Group #18070786 — subgroups

Subgroups — #18070786

Order 4864.

590 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563329	C₂	1	2	yes	maximal
2	#14561458	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	—	2	2	no	—
5	#11926299	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#389	C₄	1	2	yes	—
11	C₁₉×#389	C₂²	1	2	yes	—
12	C₁₉×#385	—	2	2	no	—
13	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₁₉×#117	—	2	4	no	—
17	C₁₉×#117	—	4	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄²×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	—	4	2	no	—
27	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×#64520	—	2	8	no	—
31	C₂×#64520	—	4	4	no	—
32	C₂×#64520	—	4	4	no	—
33	C₂²×C₁₉⋊C₈	—	2	4	no	—
34	C₁₉×#95	—	2	2	no	—
35	C₁₉×#95	—	2	2	no	—
36	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	4	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	4	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	4	4	no	—
53	C₄⋊C₄×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	—	4	2	no	—
55	C₄⋊C₄×C₁₉	M₁₆	1	4	yes	complemented
56	C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂²⋊C₄×C₁₉	—	4	2	no	—
58	C₄²×C₁₉	—	2	4	no	—
59	C₄²×C₁₉	—	4	1	no	—
60	C₄²×C₁₉	—	4	2	no	—
61	C₄²×C₁₉	—	4	1	no	—
62	C₄²×C₁₉	—	4	2	no	—
63	#64520	—	4	16	no	—
64	C₂×C₁₉⋊C₈	—	2	8	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	C₂×C₁₉⋊C₈	—	4	4	no	—
67	#7632	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	—	2	1	no	—
69	C₂³×C₁₉	—	2	1	no	—
70	C₂³×C₁₉	—	2	2	no	—
71	C₂³×C₁₉	—	2	2	no	—
72	C₂³×C₁₉	#99	1	2	yes	—
73	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	—	2	8	no	—
75	C₂×C₄×C₁₉	—	2	8	no	—
76	C₂×C₄×C₁₉	—	2	8	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	4	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	#101	1	2	yes	—
92	C₂×C₄×C₁₉	#104	1	4	yes	—
93	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×C₄×C₁₉	#137	1	2	yes	—
96	C₁₉⋊C₈	—	4	8	no	—
97	#2296	D₁₉	1	1	yes	characteristic
98	#1728	—	19	2	no	—
99	#1271	—	19	4	no	—
100	C₂²×C₁₉	—	2	2	no	—
101	C₂²×C₁₉	—	2	4	no	—
102	C₂²×C₁₉	—	4	1	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	—	4	1	no	—
105	C₂²×C₁₉	#407	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
108	C₂²×C₁₉	#417	1	2	yes	—
109	C₂²×C₁₉	C₂×#104	1	2	yes	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	2	4	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	4	4	no	—
116	C₄×C₁₉	—	8	2	no	—
117	C₂²×M₁₆	—	38	2	no	—
118	C₂×#117	Dic₁₉	1	1	yes	characteristic
119	C₂×#117	Dic₁₉	1	1	yes	characteristic
120	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
121	#389	Dic₁₉	1	2	yes	—
122	#389	C₂×D₁₉	1	2	yes	—
123	#385	—	2	2	no	—
124	C₄×C₄⋊C₄	—	2	2	no	—
125	#336	—	19	4	no	—
126	#336	—	38	2	no	—
127	C₂×C₁₉	—	4	2	no	—
128	C₂×C₁₉	#1463	1	1	yes	characteristic
129	C₂×C₁₉	#1489	1	2	yes	—
130	C₂×C₁₉	#1504	1	2	yes	—
131	C₂×C₁₉	#1526	1	1	yes	characteristic
132	C₂×C₁₉	#1561	1	1	yes	characteristic
133	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
135	C₂×M₁₆	—	38	8	no	—
136	C₂×M₁₆	—	76	4	no	—
137	C₂×M₁₆	—	76	4	no	—
138	C₂²×C₈	—	38	4	no	—
139	#117	—	2	4	no	—
140	#117	—	4	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
144	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₄²	—	2	1	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	—	4	2	no	—
150	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
153	#95	—	2	2	no	—
154	#95	—	2	2	no	—
155	C₁₉	#7632	1	1	yes	characteristic, complemented, Sylow
156	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	2	4	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
167	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
168	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
170	M₁₆	—	76	16	no	—
171	C₂×C₈	—	38	8	no	—
172	C₂×C₈	—	76	4	no	—
173	C₂×C₈	—	76	4	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	4	no	—
179	C₄⋊C₄	#64520	1	4	yes	complemented
180	C₂²⋊C₄	—	2	4	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	—	2	4	no	—
183	C₄²	—	4	1	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	4	1	no	—
186	C₄²	—	4	2	no	—
187	C₂³	—	2	2	no	—
188	C₂³	—	2	2	no	—
189	C₂³	—	2	1	no	—
190	C₂³	—	2	1	no	—
191	C₂³	#10597291	1	2	yes	—
192	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
193	C₂×C₄	—	2	8	no	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	4	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	#10597293	1	2	yes	—
211	C₂×C₄	#10597294	1	4	yes	—
212	C₂×C₄	C₂×#64520	1	2	yes	—
213	C₂×C₄	#10597395	1	2	yes	—
214	C₂×C₄	#10597397	1	2	yes	—
215	C₈	—	76	8	no	—
216	C₂²	—	2	4	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	4	2	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	#11926508	1	1	yes	characteristic
222	C₂²	C₂×#10597291	1	1	yes	characteristic
223	C₂²	C₂×#10597293	1	1	yes	characteristic
224	C₂²	#11926545	1	2	yes	—
225	C₂²	C₂×#10597294	1	2	yes	—
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	4	no	—
229	C₄	—	2	2	no	—
230	C₄	—	2	2	no	—
231	C₄	—	4	4	no	—
232	C₄	—	8	2	no	—
233	C₂	—	4	2	no	—
234	C₂	#14561965	1	1	yes	characteristic
235	C₂	#14562074	1	2	yes	—
236	C₂	#14562139	1	2	yes	—
237	C₂	#14562230	1	1	yes	characteristic
238	C₂	#14562373	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563329

C₂

yes

maximal

#14561458

C₂

yes

maximal, complemented

C₁₉×#2296

C₂

yes

maximal, characteristic

C₂²×#64520

—

#11926299

—

#11926299

C₂²

yes

—

C₂×C₁₉×#117

C₄

yes

characteristic

C₂×C₁₉×#117

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#389

C₄

yes

—

C₁₉×#389

C₂²

yes

—

C₁₉×#385

—

C₄×C₄⋊C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂²⋊C₄

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

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

M₁₆

yes

complemented

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7632

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

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

#101

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₁₉⋊C₈

—

#2296

D₁₉

yes

characteristic

#1728

—

#1271

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#407

yes

characteristic

106

C₂²×C₁₉

C₂×#99

yes

characteristic

107

C₂²×C₁₉

C₂×#101

yes

characteristic

108

C₂²×C₁₉

#417

yes

—

109

C₂²×C₁₉

C₂×#104

yes

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₂²×M₁₆

—

118

C₂×#117

Dic₁₉

yes

characteristic

119

C₂×#117

Dic₁₉

yes

characteristic

120

C₂²×C₄²

C₂×D₁₉

yes

characteristic

121

#389

Dic₁₉

yes

—

122

#389

C₂×D₁₉

yes

—

123

#385

—

124

C₄×C₄⋊C₄

—

125

#336

—

126

#336

—

127

C₂×C₁₉

—

128

C₂×C₁₉

#1463

yes

characteristic

129

C₂×C₁₉

#1489

yes

—

130

C₂×C₁₉

#1504

yes

—

131

C₂×C₁₉

#1526

yes

characteristic

132

C₂×C₁₉

#1561

yes

characteristic

133

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

134

C₂³×C₄

C₂²⋊D₁₉

yes

—

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

139

#117

—

140

#117

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

144

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

145

C₂×C₂²⋊C₄

—

146

C₂×C₂²⋊C₄

—

147

C₂×C₄²

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

151

C₂×C₄²

C₂²⋊D₁₉

yes

—

152

C₂×C₄²

C₂²×D₁₉

yes

characteristic

153

#95

—

154

#95

—

155

C₁₉

#7632

yes

characteristic, complemented, Sylow

156

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

167

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

168

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

169

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

#64520

yes

complemented

180

C₂²⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

#10597291

yes

—

192

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

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

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#10597293

yes

—

211

C₂×C₄

#10597294

yes

—

212

C₂×C₄

C₂×#64520

yes

—

213

C₂×C₄

#10597395

yes

—

214

C₂×C₄

#10597397

yes

—

215

C₈

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

#11926508

yes

characteristic

222

C₂²

C₂×#10597291

yes

characteristic

223

C₂²

C₂×#10597293

yes

characteristic

224

C₂²

#11926545

yes

—

225

C₂²

C₂×#10597294

yes

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₂

—

234

C₂

#14561965

yes

characteristic

235

C₂

#14562074

yes

—

236

C₂

#14562139

yes

—

237

C₂

#14562230

yes

characteristic

238

C₂

#14562373

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2296	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2296	D₁₉
hypocenter	C₁₉	#7632
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2296

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2296

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2296

N	H ≅ G/N	type
2. #14561458	C₂	semidirect
55. C₄⋊C₄×C₁₉	M₁₆	semidirect
155. C₁₉	#7632	semidirect
179. C₄⋊C₄	#64520	semidirect

H ≅ G/N

type

2. #14561458

C₂

semidirect

55. C₄⋊C₄×C₁₉

M₁₆

semidirect

155. C₁₉

#7632

semidirect

179. C₄⋊C₄

#64520

semidirect

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

subgroup	index
#14563329	2
#14561458	2
C₁₉×#2296	2
#7632	19

subgroup

index

#14563329

#14561458

C₁₉×#2296

#7632

Subgroups — #18070786

Conjugacy classes of subgroups

Complements

Maximal subgroups