Group #18019324 — subgroups

Subgroups — C₁₉×#13365 #18019324

Order 4864.

418 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 130 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×C₁₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#357	C₂	1	2	yes	maximal
3	C₁₉×#1970	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1380	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#125	—	2	1	no	—
8	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#499	—	2	4	no	—
10	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#107	C₂²	1	2	yes	—
12	C₂×C₁₉×#106	—	2	1	no	—
13	C₂×C₁₉×#102	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#390	—	2	1	no	—
16	C₁₉×#357	—	2	4	no	—
17	C₂²×D₄×C₁₉	—	2	1	no	—
18	C₂×D₈×C₁₉	—	2	2	no	—
19	C₂×D₈×C₁₉	—	2	2	no	—
20	C₂×D₈×C₁₉	—	2	1	no	—
21	C₂×D₈×C₁₉	Q₈	1	2	yes	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×#125	—	2	4	no	—
25	C₁₉×#125	—	4	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₁₆×C₁₉	—	2	2	no	—
32	C₂×C₁₆×C₁₉	—	2	2	no	—
33	C₂×C₁₆×C₁₉	—	2	2	no	—
34	C₁₉×#107	—	2	2	no	—
35	C₁₉×#107	—	2	2	no	—
36	C₁₉×#107	D₄	1	4	yes	—
37	C₁₉×#106	—	2	4	no	—
38	C₁₉×#102	—	4	2	no	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	C₂⁴×C₁₉	—	4	1	no	—
41	C₂×D₄×C₁₉	—	2	2	no	—
42	C₂×D₄×C₁₉	—	4	1	no	—
43	C₂×D₄×C₁₉	—	4	1	no	—
44	C₂×D₄×C₁₉	—	4	1	no	—
45	C₂×D₄×C₁₉	—	4	1	no	—
46	C₂×D₄×C₁₉	—	4	1	no	—
47	C₂²×C₄×C₁₉	—	4	2	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	D₈	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	D₈×C₁₉	—	2	4	no	—
52	D₈×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	2	1	no	—
54	C₂×C₈×C₁₉	—	2	1	no	—
55	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
56	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₉	#41	1	2	yes	—
59	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄⋊C₄×C₁₉	—	4	8	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₂²⋊C₄×C₁₉	—	8	4	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₁₆×C₁₉	—	4	2	no	—
69	#13365	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂³×C₁₉	—	4	2	no	—
71	C₂³×C₁₉	—	8	1	no	—
72	C₂³×C₁₉	—	8	1	no	—
73	C₂³×C₁₉	—	8	2	no	—
74	C₂³×C₁₉	—	8	2	no	—
75	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
76	D₄×C₁₉	—	4	2	no	—
77	D₄×C₁₉	—	4	2	no	—
78	D₄×C₁₉	—	8	1	no	—
79	D₄×C₁₉	—	8	1	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	4	no	—
84	C₂×C₄×C₁₉	—	8	2	no	—
85	C₂×C₄×C₁₉	—	8	2	no	—
86	C₂×C₄×C₁₉	—	8	1	no	—
87	C₂×C₄×C₁₉	—	8	2	no	—
88	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
94	C₈×C₁₉	—	2	2	no	—
95	C₈×C₁₉	C₂²⋊Q₈	1	2	yes	—
96	C₈×C₁₉	#124	1	2	yes	—
97	C₂×#499	C₂×C₁₉	1	1	yes	characteristic, complemented
98	C₂×#357	C₂×C₁₉	1	2	yes	—
99	#1970	C₂×C₁₉	1	1	yes	characteristic
100	#1380	C₂×C₁₉	1	2	yes	complemented
101	#1374	C₂×C₁₉	1	1	yes	characteristic, complemented
102	C₂²×C₁₉	—	8	4	no	—
103	C₂²×C₁₉	—	8	2	no	—
104	C₂²×C₁₉	—	16	2	no	—
105	C₂²×C₁₉	—	16	1	no	—
106	C₂²×C₁₉	—	16	1	no	—
107	C₂²×C₁₉	#447	1	1	yes	characteristic
108	C₂²×C₁₉	#474	1	1	yes	characteristic
109	C₂²×C₁₉	#486	1	1	yes	characteristic
110	C₂²×C₁₉	#508	1	2	yes	—
111	C₂²×C₁₉	#509	1	2	yes	—
112	C₄×C₁₉	—	4	2	no	—
113	C₄×C₁₉	—	8	4	no	—
114	C₄×C₁₉	—	16	1	no	—
115	C₄×C₁₉	#393	1	1	yes	characteristic
116	C₄×C₁₉	#448	1	1	yes	characteristic
117	C₄×C₁₉	#476	1	1	yes	characteristic
118	C₄×C₁₉	#489	1	1	yes	characteristic
119	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
120	C₂×#125	—	2	1	no	—
121	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
122	#499	—	2	4	no	—
123	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
124	C₂×#107	C₂²×C₁₉	1	2	yes	—
125	C₂×#106	—	2	1	no	—
126	C₂×#102	—	2	1	no	—
127	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
128	#390	—	2	1	no	—
129	#357	—	2	4	no	—
130	C₂×C₁₉	—	16	2	no	—
131	C₂×C₁₉	#2023	1	1	yes	characteristic
132	C₂×C₁₉	#2186	1	2	yes	—
133	C₂×C₁₉	#2228	1	2	yes	—
134	C₂×C₁₉	#2242	1	1	yes	characteristic
135	C₂×C₁₉	#2244	1	1	yes	characteristic
136	C₂²×D₄	—	2	1	no	—
137	C₂×D₈	—	2	2	no	—
138	C₂×D₈	—	2	2	no	—
139	C₂×D₈	—	2	1	no	—
140	C₂×D₈	Q₈×C₁₉	1	2	yes	—
141	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
142	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
143	#125	—	2	4	no	—
144	#125	—	4	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	4	2	no	—
148	C₂×C₂²⋊C₄	—	4	2	no	—
149	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
150	C₂×C₁₆	—	2	2	no	—
151	C₂×C₁₆	—	2	2	no	—
152	C₂×C₁₆	—	2	2	no	—
153	#107	—	2	2	no	—
154	#107	—	2	2	no	—
155	#107	D₄×C₁₉	1	4	yes	—
156	#106	—	2	4	no	—
157	#102	—	4	2	no	—
158	C₄×C₈	—	2	2	no	—
159	C₁₉	#13365	1	1	yes	characteristic, direct product factor, Sylow
160	C₂⁴	—	4	1	no	—
161	C₂×D₄	—	2	2	no	—
162	C₂×D₄	—	4	1	no	—
163	C₂×D₄	—	4	1	no	—
164	C₂×D₄	—	4	1	no	—
165	C₂×D₄	—	4	1	no	—
166	C₂×D₄	—	4	1	no	—
167	C₂²×C₄	—	4	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	D₈×C₁₉	1	2	yes	—
170	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
171	D₈	—	2	4	no	—
172	D₈	—	4	2	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
176	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
177	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
178	C₂×C₈	#41×C₁₉	1	2	yes	—
179	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	4	8	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	1	no	—
184	C₄⋊C₄	—	4	1	no	—
185	C₂²⋊C₄	—	8	4	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	1	no	—
188	C₁₆	—	4	2	no	—
189	C₂³	—	4	2	no	—
190	C₂³	—	8	1	no	—
191	C₂³	—	8	1	no	—
192	C₂³	—	8	2	no	—
193	C₂³	—	8	2	no	—
194	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
195	D₄	—	4	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	1	no	—
198	D₄	—	8	1	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	—	8	2	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
208	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
209	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
210	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
211	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	C₁₉×C₂²⋊Q₈	1	2	yes	—
215	C₈	C₁₉×#124	1	2	yes	—
216	C₂²	—	8	4	no	—
217	C₂²	—	8	2	no	—
218	C₂²	—	16	2	no	—
219	C₂²	—	16	1	no	—
220	C₂²	—	16	1	no	—
221	C₂²	C₁₉×#447	1	1	yes	characteristic
222	C₂²	C₁₉×#474	1	1	yes	characteristic
223	C₂²	C₁₉×#486	1	1	yes	characteristic
224	C₂²	C₁₉×#508	1	2	yes	—
225	C₂²	C₁₉×#509	1	2	yes	—
226	C₄	—	4	2	no	—
227	C₄	—	8	4	no	—
228	C₄	—	16	1	no	—
229	C₄	C₁₉×#393	1	1	yes	characteristic
230	C₄	C₁₉×#448	1	1	yes	characteristic
231	C₄	C₁₉×#476	1	1	yes	characteristic
232	C₄	C₁₉×#489	1	1	yes	characteristic
233	C₂	—	16	2	no	—
234	C₂	C₁₉×#2023	1	1	yes	characteristic
235	C₂	C₁₉×#2186	1	2	yes	—
236	C₂	C₁₉×#2228	1	2	yes	—
237	C₂	C₁₉×#2242	1	1	yes	characteristic
238	C₂	C₁₉×#2244	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#499

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#357

C₂

yes

maximal

C₁₉×#1970

C₂

yes

maximal, characteristic

C₁₉×#1380

C₂

yes

maximal, complemented

C₁₉×#1374

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#125

—

C₂²×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#499

—

C₂×C₁₉×#107

C₂²

yes

characteristic

C₂×C₁₉×#107

C₂²

yes

—

C₂×C₁₉×#106

—

C₂×C₁₉×#102

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#390

—

C₁₉×#357

—

C₂²×D₄×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

Q₈

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×#125

—

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

D₄

yes

—

C₁₉×#106

—

C₁₉×#102

—

C₄×C₈×C₁₉

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

#41

yes

—

C₂×C₈×C₁₉

#41

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#13365

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₈

yes

characteristic

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

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

#124

yes

—

C₂×#499

C₂×C₁₉

yes

characteristic, complemented

C₂×#357

C₂×C₁₉

yes

—

#1970

C₂×C₁₉

yes

characteristic

100

#1380

C₂×C₁₉

yes

complemented

101

#1374

C₂×C₁₉

yes

characteristic, complemented

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

#447

yes

characteristic

108

C₂²×C₁₉

#474

yes

characteristic

109

C₂²×C₁₉

#486

yes

characteristic

110

C₂²×C₁₉

#508

yes

—

111

C₂²×C₁₉

#509

yes

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#393

yes

characteristic

116

C₄×C₁₉

#448

yes

characteristic

117

C₄×C₁₉

#476

yes

characteristic

118

C₄×C₁₉

#489

yes

characteristic

119

C₂²×D₈

C₂²×C₁₉

yes

characteristic

120

C₂×#125

—

121

C₂²×C₁₆

C₂²×C₁₉

yes

—

122

#499

—

123

C₂×#107

C₂²×C₁₉

yes

characteristic

124

C₂×#107

C₂²×C₁₉

yes

—

125

C₂×#106

—

126

C₂×#102

—

127

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

128

#390

—

129

#357

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#2023

yes

characteristic

132

C₂×C₁₉

#2186

yes

—

133

C₂×C₁₉

#2228

yes

—

134

C₂×C₁₉

#2242

yes

characteristic

135

C₂×C₁₉

#2244

yes

characteristic

136

C₂²×D₄

—

137

C₂×D₈

—

138

C₂×D₈

—

139

C₂×D₈

—

140

C₂×D₈

Q₈×C₁₉

yes

—

141

C₂²×C₈

D₄×C₁₉

yes

characteristic

142

C₂²×C₈

C₂³×C₁₉

yes

characteristic

143

#125

—

144

#125

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₄²

D₄×C₁₉

yes

characteristic

150

C₂×C₁₆

—

151

C₂×C₁₆

—

152

C₂×C₁₆

—

153

#107

—

154

#107

—

155

#107

D₄×C₁₉

yes

—

156

#106

—

157

#102

—

158

C₄×C₈

—

159

C₁₉

#13365

yes

characteristic, direct product factor, Sylow

160

C₂⁴

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

D₈×C₁₉

yes

—

170

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

171

D₈

—

172

D₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

SD₁₆×C₁₉

yes

—

176

C₂×C₈

C₂×D₄×C₁₉

yes

—

177

C₂×C₈

C₂×Q₈×C₁₉

yes

characteristic

178

C₂×C₈

#41×C₁₉

yes

—

179

C₂×C₈

#41×C₁₉

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

186

C₄²

—

187

C₄²

—

188

C₁₆

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

C₂×D₈×C₁₉

yes

characteristic

195

D₄

—

196

D₄

—

197

D₄

—

198

D₄

—

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

C₁₉×#120

yes

characteristic

208

C₂×C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

209

C₂×C₄

C₁₉×#124

yes

characteristic

210

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

211

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

212

C₂×C₄

C₁₉×#137

yes

characteristic

213

C₈

—

214

C₈

C₁₉×C₂²⋊Q₈

yes

—

215

C₈

C₁₉×#124

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

C₁₉×#447

yes

characteristic

222

C₂²

C₁₉×#474

yes

characteristic

223

C₂²

C₁₉×#486

yes

characteristic

224

C₂²

C₁₉×#508

yes

—

225

C₂²

C₁₉×#509

yes

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

C₁₉×#393

yes

characteristic

230

C₄

C₁₉×#448

yes

characteristic

231

C₄

C₁₉×#476

yes

characteristic

232

C₄

C₁₉×#489

yes

characteristic

233

C₂

—

234

C₂

C₁₉×#2023

yes

characteristic

235

C₂

C₁₉×#2186

yes

—

236

C₂

C₁₉×#2228

yes

—

237

C₂

C₁₉×#2242

yes

characteristic

238

C₂

C₁₉×#2244

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₂²×D₈×C₁₉

C₂²

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×#499	C₂	semidirect
4. C₁₉×#1380	C₂	semidirect
5. C₁₉×#1374	C₂	semidirect
69. #13365	C₁₉	direct (N × H)
97. C₂×#499	C₂×C₁₉	semidirect
100. #1380	C₂×C₁₉	semidirect
101. #1374	C₂×C₁₉	semidirect
159. C₁₉	#13365	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×#499

C₂

semidirect

4. C₁₉×#1380

C₂

semidirect

5. C₁₉×#1374

C₂

semidirect

69. #13365

C₁₉

direct (N × H)

97. C₂×#499

C₂×C₁₉

semidirect

100. #1380

C₂×C₁₉

semidirect

101. #1374

C₂×C₁₉

semidirect

159. C₁₉

#13365

direct (N × H)

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

subgroup	index
C₂×C₁₉×#499	2
C₂×C₁₉×#357	2
C₁₉×#1970	2
C₁₉×#1380	2
C₁₉×#1374	2
#13365	19

subgroup

index

C₂×C₁₉×#499

C₂×C₁₉×#357

C₁₉×#1970

C₁₉×#1380

C₁₉×#1374

#13365

Subgroups — C₁₉×#13365 #18019324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13365 #18019324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13365 #18019324