Group #18075369 — subgroups

Subgroups — #18075369

Order 4864.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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	#14566202	C₂	1	1	yes	maximal, characteristic
2	#14563751	C₂	1	2	yes	maximal
3	C₂×#11926292	C₂	1	2	yes	maximal
4	#14561518	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597333	C₄	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	#11926449	C₄	1	2	yes	—
10	#11926440	—	2	2	no	—
11	C₄⋊C₄×Dic₁₉	—	2	2	no	—
12	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926298	—	2	2	no	—
14	#11926298	—	2	2	no	—
15	#11926292	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₁₉×#384	C₂²	1	1	yes	characteristic
18	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×Dic₁₉⋊C₄	—	2	2	no	—
25	C₂×C₄×Dic₁₉	—	2	2	no	—
26	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
29	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	#10597333	—	4	4	no	—
32	#10597315	—	2	2	no	—
33	#10597315	D₄	1	2	yes	—
34	#10597315	Q₈	1	2	yes	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉⋊#95	—	2	4	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×Dic₃₈	—	2	2	no	—
48	C₂×Dic₃₈	—	4	2	no	—
49	C₂×Dic₃₈	—	4	2	no	—
50	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	—	4	2	no	—
55	C₄⋊C₄×C₁₉	—	4	2	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	2	yes	—
60	C₄⋊Dic₁₉	—	2	4	no	—
61	C₄⋊Dic₁₉	—	2	4	no	—
62	Dic₁₉⋊C₄	—	4	4	no	—
63	C₄×Dic₁₉	—	2	2	no	—
64	C₄×Dic₁₉	—	2	2	no	—
65	C₄×Dic₁₉	—	2	2	no	—
66	C₄×Dic₁₉	—	2	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	C₄×Dic₁₉	—	4	1	no	—
69	C₄×Dic₁₉	—	4	4	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	#8594	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#121	1	2	yes	—
82	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₁₉	#135	1	2	yes	—
84	C₂×C₄×C₁₉	#135	1	2	yes	—
85	C₂×C₄×C₁₉	#137	1	2	yes	—
86	C₂×C₄×C₁₉	#137	1	2	yes	—
87	C₂×Dic₁₉	—	2	2	no	—
88	C₂×Dic₁₉	—	2	4	no	—
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	#100	1	2	yes	—
97	Dic₃₈	—	4	4	no	—
98	Dic₃₈	—	4	4	no	—
99	C₈×C₁₉	—	8	2	no	—
100	C₁₉⋊C₈	—	8	2	no	—
101	C₄×C₄⋊Q₈	—	19	1	no	—
102	#1831	—	19	2	no	—
103	C₂×#333	—	19	2	no	—
104	#1296	—	19	1	no	—
105	#1296	D₁₉	1	1	yes	characteristic
106	C₂²×C₁₉	#380	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
108	C₂²×C₁₉	#413	1	1	yes	characteristic
109	C₂²×C₁₉	#416	1	2	yes	—
110	C₂²×C₁₉	#419	1	2	yes	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	8	2	no	—
114	C₄×C₁₉	#464	1	2	yes	—
115	C₄×C₁₉	#464	1	2	yes	—
116	C₄×C₁₉	#479	1	2	yes	—
117	C₄×C₁₉	#479	1	2	yes	—
118	Dic₁₉	—	2	2	no	—
119	Dic₁₉	—	4	1	no	—
120	Dic₁₉	—	4	4	no	—
121	Dic₁₉	—	4	2	no	—
122	C₂×C₄⋊Q₈	—	19	1	no	—
123	C₂×C₄×Q₈	—	19	2	no	—
124	C₂×C₄⋊C₈	—	19	2	no	—
125	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
126	#391	—	19	2	no	—
127	#389	—	38	2	no	—
128	#384	C₂×D₁₉	1	1	yes	characteristic
129	C₄×C₄⋊C₄	—	38	2	no	—
130	C₄³	—	19	1	no	—
131	#336	—	38	2	no	—
132	#336	—	38	2	no	—
133	#333	—	38	4	no	—
134	C₂×C₁₉	#1543	1	1	yes	characteristic
135	C₂×C₁₉	#1554	1	2	yes	—
136	C₂×C₁₉	#1558	1	1	yes	characteristic
137	C₂×C₁₉	#1800	1	1	yes	characteristic
138	C₂×C₁₉	#1805	1	2	yes	—
139	C₂²×Q₈	—	19	2	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	38	2	no	—
142	C₄⋊Q₈	—	19	2	no	—
143	C₄⋊Q₈	—	19	2	no	—
144	C₄⋊Q₈	—	38	2	no	—
145	C₄×Q₈	—	76	4	no	—
146	C₂×C₄⋊C₄	—	2	2	no	—
147	C₂×C₄⋊C₄	—	38	2	no	—
148	C₂×C₄⋊C₄	—	38	2	no	—
149	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
150	C₂×C₄²	—	19	1	no	—
151	C₂×C₄²	—	19	2	no	—
152	C₂×C₄²	—	19	2	no	—
153	C₂×C₄²	—	19	1	no	—
154	C₂×C₄²	—	38	2	no	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₄⋊C₈	—	38	2	no	—
160	#95	—	38	4	no	—
161	C₁₉	#8594	1	1	yes	characteristic, complemented, Sylow
162	C₂×Q₈	—	19	4	no	—
163	C₂×Q₈	—	38	2	no	—
164	C₂×Q₈	—	76	2	no	—
165	C₂×Q₈	—	76	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	19	1	no	—
168	C₂²×C₄	—	19	2	no	—
169	C₂²×C₄	—	19	1	no	—
170	C₂²×C₄	—	38	2	no	—
171	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
172	C₂²×C₄	D₄×D₁₉	1	2	yes	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	76	2	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	—	76	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	38	4	no	—
183	C₄⋊C₄	—	38	4	no	—
184	C₄⋊C₄	—	76	4	no	—
185	C₄²	—	38	2	no	—
186	C₄²	—	38	2	no	—
187	C₄²	—	38	2	no	—
188	C₄²	—	38	2	no	—
189	C₄²	—	38	2	no	—
190	C₄²	—	76	1	no	—
191	C₄²	—	76	4	no	—
192	C₄²	#64541	1	2	yes	—
193	C₄²	D₄×D₁₉	1	1	yes	characteristic
194	C₄²	Q₈×D₁₉	1	1	yes	characteristic
195	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
196	Q₈	—	76	4	no	—
197	Q₈	—	76	4	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	19	2	no	—
203	C₂×C₄	—	38	2	no	—
204	C₂×C₄	—	38	2	no	—
205	C₂×C₄	—	38	2	no	—
206	C₂×C₄	—	38	2	no	—
207	C₂×C₄	—	38	4	no	—
208	C₂×C₄	—	38	1	no	—
209	C₂×C₄	—	38	2	no	—
210	C₂×C₄	—	76	2	no	—
211	C₂×C₄	—	76	2	no	—
212	C₂×C₄	#10597318	1	1	yes	characteristic
213	C₂×C₄	#10597330	1	2	yes	—
214	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
215	C₂×C₄	#10597342	1	2	yes	—
216	C₂×C₄	#10597358	1	2	yes	—
217	C₂×C₄	#10597361	1	2	yes	—
218	C₂×C₄	#10597362	1	2	yes	—
219	C₂×C₄	#10597364	1	2	yes	—
220	C₈	—	8	2	no	—
221	C₈	—	152	2	no	—
222	C₂²	#11926403	1	1	yes	characteristic
223	C₂²	#100×D₁₉	1	1	yes	characteristic
224	C₂²	#11926527	1	1	yes	characteristic
225	C₂²	#11926537	1	2	yes	—
226	C₂²	#11926551	1	2	yes	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	8	2	no	—
230	C₄	—	38	2	no	—
231	C₄	—	76	2	no	—
232	C₄	—	76	4	no	—
233	C₄	—	76	1	no	—
234	C₄	#11926765	1	2	yes	—
235	C₄	#11926769	1	2	yes	—
236	C₄	#11926850	1	2	yes	—
237	C₄	#11926854	1	2	yes	—
238	C₂	#14562294	1	1	yes	characteristic
239	C₂	#14562342	1	2	yes	—
240	C₂	#14562359	1	1	yes	characteristic
241	C₂	#14563626	1	1	yes	characteristic
242	C₂	#14563649	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566202

C₂

yes

maximal, characteristic

#14563751

C₂

yes

maximal

C₂×#11926292

C₂

yes

maximal

#14561518

C₂

yes

maximal, characteristic

C₁₉×#1296

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597333

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926449

C₄

yes

—

#11926440

—

C₄⋊C₄×Dic₁₉

—

C₄²×Dic₁₉

C₂²

yes

—

—

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

#10597333

—

#10597315

—

#10597315

D₄

yes

—

#10597315

Q₈

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8594

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#100

yes

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

100

C₁₉⋊C₈

—

101

C₄×C₄⋊Q₈

—

102

#1831

—

103

C₂×#333

—

104

#1296

—

105

#1296

D₁₉

yes

characteristic

106

C₂²×C₁₉

#380

yes

characteristic

107

C₂²×C₁₉

C₂×#100

yes

characteristic

108

C₂²×C₁₉

#413

yes

characteristic

109

C₂²×C₁₉

#416

yes

—

110

C₂²×C₁₉

#419

yes

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

#464

yes

—

115

C₄×C₁₉

#464

yes

—

116

C₄×C₁₉

#479

yes

—

117

C₄×C₁₉

#479

yes

—

118

Dic₁₉

—

119

Dic₁₉

—

120

Dic₁₉

—

121

Dic₁₉

—

122

C₂×C₄⋊Q₈

—

123

C₂×C₄×Q₈

—

124

C₂×C₄⋊C₈

—

125

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

126

#391

—

127

#389

—

128

#384

C₂×D₁₉

yes

characteristic

129

C₄×C₄⋊C₄

—

130

C₄³

—

131

#336

—

132

#336

—

133

#333

—

134

C₂×C₁₉

#1543

yes

characteristic

135

C₂×C₁₉

#1554

yes

—

136

C₂×C₁₉

#1558

yes

characteristic

137

C₂×C₁₉

#1800

yes

characteristic

138

C₂×C₁₉

#1805

yes

—

139

C₂²×Q₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

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×C₄²

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₂×C₄²

—

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#95

—

161

C₁₉

#8594

yes

characteristic, complemented, Sylow

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

172

C₂²×C₄

D₄×D₁₉

yes

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

#64541

yes

—

193

C₄²

D₄×D₁₉

yes

characteristic

194

C₄²

Q₈×D₁₉

yes

characteristic

195

C₂³

C₂²⋊C₄×D₁₉

yes

characteristic

196

Q₈

—

197

Q₈

—

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

—

211

C₂×C₄

—

212

C₂×C₄

#10597318

yes

characteristic

213

C₂×C₄

#10597330

yes

—

214

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

215

C₂×C₄

#10597342

yes

—

216

C₂×C₄

#10597358

yes

—

217

C₂×C₄

#10597361

yes

—

218

C₂×C₄

#10597362

yes

—

219

C₂×C₄

#10597364

yes

—

220

C₈

—

221

C₈

—

152

—

222

C₂²

#11926403

yes

characteristic

223

C₂²

#100×D₁₉

yes

characteristic

224

C₂²

#11926527

yes

characteristic

225

C₂²

#11926537

yes

—

226

C₂²

#11926551

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#11926765

yes

—

235

C₄

#11926769

yes

—

236

C₄

#11926850

yes

—

237

C₄

#11926854

yes

—

238

C₂

#14562294

yes

characteristic

239

C₂

#14562342

yes

—

240

C₂

#14562359

yes

characteristic

241

C₂

#14563626

yes

characteristic

242

C₂

#14563649

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#8594
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1296

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
161. C₁₉	#8594	semidirect

H ≅ G/N

type

161. C₁₉

#8594

semidirect

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

subgroup	index
#14566202	2
#14563751	2
C₂×#11926292	2
#14561518	2
C₁₉×#1296	2
#8594	19

subgroup

index

C₁₉×#1296

Subgroups — #18075369

Conjugacy classes of subgroups

Complements

Maximal subgroups