Group #18027786 — subgroups

Subgroups — C₁₉×#21827 #18027786

Order 4864.

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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×#543	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2312	C₂	1	2	yes	maximal
3	C₁₉×#1996	C₂	1	8	yes	maximal, complemented
4	C₁₉×#1819	C₂	1	4	yes	maximal
5	C₁₉×#543	—	2	8	no	—
6	C₂×C₁₉×C₂²⋊Q₈	C₄	1	8	yes	complemented
7	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#388	—	2	8	no	—
11	C₁₉×#380	C₂²	1	4	yes	—
12	C₁₉×#379	C₂²	1	4	yes	—
13	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₁₉×#342	C₂²	1	16	yes	—
15	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
18	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
19	C₁₉×C₂²⋊Q₈	—	2	8	no	—
20	C₁₉×C₂²⋊Q₈	—	2	8	no	—
21	C₁₉×C₂²⋊Q₈	—	2	32	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
28	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
29	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
30	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
31	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
32	C₂×C₄²×C₁₉	—	2	4	no	—
33	C₁₉×#95	—	2	4	no	—
34	C₁₉×#95	—	2	4	no	—
35	C₂⁴×C₁₉	—	2	4	no	—
36	C₂⁴×C₁₉	—	8	2	no	—
37	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
38	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
39	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂×Q₈×C₁₉	—	2	8	no	—
41	C₂×Q₈×C₁₉	—	8	4	no	—
42	C₂²×C₄×C₁₉	—	2	8	no	—
43	C₂²×C₄×C₁₉	—	2	8	no	—
44	C₂²×C₄×C₁₉	—	8	2	no	—
45	C₂²×C₄×C₁₉	—	8	4	no	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
50	C₄⋊C₄×C₁₉	—	2	24	no	—
51	C₄⋊C₄×C₁₉	—	8	4	no	—
52	C₂²⋊C₄×C₁₉	—	2	8	no	—
53	C₂²⋊C₄×C₁₉	—	2	8	no	—
54	C₂²⋊C₄×C₁₉	—	2	16	no	—
55	C₂²⋊C₄×C₁₉	—	8	4	no	—
56	C₂²⋊C₄×C₁₉	—	8	4	no	—
57	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
58	C₄²×C₁₉	—	8	4	no	—
59	#21827	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂³×C₁₉	—	2	4	no	—
61	C₂³×C₁₉	—	2	8	no	—
62	C₂³×C₁₉	—	4	4	no	—
63	C₂³×C₁₉	—	4	2	no	—
64	C₂³×C₁₉	—	4	4	no	—
65	C₂³×C₁₉	—	4	4	no	—
66	C₂³×C₁₉	—	8	8	no	—
67	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
68	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
69	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
70	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
71	Q₈×C₁₉	—	8	8	no	—
72	C₂×C₄×C₁₉	—	2	8	no	—
73	C₂×C₄×C₁₉	—	4	4	no	—
74	C₂×C₄×C₁₉	—	4	4	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	8	no	—
77	C₂×C₄×C₁₉	—	4	8	no	—
78	C₂×C₄×C₁₉	—	4	8	no	—
79	C₂×C₄×C₁₉	—	4	8	no	—
80	C₂×C₄×C₁₉	—	8	8	no	—
81	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
82	C₂×#543	C₂×C₁₉	1	1	yes	characteristic
83	#2312	C₂×C₁₉	1	2	yes	—
84	#1996	C₂×C₁₉	1	8	yes	complemented
85	#1819	C₂×C₁₉	1	4	yes	—
86	C₂²×C₁₉	—	2	2	no	—
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	—	2	2	no	—
89	C₂²×C₁₉	—	2	4	no	—
90	C₂²×C₁₉	—	2	8	no	—
91	C₂²×C₁₉	—	4	4	no	—
92	C₂²×C₁₉	—	4	8	no	—
93	C₂²×C₁₉	—	8	8	no	—
94	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₁₉	#519	1	2	yes	—
96	C₂²×C₁₉	#536	1	4	yes	—
97	C₄×C₁₉	—	2	8	no	—
98	C₄×C₁₉	—	4	8	no	—
99	C₄×C₁₉	—	8	8	no	—
100	#543	—	2	8	no	—
101	C₂×C₂²⋊Q₈	C₄×C₁₉	1	8	yes	complemented
102	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
103	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
104	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
105	#388	—	2	8	no	—
106	#380	C₂²×C₁₉	1	4	yes	—
107	#379	C₂²×C₁₉	1	4	yes	—
108	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
109	#342	C₂²×C₁₉	1	16	yes	—
110	C₂×C₁₉	—	2	4	no	—
111	C₂×C₁₉	—	2	2	no	—
112	C₂×C₁₉	—	4	4	no	—
113	C₂×C₁₉	#2310	1	1	yes	characteristic
114	C₂×C₁₉	#2883	1	2	yes	—
115	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
116	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
117	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
118	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
119	C₂²⋊Q₈	—	2	8	no	—
120	C₂²⋊Q₈	—	2	8	no	—
121	C₂²⋊Q₈	—	2	32	no	—
122	C₂×C₄⋊C₄	—	2	4	no	—
123	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
124	C₂×C₂²⋊C₄	—	2	8	no	—
125	C₂×C₂²⋊C₄	—	2	4	no	—
126	C₂×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
128	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
129	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
130	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
131	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
132	C₂×C₄²	—	2	4	no	—
133	#95	—	2	4	no	—
134	#95	—	2	4	no	—
135	C₁₉	#21827	1	1	yes	characteristic, direct product factor, Sylow
136	C₂⁴	—	2	4	no	—
137	C₂⁴	—	8	2	no	—
138	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
139	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
140	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
141	C₂×Q₈	—	2	8	no	—
142	C₂×Q₈	—	8	4	no	—
143	C₂²×C₄	—	2	8	no	—
144	C₂²×C₄	—	2	8	no	—
145	C₂²×C₄	—	8	2	no	—
146	C₂²×C₄	—	8	4	no	—
147	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
148	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
149	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
150	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
151	C₄⋊C₄	—	2	24	no	—
152	C₄⋊C₄	—	8	4	no	—
153	C₂²⋊C₄	—	2	8	no	—
154	C₂²⋊C₄	—	2	8	no	—
155	C₂²⋊C₄	—	2	16	no	—
156	C₂²⋊C₄	—	8	4	no	—
157	C₂²⋊C₄	—	8	4	no	—
158	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	16	yes	—
159	C₄²	—	8	4	no	—
160	C₂³	—	2	4	no	—
161	C₂³	—	2	8	no	—
162	C₂³	—	4	4	no	—
163	C₂³	—	4	2	no	—
164	C₂³	—	4	4	no	—
165	C₂³	—	4	4	no	—
166	C₂³	—	8	8	no	—
167	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
168	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
169	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
170	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
171	Q₈	—	8	8	no	—
172	C₂×C₄	—	2	8	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	8	no	—
177	C₂×C₄	—	4	8	no	—
178	C₂×C₄	—	4	8	no	—
179	C₂×C₄	—	4	8	no	—
180	C₂×C₄	—	8	8	no	—
181	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	2	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	2	4	no	—
186	C₂²	—	2	8	no	—
187	C₂²	—	4	4	no	—
188	C₂²	—	4	8	no	—
189	C₂²	—	8	8	no	—
190	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
191	C₂²	C₁₉×#519	1	2	yes	—
192	C₂²	C₁₉×#536	1	4	yes	—
193	C₄	—	2	8	no	—
194	C₄	—	4	8	no	—
195	C₄	—	8	8	no	—
196	C₂	—	2	4	no	—
197	C₂	—	2	2	no	—
198	C₂	—	4	4	no	—
199	C₂	C₁₉×#2310	1	1	yes	characteristic
200	C₂	C₁₉×#2883	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#543

C₂

yes

maximal, characteristic

C₁₉×#2312

C₂

yes

maximal

C₁₉×#1996

C₂

yes

maximal, complemented

C₁₉×#1819

C₂

yes

maximal

C₁₉×#543

—

C₂×C₁₉×C₂²⋊Q₈

C₄

yes

complemented

C₂×C₁₉×C₂²⋊Q₈

C₂²

yes

—

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#388

—

C₁₉×#380

C₂²

yes

—

C₁₉×#379

C₂²

yes

—

C₄×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#342

C₂²

yes

—

C₂⁵×C₁₉

C₂³

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂³

yes

—

C₂×C₄²×C₁₉

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²×C₄

yes

—

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

C₂⁴

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

—

#21827

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂³×C₄

yes

characteristic

C₂³×C₁₉

C₂²×D₄

yes

—

C₂³×C₁₉

2₋¹⁺⁴

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×C₂²⋊C₄

yes

—

C₂×#543

C₂×C₁₉

yes

characteristic

#2312

C₂×C₁₉

yes

—

#1996

C₂×C₁₉

yes

complemented

#1819

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#519

yes

—

C₂²×C₁₉

#536

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

#543

—

101

C₂×C₂²⋊Q₈

C₄×C₁₉

yes

complemented

102

C₂×C₂²⋊Q₈

C₂²×C₁₉

yes

—

103

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

—

104

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

characteristic

105

#388

—

106

#380

C₂²×C₁₉

yes

—

107

#379

C₂²×C₁₉

yes

—

108

C₄×C₂²⋊C₄

C₂²×C₁₉

yes

—

109

#342

C₂²×C₁₉

yes

—

110

C₂×C₁₉

—

111

C₂×C₁₉

—

112

C₂×C₁₉

—

113

C₂×C₁₉

#2310

yes

characteristic

114

C₂×C₁₉

#2883

yes

—

115

C₂⁵

C₂³×C₁₉

yes

characteristic

116

C₂²×Q₈

C₂×C₄×C₁₉

yes

—

117

C₂³×C₄

C₂×C₄×C₁₉

yes

—

118

C₂³×C₄

C₂³×C₁₉

yes

—

119

C₂²⋊Q₈

—

120

C₂²⋊Q₈

—

121

C₂²⋊Q₈

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

124

C₂×C₂²⋊C₄

—

125

C₂×C₂²⋊C₄

—

126

C₂×C₂²⋊C₄

—

127

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

—

128

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

—

129

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

130

C₂×C₂²⋊C₄

C₂³×C₁₉

yes

—

131

C₂×C₂²⋊C₄

C₂³×C₁₉

yes

—

132

C₂×C₄²

—

133

#95

—

134

#95

—

135

C₁₉

#21827

yes

characteristic, direct product factor, Sylow

136

C₂⁴

—

137

C₂⁴

—

138

C₂⁴

C₂²×C₄×C₁₉

yes

—

139

C₂⁴

C₂×D₄×C₁₉

yes

—

140

C₂⁴

C₂⁴×C₁₉

yes

characteristic

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²×C₄×C₁₉

yes

—

148

C₂²×C₄

C₂²×C₄×C₁₉

yes

—

149

C₂²×C₄

C₂×D₄×C₁₉

yes

—

150

C₂²×C₄

C₂×D₄×C₁₉

yes

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₂²⋊C₄

—

154

C₂²⋊C₄

—

155

C₂²⋊C₄

—

156

C₂²⋊C₄

—

157

C₂²⋊C₄

—

158

C₂²⋊C₄

C₂²⋊C₄×C₁₉

yes

—

159

C₄²

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

—

165

C₂³

—

166

C₂³

—

167

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

—

168

C₂³

C₂³×C₄×C₁₉

yes

characteristic

169

C₂³

C₂²×D₄×C₁₉

yes

—

170

C₂³

C₁₉×2₋¹⁺⁴

yes

—

171

Q₈

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

C₂²×C₂²⋊C₄×C₁₉

yes

characteristic

191

C₂²

C₁₉×#519

yes

—

192

C₂²

C₁₉×#536

yes

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₂

—

197

C₂

—

198

C₂

—

199

C₂

C₁₉×#2310

yes

characteristic

200

C₂

C₁₉×#2883

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₂²⋊C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂²×C₂²⋊C₄

commutator

C₂³

C₂³×C₄×C₁₉

Frattini, cosocle

C₂⁴

C₂⁴×C₁₉

prime radical

C₂⁵×C₁₉

C₂³

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₂²⋊C₄×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1996	C₂	semidirect
6. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
59. #21827	C₁₉	direct (N × H)
84. #1996	C₂×C₁₉	semidirect
101. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
135. C₁₉	#21827	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1996

C₂

semidirect

6. C₂×C₁₉×C₂²⋊Q₈

C₄

semidirect

59. #21827

C₁₉

direct (N × H)

84. #1996

C₂×C₁₉

semidirect

101. C₂×C₂²⋊Q₈

C₄×C₁₉

semidirect

135. C₁₉

#21827

direct (N × H)

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

subgroup	index
C₂×C₁₉×#543	2
C₁₉×#2312	2
C₁₉×#1996	2
C₁₉×#1819	2
#21827	19

subgroup

index

C₂×C₁₉×#543

C₁₉×#2312

C₁₉×#1996

C₁₉×#1819

#21827

Subgroups — C₁₉×#21827 #18027786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#21827 #18027786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21827 #18027786