Group #18017469 — subgroups

Subgroups — C₁₉×#11510 #18017469

Order 4864.

510 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2310	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1464	C₂	1	2	yes	maximal
3	C₁₉×#1319	C₂	1	4	yes	maximal, complemented
4	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
6	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
7	C₁₉×#432	—	2	2	no	—
8	C₁₉×#391	—	2	2	no	—
9	C₁₉×#391	C₄	1	2	yes	—
10	C₁₉×#391	C₂²	1	2	yes	—
11	C₁₉×#381	—	2	2	no	—
12	C₁₉×#324	C₂²	1	4	yes	—
13	C₁₉×#323	—	2	2	no	—
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	1	no	—
16	C₂²×Q₈×C₁₉	—	4	2	no	—
17	C₂²×Q₈×C₁₉	—	4	2	no	—
18	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₁₉×#117	—	4	2	no	—
22	C₁₉×#117	—	4	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₁₉×C₄⋊C₈	—	4	2	no	—
31	C₁₉×C₂²⋊C₈	—	2	4	no	—
32	C₁₉×#97	—	4	2	no	—
33	C₁₉×#95	—	2	4	no	—
34	C₁₉×#95	—	2	4	no	—
35	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Q₈×C₁₉	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	4	16	no	—
39	C₂×Q₈×C₁₉	—	4	2	no	—
40	C₂×Q₈×C₁₉	—	4	2	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	4	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₉	—	4	4	no	—
57	C₄⋊C₄×C₁₉	—	4	1	no	—
58	C₄⋊C₄×C₁₉	—	4	1	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₂²⋊C₄×C₁₉	—	4	2	no	—
61	C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	4	2	no	—
65	#11510	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂³×C₁₉	—	2	1	no	—
67	C₂³×C₁₉	—	2	1	no	—
68	C₂³×C₁₉	—	4	1	no	—
69	C₂³×C₁₉	—	4	1	no	—
70	C₂³×C₁₉	#100	1	2	yes	—
71	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	Q₈×C₁₉	—	4	4	no	—
73	Q₈×C₁₉	—	4	8	no	—
74	Q₈×C₁₉	—	4	4	no	—
75	C₂×C₄×C₁₉	—	2	8	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	8	no	—
84	C₂×C₄×C₁₉	—	4	2	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	#99	1	2	yes	—
92	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
93	C₈×C₁₉	—	8	4	no	—
94	#2310	C₂×C₁₉	1	1	yes	characteristic
95	#1464	C₂×C₁₉	1	2	yes	—
96	#1319	C₂×C₁₉	1	4	yes	complemented
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	—	2	2	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	—	4	2	no	—
102	C₂²×C₁₉	—	4	1	no	—
103	C₂²×C₁₉	—	4	1	no	—
104	C₂²×C₁₉	#407	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	4	2	no	—
110	C₄×C₁₉	—	4	2	no	—
111	C₄×C₁₉	—	4	4	no	—
112	C₄×C₁₉	—	8	2	no	—
113	C₂³×Q₈	C₄×C₁₉	1	1	yes	characteristic
114	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
115	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
116	#432	—	2	2	no	—
117	#391	—	2	2	no	—
118	#391	C₄×C₁₉	1	2	yes	—
119	#391	C₂²×C₁₉	1	2	yes	—
120	#381	—	2	2	no	—
121	#324	C₂²×C₁₉	1	4	yes	—
122	#323	—	2	2	no	—
123	C₂×C₁₉	—	2	1	no	—
124	C₂×C₁₉	—	2	1	no	—
125	C₂×C₁₉	—	4	2	no	—
126	C₂×C₁₉	#1462	1	1	yes	characteristic
127	C₂×C₁₉	#2129	1	1	yes	characteristic
128	C₂×C₁₉	#2135	1	1	yes	characteristic
129	C₂²×Q₈	—	2	4	no	—
130	C₂²×Q₈	—	2	1	no	—
131	C₂²×Q₈	—	4	2	no	—
132	C₂²×Q₈	—	4	2	no	—
133	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
134	C₂³×C₄	—	2	1	no	—
135	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
136	#117	—	4	2	no	—
137	#117	—	4	2	no	—
138	C₂×C₄⋊C₄	—	2	1	no	—
139	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
141	C₂×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
143	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
144	C₂×C₄²	D₄×C₁₉	1	2	yes	—
145	C₄⋊C₈	—	4	2	no	—
146	C₂²⋊C₈	—	2	4	no	—
147	#97	—	4	2	no	—
148	#95	—	2	4	no	—
149	#95	—	2	4	no	—
150	C₁₉	#11510	1	1	yes	characteristic, direct product factor, Sylow
151	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
152	C₂×Q₈	—	2	4	no	—
153	C₂×Q₈	—	2	2	no	—
154	C₂×Q₈	—	4	16	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	M₁₆×C₁₉	1	4	yes	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	—	4	2	no	—
168	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
169	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
170	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
171	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
172	C₂×C₈	—	4	4	no	—
173	C₄⋊C₄	—	4	1	no	—
174	C₄⋊C₄	—	4	1	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₂²⋊C₄	—	4	2	no	—
177	C₂²⋊C₄	—	4	2	no	—
178	C₄²	—	2	2	no	—
179	C₄²	—	2	2	no	—
180	C₄²	—	4	2	no	—
181	C₂³	—	2	1	no	—
182	C₂³	—	2	1	no	—
183	C₂³	—	4	1	no	—
184	C₂³	—	4	1	no	—
185	C₂³	C₁₉×#100	1	2	yes	—
186	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
187	Q₈	—	4	4	no	—
188	Q₈	—	4	4	no	—
189	Q₈	—	4	8	no	—
190	C₂×C₄	—	2	8	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	8	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	C₁₉×#99	1	2	yes	—
207	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
208	C₈	—	8	4	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	1	no	—
215	C₂²	—	4	1	no	—
216	C₂²	C₁₉×#407	1	1	yes	characteristic
217	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
218	C₂²	C₂×C₁₉×#100	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	4	no	—
222	C₄	—	4	2	no	—
223	C₄	—	4	2	no	—
224	C₄	—	8	2	no	—
225	C₂	—	2	1	no	—
226	C₂	—	2	1	no	—
227	C₂	—	4	2	no	—
228	C₂	C₁₉×#1462	1	1	yes	characteristic
229	C₂	C₁₉×#2129	1	1	yes	characteristic
230	C₂	C₁₉×#2135	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2310

C₂

yes

maximal, characteristic

C₁₉×#1464

C₂

yes

maximal

C₁₉×#1319

C₂

yes

maximal, complemented

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#117

C₄

yes

characteristic

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#432

—

C₁₉×#391

—

C₁₉×#391

C₄

yes

—

C₁₉×#391

C₂²

yes

—

C₁₉×#381

—

C₁₉×#324

C₂²

yes

—

C₁₉×#323

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

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

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#11510

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

—

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

#99

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₈×C₁₉

—

#2310

C₂×C₁₉

yes

characteristic

#1464

C₂×C₁₉

yes

—

#1319

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

#407

yes

characteristic

105

C₂²×C₁₉

C₂×#99

yes

characteristic

106

C₂²×C₁₉

C₂×#100

yes

characteristic

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₂³×Q₈

C₄×C₁₉

yes

characteristic

114

C₂×#117

C₄×C₁₉

yes

characteristic

115

C₂×#117

C₂²×C₁₉

yes

characteristic

116

#432

—

117

#391

—

118

#391

C₄×C₁₉

yes

—

119

#391

C₂²×C₁₉

yes

—

120

#381

—

121

#324

C₂²×C₁₉

yes

—

122

#323

—

123

C₂×C₁₉

—

124

C₂×C₁₉

—

125

C₂×C₁₉

—

126

C₂×C₁₉

#1462

yes

characteristic

127

C₂×C₁₉

#2129

yes

characteristic

128

C₂×C₁₉

#2135

yes

characteristic

129

C₂²×Q₈

—

130

C₂²×Q₈

—

131

C₂²×Q₈

—

132

C₂²×Q₈

—

133

C₂²×Q₈

C₂×C₄×C₁₉

yes

—

134

C₂³×C₄

—

135

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

136

#117

—

137

#117

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

140

C₂×C₄⋊C₄

C₂³×C₁₉

yes

characteristic

141

C₂×C₂²⋊C₄

—

142

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

143

C₂×C₄²

C₂×C₄×C₁₉

yes

—

144

C₂×C₄²

D₄×C₁₉

yes

—

145

C₄⋊C₈

—

146

C₂²⋊C₈

—

147

#97

—

148

#95

—

149

#95

—

150

C₁₉

#11510

yes

characteristic, direct product factor, Sylow

151

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

M₁₆×C₁₉

yes

—

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

C₂²⋊C₄×C₁₉

yes

characteristic

169

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

170

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

171

C₂²×C₄

C₂×D₄×C₁₉

yes

—

172

C₂×C₈

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₄²

—

179

C₄²

—

180

C₄²

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

C₁₉×#100

yes

—

186

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

187

Q₈

—

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

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

C₁₉×#99

yes

—

207

C₂×C₄

C₂×M₁₆×C₁₉

yes

—

208

C₈

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

C₁₉×#407

yes

characteristic

217

C₂²

C₂×C₁₉×#99

yes

characteristic

218

C₂²

C₂×C₁₉×#100

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₂

—

226

C₂

—

227

C₂

—

228

C₂

C₁₉×#1462

yes

characteristic

229

C₂

C₁₉×#2129

yes

characteristic

230

C₂

C₁₉×#2135

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#99

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄⋊C₄

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

N	H ≅ G/N	type
3. C₁₉×#1319	C₂	semidirect
65. #11510	C₁₉	direct (N × H)
96. #1319	C₂×C₁₉	semidirect
150. C₁₉	#11510	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1319

C₂

semidirect

65. #11510

C₁₉

direct (N × H)

96. #1319

C₂×C₁₉

semidirect

150. C₁₉

#11510

direct (N × H)

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

subgroup	index
C₁₉×#2310	2
C₁₉×#1464	2
C₁₉×#1319	2
#11510	19

subgroup

index

C₁₉×#2310

C₁₉×#1464

C₁₉×#1319

#11510

Subgroups — C₁₉×#11510 #18017469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11510 #18017469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11510 #18017469