Group #18082423 — subgroups

Subgroups — #18082423

Order 4864.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14564613	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#14562394	C₂	1	1	yes	maximal, characteristic
4	#14562090	C₂	1	2	yes	maximal
5	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₉	—	2	2	no	—
9	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
10	#11926303	—	2	4	no	—
11	#11926297	—	2	2	no	—
12	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₁₉×#533	C₂²	1	2	yes	—
14	C₁₉×#500	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#494	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#487	C₄	1	2	yes	complemented
17	C₁₉×#467	—	2	2	no	—
18	C₄×Q₁₆×C₁₉	—	2	2	no	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
24	C₁₉×#125	—	2	2	no	—
25	C₁₉×C₂²⋊Q₈	—	2	2	no	—
26	C₁₉×C₂²⋊Q₈	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₁₉×#117	—	2	2	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄×Dic₁₉	—	2	1	no	—
32	C₂×C₄×Dic₁₉	—	2	1	no	—
33	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
34	C₂×#64520	—	2	2	no	—
35	C₂²×C₁₉⋊C₈	—	2	1	no	—
36	C₁₉×#107	—	2	2	no	—
37	C₁₉×#103	—	2	4	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₈×Dic₁₉	—	2	8	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	1	no	—
45	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	2	2	no	—
52	Q₁₆×C₁₉	—	4	4	no	—
53	C₂×C₈×C₁₉	—	2	4	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₂²⋊C₄×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	—	4	2	no	—
64	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	C₄×Dic₁₉	—	2	4	no	—
69	C₄×Dic₁₉	—	2	4	no	—
70	C₄×Dic₁₉	—	2	2	no	—
71	C₄×Dic₁₉	Q₁₆	1	4	yes	complemented
72	#64520	—	4	4	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	#9845	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	#121	1	1	yes	characteristic
78	Q₈×C₁₉	—	4	4	no	—
79	Q₈×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₁₉	#135	1	2	yes	—
92	C₂×Dic₁₉	—	2	4	no	—
93	C₂×Dic₁₉	—	2	4	no	—
94	C₂×Dic₁₉	—	2	4	no	—
95	C₈×C₁₉	—	2	2	no	—
96	C₈×C₁₉	#104	1	4	yes	—
97	C₁₉⋊C₈	—	2	4	no	—
98	C₁₉⋊C₈	—	8	2	no	—
99	#3170	D₁₉	1	1	yes	characteristic
100	#1994	—	19	2	no	—
101	C₄²×C₈	—	19	1	no	—
102	#1567	—	19	1	no	—
103	#1493	—	19	2	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	#390	1	1	yes	characteristic
107	C₂²×C₁₉	#467	1	2	yes	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	8	2	no	—
111	C₄×C₁₉	—	8	2	no	—
112	C₄×C₁₉	C₂×#104	1	2	yes	—
113	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
114	C₄×C₁₉	#443	1	2	yes	—
115	C₄×C₁₉	#494	1	1	yes	characteristic
116	C₄×C₁₉	#495	1	1	yes	characteristic
117	Dic₁₉	—	2	8	no	—
118	#533	C₂×D₁₉	1	2	yes	—
119	#500	Dic₁₉	1	1	yes	characteristic, complemented
120	#494	Dic₁₉	1	1	yes	characteristic, complemented
121	#487	Dic₁₉	1	2	yes	complemented
122	#467	—	2	2	no	—
123	C₄×Q₁₆	—	2	2	no	—
124	#423	—	19	2	no	—
125	C₂×C₄×C₈	—	19	1	no	—
126	C₂×C₄×C₈	—	38	2	no	—
127	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
128	C₄³	—	19	1	no	—
129	#339	—	38	4	no	—
130	#335	—	38	2	no	—
131	Q₈⋊C₈	—	38	4	no	—
132	C₂×C₁₉	—	2	2	no	—
133	C₂×C₁₉	#1962	1	1	yes	characteristic
134	C₂×C₁₉	#1969	1	1	yes	characteristic
135	C₂×C₁₉	#1974	1	1	yes	characteristic
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×M₁₆	—	38	2	no	—
138	C₂²×C₈	—	38	1	no	—
139	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
140	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
141	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
142	#125	—	2	2	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄²	—	19	2	no	—
149	C₂×C₄²	—	38	1	no	—
150	C₂×C₄²	—	38	1	no	—
151	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
152	#107	—	2	2	no	—
153	C₄⋊C₈	—	38	2	no	—
154	C₄⋊C₈	—	38	2	no	—
155	#103	—	2	4	no	—
156	C₄×C₈	—	19	2	no	—
157	C₄×C₈	—	38	8	no	—
158	C₄×C₈	—	38	1	no	—
159	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
160	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
161	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
162	C₁₉	#9845	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂²×C₄	—	38	2	no	—
166	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
167	C₂²×C₄	#64543	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	Q₁₆	—	4	4	no	—
170	M₁₆	—	76	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	38	4	no	—
173	C₂×C₈	—	38	2	no	—
174	C₂×C₈	—	76	2	no	—
175	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
176	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	19	4	no	—
186	C₄²	—	38	4	no	—
187	C₄²	—	38	4	no	—
188	C₄²	—	38	2	no	—
189	C₄²	D₄×D₁₉	1	1	yes	characteristic
190	C₄²	#64543	1	1	yes	characteristic
191	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
192	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₂³	#10597384	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	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	38	4	no	—
201	C₂×C₄	—	38	4	no	—
202	C₂×C₄	—	38	4	no	—
203	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
204	C₂×C₄	#10597365	1	2	yes	—
205	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
206	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
207	C₂×C₄	#10597382	1	1	yes	characteristic
208	C₂×C₄	#10597384	1	1	yes	characteristic
209	C₂×C₄	#10597386	1	1	yes	characteristic
210	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
211	C₈	—	2	2	no	—
212	C₈	—	38	4	no	—
213	C₈	—	152	2	no	—
214	C₈	#10597294	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#11926447	1	1	yes	characteristic
218	C₂²	#11926782	1	2	yes	—
219	C₄	—	2	1	no	—
220	C₄	—	2	1	no	—
221	C₄	—	8	2	no	—
222	C₄	—	8	2	no	—
223	C₄	—	38	8	no	—
224	C₄	C₂×#10597294	1	2	yes	—
225	C₄	Q₁₆×Dic₁₉	1	2	yes	—
226	C₄	#11926661	1	2	yes	—
227	C₄	#11926922	1	1	yes	characteristic
228	C₄	#11926929	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#14564464	1	1	yes	characteristic
231	C₂	#14564497	1	1	yes	characteristic
232	C₂	#14564524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564613

C₂

yes

maximal

C₄×C₈×Dic₁₉

C₂

yes

maximal, characteristic

#14562394

C₂

yes

maximal, characteristic

#14562090

C₂

yes

maximal

C₁₉×#3170

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₁₉

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926303

—

#11926297

—

Q₈⋊(C₁₉⋊C₈)

—

C₁₉×#533

C₂²

yes

—

C₁₉×#500

C₄

yes

characteristic, complemented

C₁₉×#494

C₄

yes

characteristic, complemented

C₁₉×#487

C₄

yes

complemented

C₁₉×#467

—

C₄×Q₁₆×C₁₉

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#107

—

C₁₉×#103

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₁₆

yes

complemented

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#104

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3170

D₁₉

yes

characteristic

100

#1994

—

101

C₄²×C₈

—

102

#1567

—

103

#1493

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

#390

yes

characteristic

107

C₂²×C₁₉

#467

yes

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

C₂×#104

yes

—

113

C₄×C₁₉

C₄×Q₁₆

yes

—

114

C₄×C₁₉

#443

yes

—

115

C₄×C₁₉

#494

yes

characteristic

116

C₄×C₁₉

#495

yes

characteristic

117

Dic₁₉

—

118

#533

C₂×D₁₉

yes

—

119

#500

Dic₁₉

yes

characteristic, complemented

120

#494

Dic₁₉

yes

characteristic, complemented

121

#487

Dic₁₉

yes

complemented

122

#467

—

123

C₄×Q₁₆

—

124

#423

—

125

C₂×C₄×C₈

—

126

C₂×C₄×C₈

—

127

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

128

C₄³

—

129

#339

—

130

#335

—

131

Q₈⋊C₈

—

132

C₂×C₁₉

—

133

C₂×C₁₉

#1962

yes

characteristic

134

C₂×C₁₉

#1969

yes

characteristic

135

C₂×C₁₉

#1974

yes

characteristic

136

C₂×Q₁₆

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

139

C₂²×C₈

C₂²⋊D₁₉

yes

—

140

C₄⋊Q₈

C₂×Dic₁₉

yes

—

141

C₄⋊Q₈

C₂×Dic₁₉

yes

—

142

#125

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

#117

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂²×D₁₉

yes

characteristic

152

#107

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

C₂×Dic₁₉

yes

characteristic

160

C₄×C₈

C₂×Dic₁₉

yes

characteristic

161

C₄×C₈

C₂²⋊D₁₉

yes

—

162

C₁₉

#9845

yes

characteristic, complemented, Sylow

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₁₉

yes

characteristic

167

C₂²×C₄

#64543

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

169

Q₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

C₂²⋊Dic₁₉

yes

—

176

C₂×C₈

C₂²⋊Dic₁₉

yes

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

D₄×D₁₉

yes

characteristic

190

C₄²

#64543

yes

characteristic

191

C₄²

C₂²×Dic₁₉

yes

characteristic

192

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

193

C₂³

#10597384

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

Q₁₆×D₁₉

yes

—

204

C₂×C₄

#10597365

yes

—

205

C₂×C₄

D₄×Dic₁₉

yes

characteristic

206

C₂×C₄

D₄×Dic₁₉

yes

characteristic

207

C₂×C₄

#10597382

yes

characteristic

208

C₂×C₄

#10597384

yes

characteristic

209

C₂×C₄

#10597386

yes

characteristic

210

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

—

152

—

214

C₈

#10597294

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#11926447

yes

characteristic

218

C₂²

#11926782

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

C₂×#10597294

yes

—

225

C₄

Q₁₆×Dic₁₉

yes

—

226

C₄

#11926661

yes

—

227

C₄

#11926922

yes

characteristic

228

C₄

#11926929

yes

characteristic

229

C₂

—

230

C₂

#14564464

yes

characteristic

231

C₂

#14564497

yes

characteristic

232

C₂

#14564524

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3170	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3170	D₁₉
hypocenter	C₁₉	#9845
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3170

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. C₁₉×#500	C₄	semidirect
15. C₁₉×#494	C₄	semidirect
16. C₁₉×#487	C₄	semidirect
71. C₄×Dic₁₉	Q₁₆	semidirect
119. #500	Dic₁₉	semidirect
120. #494	Dic₁₉	semidirect
121. #487	Dic₁₉	semidirect
162. C₁₉	#9845	semidirect

H ≅ G/N

type

14. C₁₉×#500

C₄

semidirect

15. C₁₉×#494

C₄

semidirect

16. C₁₉×#487

C₄

semidirect

71. C₄×Dic₁₉

Q₁₆

semidirect

119. #500

Dic₁₉

semidirect

120. #494

Dic₁₉

semidirect

121. #487

Dic₁₉

semidirect

162. C₁₉

#9845

semidirect

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

subgroup	index
#14564613	2
C₄×C₈×Dic₁₉	2
#14562394	2
#14562090	2
C₁₉×#3170	2
#9845	19

subgroup

index

C₄×C₈×Dic₁₉

C₁₉×#3170

Subgroups — #18082423

Conjugacy classes of subgroups

Complements

Maximal subgroups