Group #18075469 — subgroups

Subgroups — #18075469

Order 4864.

398 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 137 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	C₂×Q₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14563631	C₂	1	1	yes	maximal, characteristic
3	#14562393	C₂	1	2	yes	maximal
4	#14561509	C₂	1	2	yes	maximal
5	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₉⋊C₈	—	2	2	no	—
7	Q₈×C₁₉⋊C₈	—	2	2	no	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597293	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926313	—	2	1	no	—
15	#11926296	—	2	2	no	—
16	#11926296	—	2	2	no	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#423	C₂²	1	2	yes	—
19	C₂×C₁₉×#101	—	2	1	no	—
20	C₁₉×#343	—	2	1	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×#64520	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×#101	—	4	2	no	—
36	#10597293	—	4	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
44	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	D₈	1	2	yes	—
48	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	M₁₆×C₁₉	—	4	2	no	—
55	M₁₆×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄²×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	C₂×D₄	1	2	yes	—
62	C₄²×C₁₉	#41	1	2	yes	—
63	#64520	—	4	2	no	—
64	#64520	—	4	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	4	1	no	—
68	C₂×C₁₉⋊C₈	—	4	2	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
72	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	#8617	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
75	Q₈×C₁₉	—	2	4	no	—
76	Q₈×C₁₉	—	2	4	no	—
77	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	#107	1	4	yes	—
85	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
89	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#135	1	2	yes	—
92	C₈×C₁₉	—	8	2	no	—
93	C₁₉⋊C₈	—	2	1	no	—
94	C₁₉⋊C₈	—	2	2	no	—
95	C₁₉⋊C₈	—	4	2	no	—
96	C₁₉⋊C₈	—	8	2	no	—
97	C₁₉⋊C₈	#101	1	2	yes	complemented
98	C₂×C₈×Q₈	—	19	1	no	—
99	#1801	—	19	1	no	—
100	#1801	D₁₉	1	1	yes	characteristic
101	#1567	—	19	2	no	—
102	#1292	—	19	2	no	—
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	#380	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
107	C₂²×C₁₉	#427	1	1	yes	characteristic
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	4	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
113	C₄×C₁₉	#413	1	1	yes	characteristic
114	C₄×C₁₉	#466	1	2	yes	—
115	C₄×C₁₉	#467	1	2	yes	—
116	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
117	C₈×Q₈	—	38	2	no	—
118	C₈×Q₈	—	38	2	no	—
119	#423	—	19	2	no	—
120	#423	C₂×D₁₉	1	2	yes	—
121	C₂×C₄⋊C₈	—	19	2	no	—
122	C₂×C₄⋊C₈	—	19	1	no	—
123	C₂×#101	—	2	1	no	—
124	C₂×#101	—	38	1	no	—
125	C₂×C₄×C₈	—	19	1	no	—
126	C₂×C₄×C₈	—	19	2	no	—
127	#343	—	2	1	no	—
128	#343	—	38	1	no	—
129	#335	—	38	2	no	—
130	#335	—	38	2	no	—
131	C₂×C₁₉	—	2	1	no	—
132	C₂×C₁₉	—	2	1	no	—
133	C₂×C₁₉	#1801	1	1	yes	characteristic
134	C₂×C₁₉	#1808	1	1	yes	characteristic
135	C₂×C₁₉	#1813	1	1	yes	characteristic
136	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
137	C₂×M₁₆	—	2	2	no	—
138	C₂×M₁₆	—	38	2	no	—
139	C₂²×C₈	—	19	1	no	—
140	C₂²×C₈	—	19	1	no	—
141	C₂²×C₈	—	19	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
145	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂×C₄²	C₄×D₁₉	1	2	yes	—
147	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
148	C₄⋊C₈	—	2	2	no	—
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	38	4	no	—
151	C₄⋊C₈	—	38	2	no	—
152	C₄⋊C₈	—	38	2	no	—
153	C₄⋊C₈	—	38	2	no	—
154	#101	—	4	2	no	—
155	#101	—	76	2	no	—
156	C₄×C₈	—	19	2	no	—
157	C₄×C₈	—	19	2	no	—
158	C₄×C₈	—	38	2	no	—
159	C₄×C₈	—	38	2	no	—
160	C₁₉	#8617	1	1	yes	characteristic, complemented, Sylow
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	#64525	1	2	yes	—
164	C₂×Q₈	#64528	1	2	yes	—
165	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
166	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
167	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
170	M₁₆	—	4	2	no	—
171	M₁₆	—	4	2	no	—
172	M₁₆	—	76	2	no	—
173	M₁₆	—	76	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	19	1	no	—
176	C₂×C₈	—	19	1	no	—
177	C₂×C₈	—	19	2	no	—
178	C₂×C₈	—	38	2	no	—
179	C₂×C₈	—	38	2	no	—
180	C₂×C₈	—	76	1	no	—
181	C₂×C₈	—	76	2	no	—
182	C₂×C₈	—	76	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	2	no	—
187	C₄²	D₄×D₁₉	1	2	yes	—
188	C₄²	#64543	1	2	yes	—
189	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
190	Q₈	—	2	4	no	—
191	Q₈	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#10597264	1	4	yes	—
200	C₂×C₄	#10597323	1	1	yes	characteristic
201	C₂×C₄	#10597324	1	2	yes	—
202	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
203	C₂×C₄	C₂×#64525	1	1	yes	characteristic
204	C₂×C₄	#10597385	1	2	yes	—
205	C₂×C₄	C₂×#64528	1	1	yes	characteristic
206	C₂×C₄	#10597396	1	2	yes	—
207	C₈	—	8	2	no	—
208	C₈	—	19	2	no	—
209	C₈	—	38	1	no	—
210	C₈	—	38	2	no	—
211	C₈	—	76	2	no	—
212	C₈	—	152	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#11926402	1	1	yes	characteristic
216	C₂²	C₂×#10597264	1	1	yes	characteristic
217	C₂²	#11926580	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	4	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	#101×D₁₉	1	1	yes	characteristic
223	C₄	#11926527	1	1	yes	characteristic
224	C₄	#11926778	1	2	yes	—
225	C₄	#11926783	1	2	yes	—
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	#14563629	1	1	yes	characteristic
229	C₂	#14563662	1	1	yes	characteristic
230	C₂	#14563683	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

#14562393

C₂

yes

maximal

#14561509

C₂

yes

maximal

C₁₉×#1801

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

Q₈×C₁₉⋊C₈

—

#11926568

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597293

—

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#101

—

C₁₉×#343

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

—

C₂×Q₈×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

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

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8617

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊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

—

C₂×C₄×C₁₉

#107

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#101

yes

complemented

C₂×C₈×Q₈

—

#1801

—

100

#1801

D₁₉

yes

characteristic

101

#1567

—

102

#1292

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#380

yes

characteristic

106

C₂²×C₁₉

C₂×#107

yes

characteristic

107

C₂²×C₁₉

#427

yes

characteristic

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

C₂×#101

yes

characteristic

113

C₄×C₁₉

#413

yes

characteristic

114

C₄×C₁₉

#466

yes

—

115

C₄×C₁₉

#467

yes

—

116

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

117

C₈×Q₈

—

118

C₈×Q₈

—

119

#423

—

120

#423

C₂×D₁₉

yes

—

121

C₂×C₄⋊C₈

—

122

C₂×C₄⋊C₈

—

123

C₂×#101

—

124

C₂×#101

—

125

C₂×C₄×C₈

—

126

C₂×C₄×C₈

—

127

#343

—

128

#343

—

129

#335

—

130

#335

—

131

C₂×C₁₉

—

132

C₂×C₁₉

—

133

C₂×C₁₉

#1801

yes

characteristic

134

C₂×C₁₉

#1808

yes

characteristic

135

C₂×C₁₉

#1813

yes

characteristic

136

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

137

C₂×M₁₆

—

138

C₂×M₁₆

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

C₂×C₄⋊C₄

Dic₃₈

yes

—

145

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

146

C₂×C₄²

C₄×D₁₉

yes

—

147

C₂×C₄²

C₂²×D₁₉

yes

characteristic

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#101

—

155

#101

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₁₉

#8617

yes

characteristic, complemented, Sylow

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

#64525

yes

—

164

C₂×Q₈

#64528

yes

—

165

C₂²×C₄

Dic₁₉⋊C₄

yes

—

166

C₂²×C₄

Dic₁₉⋊C₄

yes

—

167

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

168

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

169

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

170

M₁₆

—

171

M₁₆

—

172

M₁₆

—

173

M₁₆

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

D₄×D₁₉

yes

—

188

C₄²

#64543

yes

—

189

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#10597264

yes

—

200

C₂×C₄

#10597323

yes

characteristic

201

C₂×C₄

#10597324

yes

—

202

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

203

C₂×C₄

C₂×#64525

yes

characteristic

204

C₂×C₄

#10597385

yes

—

205

C₂×C₄

C₂×#64528

yes

characteristic

206

C₂×C₄

#10597396

yes

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

152

—

213

C₂²

—

214

C₂²

—

215

C₂²

#11926402

yes

characteristic

216

C₂²

C₂×#10597264

yes

characteristic

217

C₂²

#11926580

yes

characteristic

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#101×D₁₉

yes

characteristic

223

C₄

#11926527

yes

characteristic

224

C₄

#11926778

yes

—

225

C₄

#11926783

yes

—

226

C₂

—

227

C₂

—

228

C₂

#14563629

yes

characteristic

229

C₂

#14563662

yes

characteristic

230

C₂

#14563683

yes

characteristic

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1801	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1801	D₁₉
hypocenter	C₁₉	#8617
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#11926402

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1801

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂³×C₁₉

C₂×C₄⋊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
97. C₁₉⋊C₈	#101	semidirect
160. C₁₉	#8617	semidirect

H ≅ G/N

type

97. C₁₉⋊C₈

#101

semidirect

160. C₁₉

#8617

semidirect

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

subgroup	index
C₂×Q₈×C₁₉⋊C₈	2
#14563631	2
#14562393	2
#14561509	2
C₁₉×#1801	2
#8617	19

subgroup

index

C₂×Q₈×C₁₉⋊C₈

C₁₉×#1801

Subgroups — #18075469

Conjugacy classes of subgroups

Complements

Maximal subgroups