Group #18079917 — subgroups

Subgroups — #18079917

Order 4864.

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

normal subgroups only

This group has 470 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	#14572716	C₂	1	1	yes	maximal, characteristic
2	#14568847	C₂	1	1	yes	maximal, characteristic
3	#14562321	C₂	1	2	yes	maximal
4	#14561536	C₂	1	2	yes	maximal
5	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	Q₈×C₁₉⋊C₈	—	2	4	no	—
8	#11926597	—	2	2	no	—
9	#11926597	C₂²	1	2	yes	—
10	#11926483	C₄	1	4	yes	—
11	#11926451	—	2	1	no	—
12	#11926450	—	2	2	no	—
13	#11926409	—	2	1	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926289	—	2	4	no	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₁₉×#101	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄×Dic₁₉	—	2	1	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	2	no	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×#101	—	4	2	no	—
38	C₁₉⋊#95	—	2	4	no	—
39	C₁₉⋊#95	—	2	4	no	—
40	C₁₉⋊#95	C₂×C₄	1	2	yes	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
44	C₄×C₁₉⋊C₈	—	2	4	no	—
45	C₄×C₁₉⋊C₈	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
49	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	2	2	no	—
56	C₂²×Dic₁₉	—	2	2	no	—
57	C₂×Dic₃₈	—	4	4	no	—
58	C₂×Dic₃₈	—	4	1	no	—
59	C₂×Dic₃₈	—	4	1	no	—
60	M₁₆×C₁₉	—	4	2	no	—
61	M₁₆×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	C₂×D₄	1	2	yes	—
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₄⋊Dic₁₉	—	2	4	no	—
70	C₄⋊Dic₁₉	—	4	2	no	—
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄×Dic₁₉	—	4	2	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	#9396	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₁₉	—	2	4	no	—
77	Q₈×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	#103	1	4	yes	—
85	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#135	1	2	yes	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	4	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	Dic₃₈	—	8	2	no	—
98	Dic₃₈	—	8	2	no	—
99	C₈×C₁₉	—	8	2	no	—
100	C₁₉⋊C₈	—	4	4	no	—
101	#2982	—	19	1	no	—
102	#2568	—	19	1	no	—
103	#1801	D₁₉	1	1	yes	characteristic
104	#1549	—	19	2	no	—
105	#1303	—	19	2	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	#386	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
110	C₂²×C₁₉	#416	1	1	yes	characteristic
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	4	no	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	4	2	no	—
115	C₄×C₁₉	#454	1	2	yes	—
116	C₄×C₁₉	#465	1	2	yes	—
117	C₄×C₁₉	#467	1	2	yes	—
118	Dic₁₉	—	8	2	no	—
119	Dic₁₉	—	8	2	no	—
120	C₂×C₄⋊Q₈	—	19	1	no	—
121	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
122	C₈×Q₈	—	38	4	no	—
123	#431	—	19	2	no	—
124	#431	—	38	2	no	—
125	#423	C₂×D₁₉	1	2	yes	—
126	C₂×#101	—	2	1	no	—
127	#400	—	19	4	no	—
128	#391	—	38	1	no	—
129	#391	—	38	2	no	—
130	#382	—	38	1	no	—
131	C₄×C₄⋊C₄	—	19	1	no	—
132	#343	—	2	1	no	—
133	#332	—	38	4	no	—
134	C₂×C₁₉	—	2	1	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	#1888	1	1	yes	characteristic
137	C₂×C₁₉	#1892	1	1	yes	characteristic
138	C₂×C₁₉	#1915	1	1	yes	characteristic
139	C₂²×Q₈	—	38	1	no	—
140	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
141	C₂×M₁₆	—	2	2	no	—
142	C₄⋊Q₈	—	38	2	no	—
143	C₄⋊Q₈	—	38	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₂×C₄⋊C₄	—	19	2	no	—
147	C₂×C₄⋊C₄	—	38	1	no	—
148	C₂×C₄⋊C₄	—	38	1	no	—
149	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
150	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
151	C₂×C₄²	—	38	1	no	—
152	C₂×C₄²	D₇₆	1	2	yes	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	19	4	no	—
157	C₄⋊C₈	—	38	4	no	—
158	#101	—	4	2	no	—
159	C₂²⋊C₈	—	38	2	no	—
160	C₄×C₈	—	38	4	no	—
161	C₄×C₈	—	38	2	no	—
162	#95	—	19	2	no	—
163	#95	—	38	4	no	—
164	#95	—	38	4	no	—
165	C₁₉	#9396	1	1	yes	characteristic, complemented, Sylow
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	76	4	no	—
169	C₂×Q₈	—	76	1	no	—
170	C₂×Q₈	—	76	1	no	—
171	C₂×Q₈	#64526	1	2	yes	—
172	C₂×Q₈	#64528	1	2	yes	—
173	C₂²×C₄	—	38	2	no	—
174	C₂²×C₄	—	38	2	no	—
175	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
176	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
177	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	38	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	38	4	no	—
187	C₄⋊C₄	—	76	2	no	—
188	C₄⋊C₄	—	76	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	76	2	no	—
192	C₄²	D₄×D₁₉	1	2	yes	—
193	C₄²	#64543	1	2	yes	—
194	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
195	Q₈	—	2	4	no	—
196	Q₈	—	2	4	no	—
197	Q₈	—	152	2	no	—
198	Q₈	—	152	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	76	2	no	—
206	C₂×C₄	—	76	4	no	—
207	C₂×C₄	—	76	2	no	—
208	C₂×C₄	—	76	2	no	—
209	C₂×C₄	—	76	2	no	—
210	C₂×C₄	#10597267	1	4	yes	—
211	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
212	C₂×C₄	#10597328	1	1	yes	characteristic
213	C₂×C₄	#10597332	1	1	yes	characteristic
214	C₂×C₄	C₂×#64526	1	1	yes	characteristic
215	C₂×C₄	#10597385	1	2	yes	—
216	C₂×C₄	C₂×#64528	1	1	yes	characteristic
217	C₂×C₄	#10597396	1	2	yes	—
218	C₈	—	8	2	no	—
219	C₈	—	76	4	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#11926421	1	1	yes	characteristic
223	C₂²	C₂×#10597267	1	1	yes	characteristic
224	C₂²	#11926538	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	4	no	—
228	C₄	—	4	2	no	—
229	C₄	—	152	2	no	—
230	C₄	—	152	2	no	—
231	C₄	#11926719	1	2	yes	—
232	C₄	#11926771	1	2	yes	—
233	C₄	#11926783	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#14564036	1	1	yes	characteristic
237	C₂	#14564056	1	1	yes	characteristic
238	C₂	#14564185	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572716

C₂

yes

maximal, characteristic

#14568847

C₂

yes

maximal, characteristic

#14562321

C₂

yes

maximal

#14561536

C₂

yes

maximal

C₁₉×#1801

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

Q₈×C₁₉⋊C₈

—

#11926597

—

#11926597

C₂²

yes

—

#11926483

C₄

yes

—

#11926451

—

#11926450

—

#11926409

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926289

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#101

—

C₁₉×#343

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

—

#10597315

—

#10597315

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×Q₈×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#9396

—

maximal, Sylow

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

#103

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

100

C₁₉⋊C₈

—

101

#2982

—

102

#2568

—

103

#1801

D₁₉

yes

characteristic

104

#1549

—

105

#1303

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

#386

yes

characteristic

109

C₂²×C₁₉

C₂×#103

yes

characteristic

110

C₂²×C₁₉

#416

yes

characteristic

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#454

yes

—

116

C₄×C₁₉

#465

yes

—

117

C₄×C₁₉

#467

yes

—

118

Dic₁₉

—

119

Dic₁₉

—

120

C₂×C₄⋊Q₈

—

121

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

122

C₈×Q₈

—

123

#431

—

124

#431

—

125

#423

C₂×D₁₉

yes

—

126

C₂×#101

—

127

#400

—

128

#391

—

129

#391

—

130

#382

—

131

C₄×C₄⋊C₄

—

132

#343

—

133

#332

—

134

C₂×C₁₉

—

135

C₂×C₁₉

—

136

C₂×C₁₉

#1888

yes

characteristic

137

C₂×C₁₉

#1892

yes

characteristic

138

C₂×C₁₉

#1915

yes

characteristic

139

C₂²×Q₈

—

140

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

141

C₂×M₁₆

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

150

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

151

C₂×C₄²

—

152

C₂×C₄²

D₇₆

yes

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

#101

—

159

C₂²⋊C₈

—

160

C₄×C₈

—

161

C₄×C₈

—

162

#95

—

163

#95

—

164

#95

—

165

C₁₉

#9396

yes

characteristic, complemented, Sylow

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

#64526

yes

—

172

C₂×Q₈

#64528

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

176

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

177

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

178

C₂²×C₄

C₂×D₇₆

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

D₄×D₁₉

yes

—

193

C₄²

#64543

yes

—

194

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

152

—

198

Q₈

—

152

—

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

#10597267

yes

—

211

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

212

C₂×C₄

#10597328

yes

characteristic

213

C₂×C₄

#10597332

yes

characteristic

214

C₂×C₄

C₂×#64526

yes

characteristic

215

C₂×C₄

#10597385

yes

—

216

C₂×C₄

C₂×#64528

yes

characteristic

217

C₂×C₄

#10597396

yes

—

218

C₈

—

219

C₈

—

220

C₂²

—

221

C₂²

—

222

C₂²

#11926421

yes

characteristic

223

C₂²

C₂×#10597267

yes

characteristic

224

C₂²

#11926538

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

152

—

230

C₄

—

152

—

231

C₄

#11926719

yes

—

232

C₄

#11926771

yes

—

233

C₄

#11926783

yes

—

234

C₂

—

235

C₂

—

236

C₂

#14564036

yes

characteristic

237

C₂

#14564056

yes

characteristic

238

C₂

#14564185

yes

characteristic

	subgroup	G/H
center	C₂²	#11926421
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1801	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1801	D₁₉
hypocenter	C₁₉	#9396
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#11926421

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1801

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
165. C₁₉	#9396	semidirect

H ≅ G/N

type

165. C₁₉

#9396

semidirect

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

subgroup	index
#14572716	2
#14568847	2
#14562321	2
#14561536	2
C₁₉×#1801	2
#9396	19

subgroup

index

C₁₉×#1801

Subgroups — #18079917

Conjugacy classes of subgroups

Complements

Maximal subgroups