Group #18018247 — subgroups

Subgroups — C₁₉×#12288 #18018247

Order 4864.

354 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 82 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	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2232	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2086	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1347	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#532	—	2	1	no	—
7	C₁₉×#474	—	2	2	no	—
8	C₁₉×#466	—	2	1	no	—
9	C₁₉×#466	C₂²	1	2	yes	—
10	C₁₉×#459	—	2	2	no	—
11	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×#389	—	2	1	no	—
14	C₁₉×#366	—	2	2	no	—
15	C₁₉×#357	—	2	2	no	—
16	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
17	C₁₉×#340	—	2	1	no	—
18	C₁₉×#340	C₂²	1	1	yes	characteristic
19	C₂×#41×C₁₉	—	4	1	no	—
20	C₂×D₈×C₁₉	—	2	1	no	—
21	C₂×D₈×C₁₉	D₄	1	2	yes	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₁₉×#127	—	2	1	no	—
26	C₁₉×#124	—	4	1	no	—
27	C₁₉×#121	—	2	2	no	—
28	C₁₉×#121	—	4	1	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₄×D₄×C₁₉	—	4	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₁₉	—	2	2	no	—
36	C₁₉×#107	—	2	1	no	—
37	C₁₉×#107	—	2	2	no	—
38	C₁₉×#107	D₄	1	2	yes	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×#102	—	2	2	no	—
41	C₁₉×#102	—	2	2	no	—
42	C₁₉×#95	—	4	1	no	—
43	#41×C₁₉	—	8	2	no	—
44	#41×C₁₉	—	8	2	no	—
45	C₂×Q₈×C₁₉	—	4	1	no	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	4	1	no	—
48	C₂×D₄×C₁₉	—	4	1	no	—
49	C₂×D₄×C₁₉	—	4	2	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	D₈×C₁₉	—	4	2	no	—
57	D₈×C₁₉	—	8	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	1	no	—
61	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	4	1	no	—
66	C₄⋊C₄×C₁₉	—	4	1	no	—
67	C₄⋊C₄×C₁₉	—	4	1	no	—
68	C₄⋊C₄×C₁₉	—	8	2	no	—
69	C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	—	2	1	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₁₆×C₁₉	—	4	2	no	—
74	#12288	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₁₉	—	4	2	no	—
76	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
77	Q₈×C₁₉	—	8	2	no	—
78	D₄×C₁₉	—	4	2	no	—
79	D₄×C₁₉	—	4	2	no	—
80	D₄×C₁₉	—	8	2	no	—
81	D₄×C₁₉	—	8	2	no	—
82	D₄×C₁₉	—	8	2	no	—
83	D₄×C₁₉	—	8	2	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	8	4	no	—
93	C₂×C₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	—	8	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	D₁₆	1	2	yes	—
99	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₈×C₁₉	—	2	2	no	—
102	C₈×C₁₉	—	4	1	no	—
103	#3245	C₂×C₁₉	1	1	yes	characteristic
104	#2232	C₂×C₁₉	1	2	yes	complemented
105	#2086	C₂×C₁₉	1	1	yes	characteristic, complemented
106	#1347	C₂×C₁₉	1	2	yes	complemented
107	#1322	C₂×C₁₉	1	1	yes	characteristic, complemented
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	8	2	no	—
111	C₂²×C₁₉	—	8	2	no	—
112	C₂²×C₁₉	—	8	2	no	—
113	C₂²×C₁₉	#447	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
115	C₂²×C₁₉	#509	1	1	yes	characteristic
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	4	1	no	—
119	C₄×C₁₉	—	8	2	no	—
120	C₄×C₁₉	—	8	2	no	—
121	C₄×C₁₉	—	16	1	no	—
122	C₄×C₁₉	#456	1	1	yes	characteristic
123	C₄×C₁₉	#458	1	1	yes	characteristic
124	#532	—	2	1	no	—
125	#474	—	2	2	no	—
126	#466	—	2	1	no	—
127	#466	C₂²×C₁₉	1	2	yes	—
128	#459	—	2	2	no	—
129	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
130	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
131	#389	—	2	1	no	—
132	#366	—	2	2	no	—
133	#357	—	2	2	no	—
134	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	—
135	#340	—	2	1	no	—
136	#340	C₂²×C₁₉	1	1	yes	characteristic
137	C₂×C₁₉	—	2	1	no	—
138	C₂×C₁₉	—	2	1	no	—
139	C₂×C₁₉	—	16	2	no	—
140	C₂×C₁₉	#1610	1	1	yes	characteristic
141	C₂×C₁₉	#2184	1	1	yes	characteristic
142	C₂×C₁₉	#2191	1	1	yes	characteristic
143	C₂×#41	—	4	1	no	—
144	C₂×D₈	—	2	1	no	—
145	C₂×D₈	D₄×C₁₉	1	2	yes	—
146	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
147	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
148	C₄⋊Q₈	—	2	1	no	—
149	#127	—	2	1	no	—
150	#124	—	4	1	no	—
151	#121	—	2	2	no	—
152	#121	—	4	1	no	—
153	C₄×D₄	—	2	2	no	—
154	C₄×D₄	—	4	1	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	—	4	1	no	—
158	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
159	C₂×C₁₆	—	2	2	no	—
160	#107	—	2	1	no	—
161	#107	—	2	2	no	—
162	#107	D₄×C₁₉	1	2	yes	—
163	C₄⋊C₈	—	2	2	no	—
164	#102	—	2	2	no	—
165	#102	—	2	2	no	—
166	#95	—	4	1	no	—
167	C₁₉	#12288	1	1	yes	characteristic, direct product factor, Sylow
168	#41	—	8	2	no	—
169	#41	—	8	2	no	—
170	C₂×Q₈	—	4	1	no	—
171	C₂×D₄	—	2	2	no	—
172	C₂×D₄	—	4	1	no	—
173	C₂×D₄	—	4	1	no	—
174	C₂×D₄	—	4	2	no	—
175	C₂²×C₄	—	4	2	no	—
176	C₂²×C₄	—	4	1	no	—
177	C₂²×C₄	—	4	1	no	—
178	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
179	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
181	D₈	—	4	2	no	—
182	D₈	—	8	1	no	—
183	C₂×C₈	—	2	1	no	—
184	C₂×C₈	—	4	1	no	—
185	C₂×C₈	—	4	1	no	—
186	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄⋊C₄	—	4	1	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	8	2	no	—
194	C₂²⋊C₄	—	4	2	no	—
195	C₂²⋊C₄	—	4	2	no	—
196	C₄²	—	2	1	no	—
197	C₄²	—	2	1	no	—
198	C₁₆	—	4	2	no	—
199	C₂³	—	4	2	no	—
200	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
201	Q₈	—	8	2	no	—
202	D₄	—	4	2	no	—
203	D₄	—	4	2	no	—
204	D₄	—	8	2	no	—
205	D₄	—	8	2	no	—
206	D₄	—	8	2	no	—
207	D₄	—	8	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	4	no	—
217	C₂×C₄	—	8	1	no	—
218	C₂×C₄	—	8	1	no	—
219	C₂×C₄	—	8	1	no	—
220	C₂×C₄	—	8	1	no	—
221	C₂×C₄	—	8	1	no	—
222	C₂×C₄	C₁₉×D₁₆	1	2	yes	—
223	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
224	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₈	—	2	2	no	—
226	C₈	—	4	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	8	2	no	—
230	C₂²	—	8	2	no	—
231	C₂²	—	8	2	no	—
232	C₂²	C₁₉×#447	1	1	yes	characteristic
233	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
234	C₂²	C₁₉×#509	1	1	yes	characteristic
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	4	1	no	—
238	C₄	—	8	2	no	—
239	C₄	—	8	2	no	—
240	C₄	—	16	1	no	—
241	C₄	C₁₉×#456	1	1	yes	characteristic
242	C₄	C₁₉×#458	1	1	yes	characteristic
243	C₂	—	2	1	no	—
244	C₂	—	2	1	no	—
245	C₂	—	16	2	no	—
246	C₂	C₁₉×#1610	1	1	yes	characteristic
247	C₂	C₁₉×#2184	1	1	yes	characteristic
248	C₂	C₁₉×#2191	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3245

C₂

yes

maximal, characteristic

C₁₉×#2232

C₂

yes

maximal, complemented

C₁₉×#2086

C₂

yes

maximal, characteristic, complemented

C₁₉×#1347

C₂

yes

maximal, complemented

C₁₉×#1322

C₂

yes

maximal, characteristic, complemented

C₁₉×#532

—

C₁₉×#474

—

C₁₉×#466

—

C₁₉×#466

C₂²

yes

—

C₁₉×#459

—

C₂×C₁₉×#107

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#389

—

C₁₉×#366

—

C₁₉×#357

—

C₁₉×C₂²⋊C₁₆

C₂²

yes

—

C₁₉×#340

—

C₁₉×#340

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#127

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×#95

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#12288

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₈

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

100

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

#3245

C₂×C₁₉

yes

characteristic

104

#2232

C₂×C₁₉

yes

complemented

105

#2086

C₂×C₁₉

yes

characteristic, complemented

106

#1347

C₂×C₁₉

yes

complemented

107

#1322

C₂×C₁₉

yes

characteristic, complemented

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#447

yes

characteristic

114

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

115

C₂²×C₁₉

#509

yes

characteristic

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

#456

yes

characteristic

123

C₄×C₁₉

#458

yes

characteristic

124

#532

—

125

#474

—

126

#466

—

127

#466

C₂²×C₁₉

yes

—

128

#459

—

129

C₂×#107

C₂²×C₁₉

yes

characteristic

130

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

131

#389

—

132

#366

—

133

#357

—

134

C₂²⋊C₁₆

C₂²×C₁₉

yes

—

135

#340

—

136

#340

C₂²×C₁₉

yes

characteristic

137

C₂×C₁₉

—

138

C₂×C₁₉

—

139

C₂×C₁₉

—

140

C₂×C₁₉

#1610

yes

characteristic

141

C₂×C₁₉

#2184

yes

characteristic

142

C₂×C₁₉

#2191

yes

characteristic

143

C₂×#41

—

144

C₂×D₈

—

145

C₂×D₈

D₄×C₁₉

yes

—

146

C₂²×C₈

D₄×C₁₉

yes

characteristic

147

C₂²×C₈

C₂³×C₁₉

yes

characteristic

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

151

#121

—

152

#121

—

153

C₄×D₄

—

154

C₄×D₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄²

D₄×C₁₉

yes

characteristic

159

C₂×C₁₆

—

160

#107

—

161

#107

—

162

#107

D₄×C₁₉

yes

—

163

C₄⋊C₈

—

164

#102

—

165

#102

—

166

#95

—

167

C₁₉

#12288

yes

characteristic, direct product factor, Sylow

168

#41

—

169

#41

—

170

C₂×Q₈

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

D₈×C₁₉

yes

characteristic

179

C₂²×C₄

D₈×C₁₉

yes

characteristic

180

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

181

D₈

—

182

D₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

C₂×D₄×C₁₉

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₂²⋊C₄

—

195

C₂²⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₁₆

—

199

C₂³

—

200

C₂³

C₂×D₈×C₁₉

yes

characteristic

201

Q₈

—

202

D₄

—

203

D₄

—

204

D₄

—

205

D₄

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

C₁₉×D₁₆

yes

—

223

C₂×C₄

C₁₉×#120

yes

characteristic

224

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

225

C₈

—

226

C₈

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

C₁₉×#447

yes

characteristic

233

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

234

C₂²

C₁₉×#509

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

C₁₉×#456

yes

characteristic

242

C₄

C₁₉×#458

yes

characteristic

243

C₂

—

244

C₂

—

245

C₂

—

246

C₂

C₁₉×#1610

yes

characteristic

247

C₂

C₁₉×#2184

yes

characteristic

248

C₂

C₁₉×#2191

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3245	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊C₈ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#447

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₁₉×#3245

C₂

LCS

G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊C₈ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2232	C₂	semidirect
3. C₁₉×#2086	C₂	semidirect
4. C₁₉×#1347	C₂	semidirect
5. C₁₉×#1322	C₂	semidirect
74. #12288	C₁₉	direct (N × H)
104. #2232	C₂×C₁₉	semidirect
105. #2086	C₂×C₁₉	semidirect
106. #1347	C₂×C₁₉	semidirect
107. #1322	C₂×C₁₉	semidirect
167. C₁₉	#12288	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2232

C₂

semidirect

3. C₁₉×#2086

C₂

semidirect

4. C₁₉×#1347

C₂

semidirect

5. C₁₉×#1322

C₂

semidirect

74. #12288

C₁₉

direct (N × H)

104. #2232

C₂×C₁₉

semidirect

105. #2086

C₂×C₁₉

semidirect

106. #1347

C₂×C₁₉

semidirect

107. #1322

C₂×C₁₉

semidirect

167. C₁₉

#12288

direct (N × H)

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

subgroup	index
C₁₉×#3245	2
C₁₉×#2232	2
C₁₉×#2086	2
C₁₉×#1347	2
C₁₉×#1322	2
#12288	19

subgroup

index

C₁₉×#3245

C₁₉×#2232

C₁₉×#2086

C₁₉×#1347

C₁₉×#1322

#12288

Subgroups — C₁₉×#12288 #18018247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12288 #18018247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12288 #18018247