Group #18038826 — subgroups

Subgroups — C₁₉×#32867 #18038826

Order 4864.

630 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 206 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×#2644	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2087	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2067	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2054	C₂	1	3	yes	maximal
5	C₁₉×#1843	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#107	C₂²	1	3	yes	—
8	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
10	C₂×C₁₉×#102	C₂²	1	6	yes	—
11	C₁₉×#397	—	2	6	no	—
12	C₁₉×#396	—	2	2	no	—
13	C₁₉×#390	C₂²	1	6	yes	—
14	C₁₉×#389	C₂²	1	6	yes	—
15	C₁₉×#376	C₂²	1	1	yes	characteristic
16	C₁₉×#340	C₂²	1	3	yes	—
17	C₁₉×#340	C₂²	1	3	yes	—
18	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
19	C₂×D₈×C₁₉	—	4	3	no	—
20	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
22	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
23	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
26	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
27	C₁₉×#107	—	4	3	no	—
28	C₁₉×C₄⋊C₈	—	4	3	no	—
29	C₁₉×C₄⋊C₈	—	4	3	no	—
30	C₁₉×#102	—	4	6	no	—
31	C₁₉×#95	—	2	6	no	—
32	C₁₉×#95	D₄	1	1	yes	characteristic
33	C₁₉×#95	D₄	1	3	yes	—
34	C₂⁴×C₁₉	—	2	2	no	—
35	C₂×D₄×C₁₉	—	2	6	no	—
36	C₂×D₄×C₁₉	—	2	6	no	—
37	C₂²×C₄×C₁₉	—	2	6	no	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
40	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
41	D₈×C₁₉	—	4	4	no	—
42	C₂×C₈×C₁₉	—	2	3	no	—
43	C₂×C₈×C₁₉	—	2	6	no	—
44	C₂×C₈×C₁₉	—	2	3	no	—
45	C₄⋊C₄×C₁₉	—	2	6	no	—
46	C₄⋊C₄×C₁₉	—	2	6	no	—
47	C₄⋊C₄×C₁₉	—	8	6	no	—
48	C₂²⋊C₄×C₁₉	—	8	6	no	—
49	C₂²⋊C₄×C₁₉	—	8	6	no	—
50	C₄²×C₁₉	—	2	3	no	—
51	C₄²×C₁₉	—	2	3	no	—
52	#32867	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂³×C₁₉	—	4	6	no	—
54	C₂³×C₁₉	—	4	6	no	—
55	C₂³×C₁₉	—	4	2	no	—
56	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
57	D₄×C₁₉	—	4	2	no	—
58	D₄×C₁₉	—	4	6	no	—
59	C₂×C₄×C₁₉	—	2	3	no	—
60	C₂×C₄×C₁₉	—	2	3	no	—
61	C₂×C₄×C₁₉	—	2	3	no	—
62	C₂×C₄×C₁₉	—	2	6	no	—
63	C₂×C₄×C₁₉	—	2	3	no	—
64	C₂×C₄×C₁₉	—	4	6	no	—
65	C₂×C₄×C₁₉	—	4	6	no	—
66	C₂×C₄×C₁₉	—	4	6	no	—
67	C₂×C₄×C₁₉	H(5,𝔽₂)	1	3	yes	—
68	C₂×C₄×C₁₉	2₋¹⁺⁴	1	3	yes	—
69	C₈×C₁₉	—	4	3	no	—
70	C₈×C₁₉	—	4	1	no	—
71	#2644	C₂×C₁₉	1	2	yes	complemented
72	#2087	C₂×C₁₉	1	3	yes	complemented
73	#2067	C₂×C₁₉	1	6	yes	complemented
74	#2054	C₂×C₁₉	1	3	yes	—
75	#1843	C₂×C₁₉	1	1	yes	characteristic, complemented
76	C₂²×C₁₉	—	8	2	no	—
77	C₂²×C₁₉	—	8	6	no	—
78	C₂²×C₁₉	—	8	6	no	—
79	C₂²×C₁₉	#537	1	3	yes	—
80	C₂²×C₁₉	#576	1	3	yes	—
81	C₂²×C₁₉	#578	1	1	yes	characteristic
82	C₄×C₁₉	—	4	3	no	—
83	C₄×C₁₉	—	4	3	no	—
84	C₄×C₁₉	—	8	6	no	—
85	C₄×C₁₉	#560	1	1	yes	characteristic
86	C₄×C₁₉	#563	1	3	yes	—
87	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
88	C₂×#107	C₂²×C₁₉	1	3	yes	—
89	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
90	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
91	C₂×#102	C₂²×C₁₉	1	6	yes	—
92	#397	—	2	6	no	—
93	#396	—	2	2	no	—
94	#390	C₂²×C₁₉	1	6	yes	—
95	#389	C₂²×C₁₉	1	6	yes	—
96	#376	C₂²×C₁₉	1	1	yes	characteristic
97	#340	C₂²×C₁₉	1	3	yes	—
98	#340	C₂²×C₁₉	1	3	yes	—
99	C₂×C₁₉	—	16	2	no	—
100	C₂×C₁₉	#2823	1	1	yes	characteristic
101	C₂×C₁₉	#3259	1	3	yes	—
102	C₂×C₁₉	#3262	1	3	yes	—
103	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
104	C₂×D₈	—	4	3	no	—
105	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
106	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
107	C₂×C₄⋊C₄	—	2	6	no	—
108	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
109	C₂×C₂²⋊C₄	—	2	6	no	—
110	C₂×C₂²⋊C₄	—	2	6	no	—
111	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
112	#107	—	4	3	no	—
113	C₄⋊C₈	—	4	3	no	—
114	C₄⋊C₈	—	4	3	no	—
115	#102	—	4	6	no	—
116	#95	—	2	6	no	—
117	#95	D₄×C₁₉	1	1	yes	characteristic
118	#95	D₄×C₁₉	1	3	yes	—
119	C₁₉	#32867	1	1	yes	characteristic, direct product factor, Sylow
120	C₂⁴	—	2	2	no	—
121	C₂×D₄	—	2	6	no	—
122	C₂×D₄	—	2	6	no	—
123	C₂²×C₄	—	2	6	no	—
124	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
125	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
126	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
127	D₈	—	4	4	no	—
128	C₂×C₈	—	2	6	no	—
129	C₂×C₈	—	2	3	no	—
130	C₂×C₈	—	2	3	no	—
131	C₄⋊C₄	—	2	6	no	—
132	C₄⋊C₄	—	2	6	no	—
133	C₄⋊C₄	—	8	6	no	—
134	C₂²⋊C₄	—	8	6	no	—
135	C₂²⋊C₄	—	8	6	no	—
136	C₄²	—	2	3	no	—
137	C₄²	—	2	3	no	—
138	C₂³	—	4	6	no	—
139	C₂³	—	4	6	no	—
140	C₂³	—	4	2	no	—
141	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
142	D₄	—	4	2	no	—
143	D₄	—	4	6	no	—
144	C₂×C₄	—	2	3	no	—
145	C₂×C₄	—	2	3	no	—
146	C₂×C₄	—	2	3	no	—
147	C₂×C₄	—	2	6	no	—
148	C₂×C₄	—	2	3	no	—
149	C₂×C₄	—	4	6	no	—
150	C₂×C₄	—	4	6	no	—
151	C₂×C₄	—	4	6	no	—
152	C₂×C₄	C₁₉×H(5,𝔽₂)	1	3	yes	—
153	C₂×C₄	C₁₉×2₋¹⁺⁴	1	3	yes	—
154	C₈	—	4	1	no	—
155	C₈	—	4	3	no	—
156	C₂²	—	8	6	no	—
157	C₂²	—	8	6	no	—
158	C₂²	—	8	2	no	—
159	C₂²	C₁₉×#537	1	3	yes	—
160	C₂²	C₁₉×#576	1	3	yes	—
161	C₂²	C₁₉×#578	1	1	yes	characteristic
162	C₄	—	4	3	no	—
163	C₄	—	4	3	no	—
164	C₄	—	8	6	no	—
165	C₄	C₁₉×#560	1	1	yes	characteristic
166	C₄	C₁₉×#563	1	3	yes	—
167	C₂	—	16	2	no	—
168	C₂	C₁₉×#2823	1	1	yes	characteristic
169	C₂	C₁₉×#3259	1	3	yes	—
170	C₂	C₁₉×#3262	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2644

C₂

yes

maximal, complemented

C₁₉×#2087

C₂

yes

maximal, complemented

C₁₉×#2067

C₂

yes

maximal, complemented

C₁₉×#2054

C₂

yes

maximal

C₁₉×#1843

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#107

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₁₉×#102

C₂²

yes

—

C₁₉×#397

—

C₁₉×#396

—

C₁₉×#390

C₂²

yes

—

C₁₉×#389

C₂²

yes

—

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#340

C₂²

yes

—

C₁₉×#340

C₂²

yes

—

C₂²×D₄×C₁₉

C₂³

yes

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₁₉×#95

—

C₁₉×#95

D₄

yes

characteristic

C₁₉×#95

D₄

yes

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂⁴

yes

characteristic

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#32867

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×D₄

yes

characteristic

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

H(5,𝔽₂)

yes

—

C₂×C₄×C₁₉

2₋¹⁺⁴

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#2644

C₂×C₁₉

yes

complemented

#2087

C₂×C₁₉

yes

complemented

#2067

C₂×C₁₉

yes

complemented

#2054

C₂×C₁₉

yes

—

#1843

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#537

yes

—

C₂²×C₁₉

#576

yes

—

C₂²×C₁₉

#578

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#560

yes

characteristic

C₄×C₁₉

#563

yes

—

C₂²×D₈

C₂²×C₁₉

yes

characteristic

C₂×#107

C₂²×C₁₉

yes

—

C₂×C₄⋊C₈

C₂²×C₁₉

yes

—

C₂×C₄⋊C₈

C₂²×C₁₉

yes

—

C₂×#102

C₂²×C₁₉

yes

—

#397

—

#396

—

#390

C₂²×C₁₉

yes

—

#389

C₂²×C₁₉

yes

—

#376

C₂²×C₁₉

yes

characteristic

#340

C₂²×C₁₉

yes

—

#340

C₂²×C₁₉

yes

—

C₂×C₁₉

—

100

C₂×C₁₉

#2823

yes

characteristic

101

C₂×C₁₉

#3259

yes

—

102

C₂×C₁₉

#3262

yes

—

103

C₂²×D₄

C₂³×C₁₉

yes

—

104

C₂×D₈

—

105

C₂²×C₈

C₂³×C₁₉

yes

characteristic

106

C₂²×C₈

C₂³×C₁₉

yes

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

C₂³×C₁₉

yes

—

109

C₂×C₂²⋊C₄

—

110

C₂×C₂²⋊C₄

—

111

C₂×C₄²

C₂³×C₁₉

yes

—

112

#107

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

#102

—

116

#95

—

117

#95

D₄×C₁₉

yes

characteristic

118

#95

D₄×C₁₉

yes

—

119

C₁₉

#32867

yes

characteristic, direct product factor, Sylow

120

C₂⁴

—

121

C₂×D₄

—

122

C₂×D₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂×D₄×C₁₉

yes

—

125

C₂²×C₄

C₂×D₄×C₁₉

yes

—

126

C₂²×C₄

C₂⁴×C₁₉

yes

characteristic

127

D₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₂²⋊C₄

—

135

C₂²⋊C₄

—

136

C₄²

—

137

C₄²

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

C₂²×D₄×C₁₉

yes

characteristic

142

D₄

—

143

D₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

C₁₉×H(5,𝔽₂)

yes

—

153

C₂×C₄

C₁₉×2₋¹⁺⁴

yes

—

154

C₈

—

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

C₁₉×#537

yes

—

160

C₂²

C₁₉×#576

yes

—

161

C₂²

C₁₉×#578

yes

characteristic

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

C₁₉×#560

yes

characteristic

166

C₄

C₁₉×#563

yes

—

167

C₂

—

168

C₂

C₁₉×#2823

yes

characteristic

169

C₂

C₁₉×#3259

yes

—

170

C₂

C₁₉×#3262

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₉

prime radical

C₂²×D₈×C₁₉

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

N	H ≅ G/N	type
1. C₁₉×#2644	C₂	semidirect
2. C₁₉×#2087	C₂	semidirect
3. C₁₉×#2067	C₂	semidirect
5. C₁₉×#1843	C₂	semidirect
52. #32867	C₁₉	direct (N × H)
71. #2644	C₂×C₁₉	semidirect
72. #2087	C₂×C₁₉	semidirect
73. #2067	C₂×C₁₉	semidirect
75. #1843	C₂×C₁₉	semidirect
119. C₁₉	#32867	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2644

C₂

semidirect

2. C₁₉×#2087

C₂

semidirect

3. C₁₉×#2067

C₂

semidirect

5. C₁₉×#1843

C₂

semidirect

52. #32867

C₁₉

direct (N × H)

71. #2644

C₂×C₁₉

semidirect

72. #2087

C₂×C₁₉

semidirect

73. #2067

C₂×C₁₉

semidirect

75. #1843

C₂×C₁₉

semidirect

119. C₁₉

#32867

direct (N × H)

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

subgroup	index
C₁₉×#2644	2
C₁₉×#2087	2
C₁₉×#2067	2
C₁₉×#2054	2
C₁₉×#1843	2
#32867	19

subgroup

index

C₁₉×#2644

C₁₉×#2087

C₁₉×#2067

C₁₉×#2054

C₁₉×#1843

#32867

Subgroups — C₁₉×#32867 #18038826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#32867 #18038826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32867 #18038826