Group #18085551 — subgroups

Subgroups — #18085551

Order 4864.

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

normal subgroups only

This group has 504 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	#14564583	C₂	1	2	yes	maximal
2	#14564436	C₂	1	1	yes	maximal, characteristic
3	#14561518	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	2	yes	maximal
5	C₁₉×#2551	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×#10597267	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926306	—	2	2	no	—
11	#11926306	—	2	2	no	—
12	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
13	C₁₉×#395	—	2	2	no	—
14	C₁₉×#389	—	2	2	no	—
15	C₁₉×#384	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×Q₈×C₁₉	—	2	2	no	—
18	C₂²×Dic₃₈	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	—	4	4	no	—
20	C₁₉×C₄⋊Q₈	—	4	4	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	#10597315	—	2	2	no	—
32	#10597315	—	2	1	no	—
33	#10597315	Q₈	1	2	yes	complemented
34	C₁₉×#95	—	2	2	no	—
35	C₁₉×#95	—	2	2	no	—
36	#10597267	—	4	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₂×Q₈×C₁₉	—	4	8	no	—
41	C₂×Q₈×C₁₉	—	8	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
48	C₂×Dic₃₈	—	2	2	no	—
49	C₂×Dic₃₈	—	4	2	no	—
50	C₂×Dic₃₈	—	4	2	no	—
51	C₂×Dic₃₈	—	4	1	no	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	4	2	no	—
55	C₄⋊C₄×C₁₉	—	4	8	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	—
59	C₄⋊C₄×C₁₉	Q₁₆	1	4	yes	—
60	C₄²×C₁₉	—	4	2	no	—
61	C₄²×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₄²×C₁₉	#41	1	1	yes	characteristic
65	C₄⋊Dic₁₉	—	2	4	no	—
66	C₄⋊Dic₁₉	—	4	2	no	—
67	C₂×C₁₉⋊C₈	—	2	2	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	#10349	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	#120	1	1	yes	characteristic
75	Q₈×C₁₉	—	8	8	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	—	2	4	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	4	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#124	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₁₉	#137	1	2	yes	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	8	1	no	—
96	C₂×Dic₁₉	—	8	1	no	—
97	Dic₃₈	—	4	4	no	—
98	Dic₃₈	—	8	2	no	—
99	C₁₉⋊C₈	—	4	2	no	—
100	C₁₉⋊C₈	—	8	2	no	—
101	#2551	D₁₉	1	1	yes	characteristic
102	#1987	—	19	2	no	—
103	#1956	—	19	1	no	—
104	#1296	—	19	1	no	—
105	#1279	—	19	2	no	—
106	C₂²×C₁₉	#393	1	1	yes	characteristic
107	C₂²×C₁₉	#450	1	2	yes	—
108	C₂²×C₁₉	#451	1	2	yes	—
109	C₂²×C₁₉	#453	1	1	yes	characteristic
110	C₂²×C₁₉	#454	1	1	yes	characteristic
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	4	4	no	—
114	C₄×C₁₉	—	4	4	no	—
115	C₄×C₁₉	—	8	2	no	—
116	C₄×C₁₉	#475	1	2	yes	—
117	C₄×C₁₉	#477	1	2	yes	—
118	C₄×C₁₉	#487	1	2	yes	—
119	C₄×C₁₉	#489	1	2	yes	—
120	Dic₁₉	—	8	2	no	—
121	C₂×C₄⋊Q₈	—	2	2	no	—
122	C₂×C₄⋊Q₈	—	19	1	no	—
123	C₂×C₄⋊C₈	—	19	2	no	—
124	C₂×#103	—	38	2	no	—
125	C₂×C₄×C₈	—	19	1	no	—
126	#395	—	2	2	no	—
127	#389	—	2	2	no	—
128	#384	C₂×D₁₉	1	1	yes	characteristic
129	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
130	#340	—	38	2	no	—
131	#340	—	38	2	no	—
132	C₂×C₁₉	#1629	1	1	yes	characteristic
133	C₂×C₁₉	#1633	1	1	yes	characteristic
134	C₂×C₁₉	#1637	1	2	yes	—
135	C₂×C₁₉	#2024	1	2	yes	—
136	C₂×C₁₉	#2027	1	1	yes	characteristic
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	38	1	no	—
139	C₂²×C₈	—	38	1	no	—
140	C₂²×C₈	—	38	2	no	—
141	C₄⋊Q₈	—	4	4	no	—
142	C₄⋊Q₈	—	4	4	no	—
143	C₄⋊Q₈	—	19	2	no	—
144	C₄⋊Q₈	—	38	2	no	—
145	C₄⋊Q₈	—	38	1	no	—
146	C₂×C₄⋊C₄	—	2	4	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	38	2	no	—
149	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
150	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	38	2	no	—
155	C₄⋊C₈	—	38	2	no	—
156	#103	—	76	4	no	—
157	C₄×C₈	—	38	2	no	—
158	#95	—	2	2	no	—
159	#95	—	2	2	no	—
160	C₁₉	#10349	1	1	yes	characteristic, complemented, Sylow
161	C₂×Q₈	—	4	8	no	—
162	C₂×Q₈	—	8	2	no	—
163	C₂×Q₈	—	38	2	no	—
164	C₂×Q₈	—	76	2	no	—
165	C₂×Q₈	—	76	2	no	—
166	C₂×Q₈	—	76	1	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	76	1	no	—
171	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
173	C₂×C₈	—	38	2	no	—
174	C₂×C₈	—	76	1	no	—
175	C₂×C₈	—	76	1	no	—
176	C₂×C₈	—	76	2	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	—	76	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	8	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	38	4	no	—
186	C₄⋊C₄	—	76	2	no	—
187	C₄⋊C₄	#64526	1	4	yes	—
188	C₄⋊C₄	#64528	1	4	yes	—
189	C₄²	—	4	2	no	—
190	C₄²	—	4	2	no	—
191	C₄²	Q₈×D₁₉	1	1	yes	characteristic
192	C₄²	#64545	1	2	yes	—
193	C₄²	#64545	1	1	yes	characteristic
194	C₂³	#10597399	1	1	yes	characteristic
195	Q₈	—	8	8	no	—
196	Q₈	—	76	4	no	—
197	Q₈	—	152	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	76	2	no	—
209	C₂×C₄	—	152	1	no	—
210	C₂×C₄	—	152	1	no	—
211	C₂×C₄	#10597378	1	2	yes	—
212	C₂×C₄	C₂×#64526	1	2	yes	—
213	C₂×C₄	#10597388	1	2	yes	—
214	C₂×C₄	C₂×#64528	1	2	yes	—
215	C₂×C₄	#10597392	1	1	yes	characteristic
216	C₂×C₄	#10597392	1	2	yes	—
217	C₂×C₄	#10597393	1	1	yes	characteristic
218	C₂×C₄	#10597393	1	2	yes	—
219	C₈	—	76	2	no	—
220	C₈	—	152	2	no	—
221	C₂²	#11926455	1	1	yes	characteristic
222	C₂²	#11926695	1	2	yes	—
223	C₂²	#11926700	1	2	yes	—
224	C₂²	#11926712	1	1	yes	characteristic
225	C₂²	#11926717	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	4	no	—
230	C₄	—	8	2	no	—
231	C₄	—	152	2	no	—
232	C₄	#11926826	1	2	yes	—
233	C₄	#11926836	1	2	yes	—
234	C₄	#11926896	1	2	yes	—
235	C₄	#11926906	1	2	yes	—
236	C₂	#14562751	1	1	yes	characteristic
237	C₂	#14562775	1	1	yes	characteristic
238	C₂	#14562800	1	2	yes	—
239	C₂	#14564773	1	2	yes	—
240	C₂	#14564788	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564583

C₂

yes

maximal

#14564436

C₂

yes

maximal, characteristic

#14561518

C₂

yes

maximal, characteristic

#14561476

C₂

yes

maximal

C₁₉×#2551

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597267

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926306

—

#11926306

—

C₂×C₁₉×C₄⋊Q₈

—

C₁₉×#395

—

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597315

—

#10597315

—

#10597315

Q₈

yes

complemented

C₁₉×#95

—

C₁₉×#95

—

#10597267

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

—

101

#2551

D₁₉

yes

characteristic

102

#1987

—

103

#1956

—

104

#1296

—

105

#1279

—

106

C₂²×C₁₉

#393

yes

characteristic

107

C₂²×C₁₉

#450

yes

—

108

C₂²×C₁₉

#451

yes

—

109

C₂²×C₁₉

#453

yes

characteristic

110

C₂²×C₁₉

#454

yes

characteristic

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

#475

yes

—

117

C₄×C₁₉

#477

yes

—

118

C₄×C₁₉

#487

yes

—

119

C₄×C₁₉

#489

yes

—

120

Dic₁₉

—

121

C₂×C₄⋊Q₈

—

122

C₂×C₄⋊Q₈

—

123

C₂×C₄⋊C₈

—

124

C₂×#103

—

125

C₂×C₄×C₈

—

126

#395

—

127

#389

—

128

#384

C₂×D₁₉

yes

characteristic

129

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

130

#340

—

131

#340

—

132

C₂×C₁₉

#1629

yes

characteristic

133

C₂×C₁₉

#1633

yes

characteristic

134

C₂×C₁₉

#1637

yes

—

135

C₂×C₁₉

#2024

yes

—

136

C₂×C₁₉

#2027

yes

characteristic

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₄⋊Q₈

—

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

C₂²⋊D₁₉

yes

—

150

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

151

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#103

—

157

C₄×C₈

—

158

#95

—

159

#95

—

160

C₁₉

#10349

yes

characteristic, complemented, Sylow

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

172

C₂²×C₄

C₂×C₂²⋊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

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

#64526

yes

—

188

C₄⋊C₄

#64528

yes

—

189

C₄²

—

190

C₄²

—

191

C₄²

Q₈×D₁₉

yes

characteristic

192

C₄²

#64545

yes

—

193

C₄²

#64545

yes

characteristic

194

C₂³

#10597399

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

152

—

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

—

152

—

210

C₂×C₄

—

152

—

211

C₂×C₄

#10597378

yes

—

212

C₂×C₄

C₂×#64526

yes

—

213

C₂×C₄

#10597388

yes

—

214

C₂×C₄

C₂×#64528

yes

—

215

C₂×C₄

#10597392

yes

characteristic

216

C₂×C₄

#10597392

yes

—

217

C₂×C₄

#10597393

yes

characteristic

218

C₂×C₄

#10597393

yes

—

219

C₈

—

220

C₈

—

152

—

221

C₂²

#11926455

yes

characteristic

222

C₂²

#11926695

yes

—

223

C₂²

#11926700

yes

—

224

C₂²

#11926712

yes

characteristic

225

C₂²

#11926717

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

152

—

232

C₄

#11926826

yes

—

233

C₄

#11926836

yes

—

234

C₄

#11926896

yes

—

235

C₄

#11926906

yes

—

236

C₂

#14562751

yes

characteristic

237

C₂

#14562775

yes

characteristic

238

C₂

#14562800

yes

—

239

C₂

#14564773

yes

—

240

C₂

#14564788

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2551	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#2551	D₁₉
hypocenter	C₁₉	#10349
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2551

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

N	H ≅ G/N	type
33. #10597315	Q₈	semidirect
160. C₁₉	#10349	semidirect

H ≅ G/N

type

33. #10597315

Q₈

semidirect

160. C₁₉

#10349

semidirect

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

subgroup	index
#14564583	2
#14564436	2
#14561518	2
#14561476	2
C₁₉×#2551	2
#10349	19

subgroup

index

C₁₉×#2551

Subgroups — #18085551

Conjugacy classes of subgroups

Complements

Maximal subgroups