2920	2
C₁₉×#2165	2
C₁₉×#1327	2
C₁₉×#1320	2
#11521	19

subgroup

index

C₁₉×#2920

C₁₉×#2165

C₁₉×#1327

C₁₉×#1320

#11521

Subgroups — C₁₉×#11521 #18017480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11521 #18017480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11521 #18017480