Group #18077011 — subgroups

Subgroups — #18077011

Order 4864.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14566725	C₂	1	1	yes	maximal, characteristic
2	#14564438	C₂	1	1	yes	maximal, characteristic
3	#14564394	C₂	1	2	yes	maximal
4	#14561474	C₂	1	2	yes	maximal
5	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	2	no	—
7	C₂×#10597292	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926451	—	2	2	no	—
10	#11926443	—	2	2	no	—
11	#11926414	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₁₉	—	2	2	no	—
13	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	#11926307	—	2	2	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₁₉×#333	C₄	1	4	yes	complemented
18	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₁₉×C₄⋊Q₈	—	2	2	no	—
21	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	—	2	1	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
30	C₂×C₄×Dic₁₉	—	2	2	no	—
31	C₂×C₄×Dic₁₉	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	—	2	1	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
35	#10597292	—	4	4	no	—
36	C₁₉⋊#95	—	2	4	no	—
37	C₁₉⋊#95	—	2	2	no	—
38	#10597275	—	4	4	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂²×Dic₁₉	—	2	2	no	—
48	C₂²×Dic₁₉	—	2	2	no	—
49	C₂²×Dic₁₉	—	4	1	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	C₄²×C₁₉	#41	1	2	yes	—
58	C₄⋊Dic₁₉	—	2	2	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	C₄⋊Dic₁₉	—	2	2	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₄⋊Dic₁₉	—	8	2	no	—
65	C₄⋊Dic₁₉	Q₁₆	1	4	yes	—
66	C₄×Dic₁₉	—	4	2	no	—
67	C₄×Dic₁₉	—	4	2	no	—
68	C₄×Dic₁₉	—	8	2	no	—
69	C₂×C₁₉⋊C₈	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	#8929	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	#120	1	1	yes	characteristic
74	Q₈×C₁₉	—	4	4	no	—
75	Q₈×C₁₉	—	8	2	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₉	#135	1	2	yes	—
87	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×C₄×C₁₉	#137	1	2	yes	—
89	C₂×Dic₁₉	—	2	4	no	—
90	C₂×Dic₁₉	—	4	2	no	—
91	C₂×Dic₁₉	—	4	2	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	8	2	no	—
96	C₂×Dic₁₉	—	8	1	no	—
97	C₈×C₁₉	—	4	4	no	—
98	C₁₉⋊C₈	—	4	2	no	—
99	#2369	—	19	1	no	—
100	#1956	—	19	1	no	—
101	#1947	—	19	2	no	—
102	C₂×#333	D₁₉	1	1	yes	characteristic
103	#1279	—	19	2	no	—
104	C₂²×C₁₉	#385	1	1	yes	characteristic
105	C₂²×C₁₉	#449	1	2	yes	—
106	C₂²×C₁₉	#451	1	2	yes	—
107	C₂²×C₁₉	#453	1	1	yes	characteristic
108	C₂²×C₁₉	#455	1	1	yes	characteristic
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	4	4	no	—
112	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
113	C₄×C₁₉	#440	1	2	yes	—
114	C₄×C₁₉	#477	1	2	yes	—
115	C₄×C₁₉	#479	1	2	yes	—
116	Dic₁₉	—	4	4	no	—
117	Dic₁₉	—	8	2	no	—
118	Dic₁₉	—	16	1	no	—
119	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
120	C₂×#107	—	38	2	no	—
121	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
122	C₂×#103	—	38	2	no	—
123	C₂×C₄×C₈	—	19	1	no	—
124	#391	—	38	2	no	—
125	#389	—	38	2	no	—
126	#384	—	19	1	no	—
127	C₄×C₄⋊C₄	—	19	2	no	—
128	C₄×C₄⋊C₄	—	38	2	no	—
129	#340	—	38	2	no	—
130	#333	Dic₁₉	1	4	yes	complemented
131	C₂×C₁₉	#1624	1	1	yes	characteristic
132	C₂×C₁₉	#1633	1	1	yes	characteristic
133	C₂×C₁₉	#1644	1	2	yes	—
134	C₂×C₁₉	#1856	1	1	yes	characteristic
135	C₂×C₁₉	#1863	1	2	yes	—
136	C₂²×Q₈	D₇₆	1	2	yes	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	38	1	no	—
139	C₄⋊Q₈	—	2	2	no	—
140	C₄⋊Q₈	Dic₃₈	1	2	yes	—
141	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	19	2	no	—
144	C₂×C₄⋊C₄	—	19	2	no	—
145	C₂×C₄⋊C₄	—	38	1	no	—
146	C₂×C₄⋊C₄	—	38	2	no	—
147	C₂×C₄⋊C₄	—	38	2	no	—
148	C₂×C₄²	—	38	2	no	—
149	C₂×C₄²	—	38	2	no	—
150	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
151	#107	—	76	4	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	—
154	#103	—	76	4	no	—
155	C₄×C₈	—	38	2	no	—
156	#95	—	38	4	no	—
157	#95	—	38	2	no	—
158	C₁₉	#8929	1	1	yes	characteristic, complemented, Sylow
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	C₄⋊Dic₁₉	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	38	2	no	—
165	C₂²×C₄	—	38	2	no	—
166	C₂²×C₄	—	76	1	no	—
167	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
168	C₂²×C₄	D₄×D₁₉	1	2	yes	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	38	2	no	—
173	C₂×C₈	—	76	1	no	—
174	C₂×C₈	—	76	1	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	19	4	no	—
178	C₄⋊C₄	—	38	2	no	—
179	C₄⋊C₄	—	38	2	no	—
180	C₄⋊C₄	—	38	2	no	—
181	C₄⋊C₄	—	76	2	no	—
182	C₄⋊C₄	—	76	2	no	—
183	C₄⋊C₄	—	76	2	no	—
184	C₄⋊C₄	—	152	2	no	—
185	C₄²	—	76	2	no	—
186	C₄²	—	76	2	no	—
187	C₄²	—	152	2	no	—
188	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
189	C₄²	#64543	1	2	yes	—
190	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
191	C₂³	#10597328	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	38	4	no	—
200	C₂×C₄	—	76	2	no	—
201	C₂×C₄	—	76	2	no	—
202	C₂×C₄	—	76	2	no	—
203	C₂×C₄	—	76	2	no	—
204	C₂×C₄	—	76	2	no	—
205	C₂×C₄	—	152	2	no	—
206	C₂×C₄	—	152	1	no	—
207	C₂×C₄	#10597324	1	2	yes	—
208	C₂×C₄	#10597332	1	1	yes	characteristic
209	C₂×C₄	#10597360	1	2	yes	—
210	C₂×C₄	#10597361	1	2	yes	—
211	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
212	C₂×C₄	#10597365	1	2	yes	—
213	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
214	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
215	C₈	—	4	4	no	—
216	C₈	—	76	2	no	—
217	C₂²	#11926419	1	1	yes	characteristic
218	C₂²	#11926692	1	2	yes	—
219	C₂²	#11926701	1	2	yes	—
220	C₂²	#11926714	1	1	yes	characteristic
221	C₂²	#11926724	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	304	1	no	—
226	C₄	—	76	4	no	—
227	C₄	—	152	2	no	—
228	C₄	Q₁₆×Dic₁₉	1	2	yes	—
229	C₄	#11926645	1	2	yes	—
230	C₄	#11926837	1	2	yes	—
231	C₄	#11926853	1	2	yes	—
232	C₂	#14562719	1	1	yes	characteristic
233	C₂	#14562776	1	1	yes	characteristic
234	C₂	#14562850	1	2	yes	—
235	C₂	#14563847	1	1	yes	characteristic
236	C₂	#14563891	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566725

C₂

yes

maximal, characteristic

#14564438

C₂

yes

maximal, characteristic

#14564394

C₂

yes

maximal

#14561474

C₂

yes

maximal

C₂×C₁₉×#333

C₂

yes

maximal, characteristic

C₂×#10597275

—

C₂×#10597292

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊C₄×Dic₁₉

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926307

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#333

C₄

yes

complemented

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597275

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₁₆

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2369

—

100

#1956

—

101

#1947

—

102

C₂×#333

D₁₉

yes

characteristic

103

#1279

—

104

C₂²×C₁₉

#385

yes

characteristic

105

C₂²×C₁₉

#449

yes

—

106

C₂²×C₁₉

#451

yes

—

107

C₂²×C₁₉

#453

yes

characteristic

108

C₂²×C₁₉

#455

yes

characteristic

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

C₄×Q₁₆

yes

—

113

C₄×C₁₉

#440

yes

—

114

C₄×C₁₉

#477

yes

—

115

C₄×C₁₉

#479

yes

—

116

Dic₁₉

—

117

Dic₁₉

—

118

Dic₁₉

—

119

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

120

C₂×#107

—

121

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

122

C₂×#103

—

123

C₂×C₄×C₈

—

124

#391

—

125

#389

—

126

#384

—

127

C₄×C₄⋊C₄

—

128

C₄×C₄⋊C₄

—

129

#340

—

130

#333

Dic₁₉

yes

complemented

131

C₂×C₁₉

#1624

yes

characteristic

132

C₂×C₁₉

#1633

yes

characteristic

133

C₂×C₁₉

#1644

yes

—

134

C₂×C₁₉

#1856

yes

characteristic

135

C₂×C₁₉

#1863

yes

—

136

C₂²×Q₈

D₇₆

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

Dic₃₈

yes

—

141

C₄⋊Q₈

C₂×Dic₁₉

yes

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂²×D₁₉

yes

characteristic

151

#107

—

152

C₄⋊C₈

—

153

C₄⋊C₈

C₂×Dic₁₉

yes

—

154

#103

—

155

C₄×C₈

—

156

#95

—

157

#95

—

158

C₁₉

#8929

yes

characteristic, complemented, Sylow

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

C₄⋊Dic₁₉

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

C₂×D₇₆

yes

characteristic

168

C₂²×C₄

D₄×D₁₉

yes

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

152

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

152

—

188

C₄²

C₂×Dic₃₈

yes

characteristic

189

C₄²

#64543

yes

—

190

C₄²

C₂²×Dic₁₉

yes

characteristic

191

C₂³

#10597328

yes

characteristic

192

Q₈

—

193

Q₈

—

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

—

152

—

206

C₂×C₄

—

152

—

207

C₂×C₄

#10597324

yes

—

208

C₂×C₄

#10597332

yes

characteristic

209

C₂×C₄

#10597360

yes

—

210

C₂×C₄

#10597361

yes

—

211

C₂×C₄

Q₁₆×D₁₉

yes

—

212

C₂×C₄

#10597365

yes

—

213

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

214

C₂×C₄

D₄×Dic₁₉

yes

—

215

C₈

—

216

C₈

—

217

C₂²

#11926419

yes

characteristic

218

C₂²

#11926692

yes

—

219

C₂²

#11926701

yes

—

220

C₂²

#11926714

yes

characteristic

221

C₂²

#11926724

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

304

—

226

C₄

—

227

C₄

—

152

—

228

C₄

Q₁₆×Dic₁₉

yes

—

229

C₄

#11926645

yes

—

230

C₄

#11926837

yes

—

231

C₄

#11926853

yes

—

232

C₂

#14562719

yes

characteristic

233

C₂

#14562776

yes

characteristic

234

C₂

#14562850

yes

—

235

C₂

#14563847

yes

characteristic

236

C₂

#14563891

yes

—

	subgroup	G/H
center	C₂³	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#333	C₂
socle, prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#333	D₁₉
hypocenter	C₁₉	#8929
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#333

C₂

socle, prime radical

C₂³×C₁₉

#120

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
17. C₁₉×#333	C₄	semidirect
130. #333	Dic₁₉	semidirect
158. C₁₉	#8929	semidirect

H ≅ G/N

type

17. C₁₉×#333

C₄

semidirect

130. #333

Dic₁₉

semidirect

158. C₁₉

#8929

semidirect

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

subgroup	index
#14566725	2
#14564438	2
#14564394	2
#14561474	2
C₂×C₁₉×#333	2
#8929	19

subgroup

index

C₂×C₁₉×#333

Subgroups — #18077011

Conjugacy classes of subgroups

Complements

Maximal subgroups