Group #18073217 — subgroups

Subgroups — #18073217

Order 4864.

514 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 195 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	C₄×#10597347	C₂	1	1	yes	maximal, characteristic
2	#14562018	C₂	1	2	yes	maximal
3	#14561918	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561472	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	C₄	1	2	yes	—
7	C₄×#64541	C₂²	1	1	yes	characteristic
8	#11926597	C₂²	1	2	yes	—
9	#11926499	C₄	1	2	yes	—
10	#11926498	—	2	2	no	—
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	C₄×#64515	—	2	1	no	—
13	C₄×C₈×D₁₉	—	2	1	no	—
14	#11926276	C₄	1	4	yes	—
15	#11926273	C₄	1	4	yes	—
16	#11926265	—	2	1	no	—
17	C₈×C₁₉⋊C₈	—	2	1	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#322	—	2	2	no	—
21	C₂×#64541	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₄×C₂²⋊D₁₉	—	2	2	no	—
26	#10597372	C₂×C₄	1	1	yes	characteristic
27	C₂×#64520	C₂×C₄	1	2	yes	—
28	#10597347	—	2	4	no	—
29	#10597347	C₈	1	8	yes	complemented
30	C₂×#64515	—	2	2	no	—
31	C₂×C₈×D₁₉	—	2	2	no	—
32	C₄×D₇₆	C₂×C₄	1	2	yes	—
33	#10597318	—	2	1	no	—
34	C₄²×D₁₉	—	2	1	no	—
35	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
38	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	#10597272	—	2	2	no	—
43	C₈×Dic₁₉	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
45	#10597260	—	2	1	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₄×C₁₉⋊C₈	—	2	1	no	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	2	yes	—
50	C₂×C₂²⋊D₁₉	—	2	1	no	—
51	#64541	—	2	2	no	—
52	#64541	C₂×C₈	1	4	yes	—
53	C₂×D₇₆	C₄²	1	1	yes	characteristic
54	C₂×C₄×D₁₉	—	2	1	no	—
55	C₂×C₄×D₁₉	—	2	2	no	—
56	C₂×Dic₃₈	C₄²	1	1	yes	characteristic
57	C₂×C₈×C₁₉	—	2	4	no	—
58	C₂×C₈×C₁₉	—	4	4	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
62	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
63	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²⋊Dic₁₉	—	2	1	no	—
67	(C₂×D₁₉)⋊C₄	—	2	2	no	—
68	C₄⋊Dic₁₉	C₄²	1	2	yes	—
69	Dic₁₉⋊C₄	—	2	2	no	—
70	C₄×Dic₁₉	—	2	1	no	—
71	C₄×Dic₁₉	—	2	2	no	—
72	#64520	—	2	2	no	—
73	#64520	C₂×C₈	1	4	yes	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	#64515	—	2	8	no	—
77	C₈×D₁₉	—	2	8	no	—
78	#8185	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	#117	1	1	yes	characteristic
80	C₂²×D₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	4	no	—
82	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
88	C₂²⋊D₁₉	—	2	4	no	—
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	D₇₆	—	2	1	no	—
92	D₇₆	C₄×C₈	1	2	yes	—
93	C₄×D₁₉	—	2	4	no	—
94	C₄×D₁₉	—	4	4	no	—
95	Dic₃₈	—	2	1	no	—
96	Dic₃₈	C₄×C₈	1	2	yes	—
97	C₈×C₁₉	—	4	4	no	—
98	C₈×C₁₉	C₂²⋊C₈	1	4	yes	—
99	C₈×C₁₉	C₂²⋊C₈	1	4	yes	—
100	C₁₉⋊C₈	—	2	4	no	—
101	C₁₉⋊C₈	—	4	4	no	—
102	C₄×#131	—	19	1	no	—
103	#1476	—	19	2	no	—
104	#1450	—	19	1	no	—
105	C₂×#322	D₁₉	1	1	yes	characteristic, complemented
106	#1278	—	19	2	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₁₉	#431	1	2	yes	—
110	C₂×D₁₉	—	2	2	no	—
111	C₂×D₁₉	—	4	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
114	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
115	C₄×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
116	C₄×C₁₉	#444	1	4	yes	—
117	Dic₁₉	—	2	2	no	—
118	Dic₁₉	—	4	2	no	—
119	C₂×#131	—	19	2	no	—
120	C₄×#41	—	19	1	no	—
121	#431	—	19	2	no	—
122	#405	—	19	2	no	—
123	#405	—	38	2	no	—
124	C₄×M₁₆	—	19	1	no	—
125	C₄×M₁₆	—	38	1	no	—
126	C₂×C₄×C₈	—	38	1	no	—
127	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
128	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
129	Q₈⋊C₈	—	19	4	no	—
130	D₄⋊C₈	—	19	4	no	—
131	#322	—	2	2	no	—
132	#322	—	38	1	no	—
133	C₈²	—	38	1	no	—
134	C₂×C₁₉	—	2	2	no	—
135	C₂×C₁₉	C₄×C₂²⋊C₈	1	1	yes	characteristic
136	C₂×C₁₉	#1765	1	2	yes	—
137	D₁₉	—	4	2	no	—
138	C₂×#41	—	19	1	no	—
139	#131	—	19	8	no	—
140	#131	—	38	4	no	—
141	C₂×M₁₆	—	19	2	no	—
142	C₂×M₁₆	—	38	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	38	2	no	—
145	C₂²×C₈	C₄×D₁₉	1	2	yes	—
146	C₄×Q₈	—	19	2	no	—
147	C₄×D₄	—	19	2	no	—
148	C₄×D₄	—	38	2	no	—
149	#117	—	19	1	no	—
150	#117	—	38	1	no	—
151	C₂×C₄²	—	38	1	no	—
152	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
153	C₄⋊C₈	—	19	4	no	—
154	C₂²⋊C₈	—	38	2	no	—
155	#97	—	38	2	no	—
156	#97	—	38	1	no	—
157	C₄×C₈	—	2	2	no	—
158	C₄×C₈	—	38	2	no	—
159	C₄×C₈	—	38	2	no	—
160	C₄×C₈	—	38	1	no	—
161	C₄×C₈	C₄×D₁₉	1	4	yes	—
162	C₄×C₈	D₇₆	1	1	yes	characteristic
163	C₄×C₈	D₇₆	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
165	C₁₉	#8185	1	1	yes	characteristic, complemented, Sylow
166	#41	—	19	4	no	—
167	#41	—	38	2	no	—
168	C₂×Q₈	—	19	1	no	—
169	C₂×D₄	—	19	1	no	—
170	C₂×D₄	—	38	1	no	—
171	C₂²×C₄	—	38	1	no	—
172	C₂²×C₄	—	38	2	no	—
173	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₂²×C₄	#64541	1	2	yes	—
175	M₁₆	—	19	4	no	—
176	M₁₆	—	38	2	no	—
177	M₁₆	—	38	8	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	4	4	no	—
180	C₂×C₈	—	38	2	no	—
181	C₂×C₈	—	38	8	no	—
182	C₂×C₈	—	38	4	no	—
183	C₂×C₈	C₈×D₁₉	1	4	yes	—
184	C₂×C₈	#64515	1	4	yes	—
185	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
186	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
187	C₄⋊C₄	—	19	2	no	—
188	C₄⋊C₄	—	38	2	no	—
189	C₂²⋊C₄	—	38	1	no	—
190	C₂²⋊C₄	—	38	2	no	—
191	C₄²	—	38	2	no	—
192	C₄²	—	38	1	no	—
193	C₄²	C₂×C₄×D₁₉	1	2	yes	—
194	C₄²	C₂×D₇₆	1	1	yes	characteristic
195	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
196	C₂³	—	38	1	no	—
197	C₂³	#10597318	1	1	yes	characteristic
198	Q₈	—	19	2	no	—
199	Q₈	—	38	1	no	—
200	D₄	—	19	2	no	—
201	D₄	—	38	4	no	—
202	D₄	—	38	1	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	38	1	no	—
205	C₂×C₄	—	38	4	no	—
206	C₂×C₄	—	38	2	no	—
207	C₂×C₄	—	76	4	no	—
208	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
209	C₂×C₄	C₄×D₇₆	1	2	yes	—
210	C₂×C₄	C₂×C₈×D₁₉	1	2	yes	—
211	C₂×C₄	C₂×#64515	1	2	yes	—
212	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
214	C₈	—	4	4	no	—
215	C₈	—	38	4	no	—
216	C₈	—	76	4	no	—
217	C₈	(C₂×D₁₉)⋊C₈	1	4	yes	—
218	C₈	(C₂×D₁₉)⋊C₈	1	4	yes	—
219	C₂²	—	2	2	no	—
220	C₂²	—	38	2	no	—
221	C₂²	—	76	2	no	—
222	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
223	C₂²	#11926595	1	2	yes	—
224	C₄	—	2	2	no	—
225	C₄	—	38	2	no	—
226	C₄	—	76	2	no	—
227	C₄	C₄×C₈×D₁₉	1	1	yes	characteristic
228	C₄	C₄×#64515	1	1	yes	characteristic
229	C₄	C₂×(C₂×D₁₉)⋊C₈	1	2	yes	—
230	C₄	#11926667	1	4	yes	—
231	C₂	—	2	2	no	—
232	C₂	—	76	2	no	—
233	C₂	C₄×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
234	C₂	#14563479	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597347

C₂

yes

maximal, characteristic

#14562018

C₂

yes

maximal

#14561918

C₂

yes

maximal, characteristic, complemented

#14561472

C₂

yes

maximal, complemented

C₂×C₁₉×#322

C₂

yes

maximal, characteristic, complemented

C₂×#10597347

C₄

yes

—

C₄×#64541

C₂²

yes

characteristic

#11926597

C₂²

yes

—

#11926499

C₄

yes

—

#11926498

—

C₄×#64520

C₂²

yes

characteristic

C₄×#64515

—

C₄×C₈×D₁₉

—

#11926276

C₄

yes

—

#11926273

C₄

yes

—

#11926265

—

C₈×C₁₉⋊C₈

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂×#64541

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₄×C₂²⋊D₁₉

—

#10597372

C₂×C₄

yes

characteristic

C₂×#64520

C₂×C₄

yes

—

#10597347

—

#10597347

C₈

yes

complemented

C₂×#64515

—

C₂×C₈×D₁₉

—

C₄×D₇₆

C₂×C₄

yes

—

#10597318

—

C₄²×D₁₉

—

C₄×Dic₃₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

C₂×C₈

yes

—

C₂×D₇₆

C₄²

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄²

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

C₄²

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

C₂×C₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

C₄×C₈

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

C₄×C₈

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

—

C₈×C₁₉

C₂²⋊C₈

yes

—

100

C₁₉⋊C₈

—

101

C₁₉⋊C₈

—

102

C₄×#131

—

103

#1476

—

104

#1450

—

105

C₂×#322

D₁₉

yes

characteristic, complemented

106

#1278

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

109

C₂²×C₁₉

#431

yes

—

110

C₂×D₁₉

—

111

C₂×D₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

C₂×C₄×C₈

yes

characteristic

114

C₄×C₁₉

C₄×M₁₆

yes

characteristic

115

C₄×C₁₉

C₂×C₂²⋊C₈

yes

—

116

C₄×C₁₉

#444

yes

—

117

Dic₁₉

—

118

Dic₁₉

—

119

C₂×#131

—

120

C₄×#41

—

121

#431

—

122

#405

—

123

#405

—

124

C₄×M₁₆

—

125

C₄×M₁₆

—

126

C₂×C₄×C₈

—

127

C₂×C₄×C₈

C₂×D₁₉

yes

—

128

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

129

Q₈⋊C₈

—

130

D₄⋊C₈

—

131

#322

—

132

#322

—

133

C₈²

—

134

C₂×C₁₉

—

135

C₂×C₁₉

C₄×C₂²⋊C₈

yes

characteristic

136

C₂×C₁₉

#1765

yes

—

137

D₁₉

—

138

C₂×#41

—

139

#131

—

140

#131

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

C₄×D₁₉

yes

—

146

C₄×Q₈

—

147

C₄×D₄

—

148

C₄×D₄

—

149

#117

—

150

#117

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₁₉

yes

characteristic

153

C₄⋊C₈

—

154

C₂²⋊C₈

—

155

#97

—

156

#97

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

C₄×D₁₉

yes

—

162

C₄×C₈

D₇₆

yes

characteristic

163

C₄×C₈

D₇₆

yes

characteristic

164

C₄×C₈

C₂²⋊D₁₉

yes

—

165

C₁₉

#8185

yes

characteristic, complemented, Sylow

166

#41

—

167

#41

—

168

C₂×Q₈

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

174

C₂²×C₄

#64541

yes

—

175

M₁₆

—

176

M₁₆

—

177

M₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

C₈×D₁₉

yes

—

184

C₂×C₈

#64515

yes

—

185

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

186

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

C₂×C₄×D₁₉

yes

—

194

C₄²

C₂×D₇₆

yes

characteristic

195

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

196

C₂³

—

197

C₂³

#10597318

yes

characteristic

198

Q₈

—

199

Q₈

—

200

D₄

—

201

D₄

—

202

D₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

C₄²×D₁₉

yes

characteristic

209

C₂×C₄

C₄×D₇₆

yes

—

210

C₂×C₄

C₂×C₈×D₁₉

yes

—

211

C₂×C₄

C₂×#64515

yes

—

212

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

213

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

(C₂×D₁₉)⋊C₈

yes

—

218

C₈

(C₂×D₁₉)⋊C₈

yes

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

C₄×(C₂×D₁₉)⋊C₄

yes

characteristic

223

C₂²

#11926595

yes

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

C₄×C₈×D₁₉

yes

characteristic

228

C₄

C₄×#64515

yes

characteristic

229

C₄

C₂×(C₂×D₁₉)⋊C₈

yes

—

230

C₄

#11926667

yes

—

231

C₂

—

232

C₂

—

233

C₂

C₄×(C₂×D₁₉)⋊C₈

yes

characteristic

234

C₂

#14563479

yes

—

	subgroup	G/H
center	C₄²	C₂×D₇₆
commutator	C₄×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂×#64541	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#8185
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

subgroup

G/H

center

C₄²

C₂×D₇₆

commutator

C₄×C₁₉

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

prime radical

C₂×#64541

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

N	H ≅ G/N	type
3. #14561918	C₂	semidirect
4. #14561472	C₂	semidirect
5. C₂×C₁₉×#322	C₂	semidirect
29. #10597347	C₈	semidirect
105. C₂×#322	D₁₉	semidirect
165. C₁₉	#8185	semidirect

H ≅ G/N

type

3. #14561918

C₂

semidirect

4. #14561472

C₂

semidirect

5. C₂×C₁₉×#322

C₂

semidirect

29. #10597347

C₈

semidirect

105. C₂×#322

D₁₉

semidirect

165. C₁₉

#8185

semidirect

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

subgroup	index
C₄×#10597347	2
#14562018	2
#14561918	2
#14561472	2
C₂×C₁₉×#322	2
#8185	19

subgroup

index

C₂×C₁₉×#322

Subgroups — #18073217

Conjugacy classes of subgroups

Complements

Maximal subgroups