Group #14565325 — subgroups

Subgroups — #14565325

Order 2432.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11927112	C₂	1	1	yes	maximal, characteristic
2	#11926527	C₂	1	2	yes	maximal, complemented
3	#11926341	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926340	C₂	1	2	yes	maximal, complemented
5	C₁₉×#355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64545	C₂²	1	1	yes	characteristic
7	C₂×D₄×D₁₉	C₄	1	1	yes	characteristic
8	C₁₉×#124	C₂²	1	1	yes	characteristic
9	#10597393	C₂²	1	1	yes	characteristic
10	#10597386	C₄	1	1	yes	characteristic
11	M₁₆×D₁₉	—	2	2	no	—
12	#10597330	—	2	2	no	—
13	#10597328	—	2	2	no	—
14	#10597320	C₄	1	1	yes	characteristic
15	#10597318	C₄	1	1	yes	characteristic
16	C₁₉×#101	C₂²	1	2	yes	complemented
17	#10597293	C₂²	1	2	yes	complemented
18	#10597280	—	2	2	no	—
19	C₂³×D₁₉	—	2	1	no	—
20	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₂²⋊D₁₉	—	2	2	no	—
23	C₂×C₂²⋊D₁₉	—	2	1	no	—
24	#64545	—	4	2	no	—
25	D₄×D₁₉	—	4	2	no	—
26	C₂×D₇₆	—	2	2	no	—
27	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
28	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
29	C₂×D₇₆	D₄	1	2	yes	—
30	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×D₁₉	D₄	1	2	yes	—
32	M₁₆×C₁₉	—	2	2	no	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	(C₂×D₁₉)⋊C₄	—	2	1	no	—
36	(C₂×D₁₉)⋊C₄	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	1	no	—
38	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
39	#64520	—	2	2	no	—
40	#64515	—	4	2	no	—
41	C₈×D₁₉	—	4	2	no	—
42	C₂³×C₁₉	—	2	1	no	—
43	C₂²×D₁₉	—	2	1	no	—
44	C₂²×D₁₉	—	4	2	no	—
45	C₂²×D₁₉	—	8	2	no	—
46	C₂²×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×D₁₉	C₂²⋊C₄	1	2	yes	—
48	Q₈×C₁₉	—	4	1	no	—
49	D₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂²⋊D₁₉	—	4	2	no	—
54	C₂²⋊D₁₉	—	8	2	no	—
55	C₂×Dic₁₉	—	2	1	no	—
56	C₂×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	D₇₆	—	4	1	no	—
58	D₇₆	—	4	2	no	—
59	D₇₆	—	4	1	no	—
60	D₇₆	—	8	2	no	—
61	C₄×D₁₉	—	2	2	no	—
62	C₄×D₁₉	—	2	2	no	—
63	C₄×D₁₉	—	2	2	no	—
64	C₈×C₁₉	—	4	2	no	—
65	C₁₉⋊C₈	—	4	2	no	—
66	#2134	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×D₁₉	—	2	1	no	—
71	C₂×D₁₉	—	2	2	no	—
72	C₂×D₁₉	—	4	2	no	—
73	C₂×D₁₉	—	4	1	no	—
74	C₂×D₁₉	—	4	2	no	—
75	C₂×D₁₉	—	4	1	no	—
76	C₂×D₁₉	—	8	4	no	—
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	4	1	no	—
80	Dic₁₉	—	4	1	no	—
81	Dic₁₉	#99	1	2	yes	—
82	#535	—	19	1	no	—
83	#413	—	19	2	no	—
84	#355	—	19	1	no	—
85	#355	—	19	2	no	—
86	#355	D₁₉	1	1	yes	characteristic, complemented
87	C₂×C₁₉	—	2	1	no	—
88	C₂×C₁₉	—	8	1	no	—
89	C₂×C₁₉	C₂×#99	1	1	yes	characteristic
90	D₁₉	—	4	2	no	—
91	D₁₉	—	4	1	no	—
92	D₁₉	—	8	1	no	—
93	C₂×#41	—	19	1	no	—
94	C₂²×D₄	—	19	1	no	—
95	C₂×M₁₆	—	38	2	no	—
96	#127	—	19	1	no	—
97	#127	—	19	1	no	—
98	#124	—	19	1	no	—
99	#124	C₂×D₁₉	1	1	yes	characteristic
100	#121	—	38	2	no	—
101	#120	—	38	2	no	—
102	#117	—	19	1	no	—
103	#101	—	19	2	no	—
104	#101	C₂×D₁₉	1	2	yes	complemented
105	#100	—	38	2	no	—
106	C₁₉	#2134	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	—	38	1	no	—
108	#41	—	76	2	no	—
109	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
110	C₂×D₄	—	19	1	no	—
111	C₂×D₄	—	19	1	no	—
112	C₂×D₄	—	19	2	no	—
113	C₂×D₄	—	38	2	no	—
114	C₂×D₄	—	38	1	no	—
115	C₂×D₄	—	38	2	no	—
116	C₂×D₄	—	76	2	no	—
117	C₂×D₄	C₄×D₁₉	1	1	yes	characteristic
118	C₂²×C₄	—	19	1	no	—
119	C₂²×C₄	—	19	2	no	—
120	M₁₆	—	2	2	no	—
121	M₁₆	—	38	2	no	—
122	M₁₆	—	76	2	no	—
123	C₂×C₈	—	76	2	no	—
124	C₄⋊C₄	—	38	1	no	—
125	C₂²⋊C₄	—	2	2	no	—
126	C₂²⋊C₄	—	38	1	no	—
127	C₂²⋊C₄	—	38	2	no	—
128	C₄²	—	19	1	no	—
129	C₄²	C₄×D₁₉	1	1	yes	characteristic
130	C₂³	—	2	1	no	—
131	C₂³	—	19	1	no	—
132	C₂³	—	19	2	no	—
133	C₂³	—	38	1	no	—
134	C₂³	—	76	2	no	—
135	C₂³	—	152	2	no	—
136	Q₈	—	4	1	no	—
137	D₄	—	4	1	no	—
138	D₄	—	76	2	no	—
139	D₄	—	76	1	no	—
140	D₄	—	76	1	no	—
141	D₄	—	76	2	no	—
142	D₄	—	152	2	no	—
143	D₄	—	152	2	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	19	1	no	—
146	C₂×C₄	—	38	2	no	—
147	C₂×C₄	—	38	2	no	—
148	C₂×C₄	—	38	2	no	—
149	C₂×C₄	—	38	1	no	—
150	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
151	C₂×C₄	D₄×D₁₉	1	2	yes	—
152	C₈	—	4	2	no	—
153	C₈	—	76	2	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	1	no	—
156	C₂²	—	38	1	no	—
157	C₂²	—	38	2	no	—
158	C₂²	—	76	2	no	—
159	C₂²	—	76	1	no	—
160	C₂²	—	76	2	no	—
161	C₂²	—	76	1	no	—
162	C₂²	—	152	4	no	—
163	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
164	C₄	—	2	2	no	—
165	C₄	—	2	1	no	—
166	C₄	—	4	1	no	—
167	C₄	—	19	2	no	—
168	C₄	—	76	1	no	—
169	C₂	—	2	1	no	—
170	C₂	—	8	1	no	—
171	C₂	—	76	1	no	—
172	C₂	—	76	2	no	—
173	C₂	—	152	1	no	—
174	C₂	#99×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927112

C₂

yes

maximal, characteristic

#11926527

C₂

yes

maximal, complemented

#11926341

C₂

yes

maximal, characteristic, complemented

#11926340

C₂

yes

maximal, complemented

C₁₉×#355

C₂

yes

maximal, characteristic, complemented

C₂×#64545

C₂²

yes

characteristic

C₂×D₄×D₁₉

C₄

yes

characteristic

C₁₉×#124

C₂²

yes

characteristic

#10597393

C₂²

yes

characteristic

#10597386

C₄

yes

characteristic

M₁₆×D₁₉

—

#10597330

—

#10597328

—

#10597320

C₄

yes

characteristic

#10597318

C₄

yes

characteristic

C₁₉×#101

C₂²

yes

complemented

#10597293

C₂²

yes

complemented

#10597280

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

#64545

—

D₄×D₁₉

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

characteristic

C₂×D₇₆

C₂×C₄

yes

characteristic

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

—

M₁₆×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

C₂×C₄

yes

characteristic

#64520

—

#64515

—

C₈×D₁₉

—

C₂³×C₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

C₂²⋊C₄

yes

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²⋊C₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2134

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

#99

yes

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#99

yes

characteristic

D₁₉

—

D₁₉

—

D₁₉

—

C₂×#41

—

C₂²×D₄

—

C₂×M₁₆

—

—

—

—

C₂×D₁₉

yes

characteristic

100

#121

—

101

#120

—

102

#117

—

103

#101

—

104

#101

C₂×D₁₉

yes

complemented

105

#100

—

106

C₁₉

#2134

yes

characteristic, complemented, Sylow

107

C₂⁴

—

108

#41

—

109

C₂×Q₈

C₂²×D₁₉

yes

characteristic

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

C₄×D₁₉

yes

characteristic

118

C₂²×C₄

—

119

C₂²×C₄

—

120

M₁₆

—

121

M₁₆

—

122

M₁₆

—

123

C₂×C₈

—

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

C₄×D₁₉

yes

characteristic

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

152

—

136

Q₈

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

D₄

—

142

D₄

—

152

—

143

D₄

—

152

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

151

C₂×C₄

D₄×D₁₉

yes

—

152

C₈

—

153

C₈

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

152

—

163

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

169

C₂

—

170

C₂

—

171

C₂

—

172

C₂

—

173

C₂

—

152

—

174

C₂

#99×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂	#99×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂×Q₈	C₂²×D₁₉
Fitting	C₁₉×#355	C₂
socle	C₂×C₁₉	C₂×#99
prime radical	#11927112	C₂
cosocle	C₂×Q₈×C₁₉	C₂³
hypercenter	#355	D₁₉
hypocenter	C₁₉	#2134
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #355

subgroup

G/H

center

C₂

#99×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂×Q₈

C₂²×D₁₉

Fitting

C₁₉×#355

C₂

socle

C₂×C₁₉

C₂×#99

prime radical

#11927112

C₂

cosocle

C₂×Q₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #355

N	H ≅ G/N	type
2. #11926527	C₂	semidirect
3. #11926341	C₂	semidirect
4. #11926340	C₂	semidirect
5. C₁₉×#355	C₂	semidirect
16. C₁₉×#101	C₂²	semidirect
17. #10597293	C₂²	semidirect
86. #355	D₁₉	semidirect
104. #101	C₂×D₁₉	semidirect
106. C₁₉	#2134	semidirect

H ≅ G/N

type

2. #11926527

C₂

semidirect

3. #11926341

C₂

semidirect

4. #11926340

C₂

semidirect

5. C₁₉×#355

C₂

semidirect

16. C₁₉×#101

C₂²

semidirect

17. #10597293

C₂²

semidirect

86. #355

D₁₉

semidirect

104. #101

C₂×D₁₉

semidirect

106. C₁₉

#2134

semidirect

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

subgroup	index
#11927112	2
#11926527	2
#11926341	2
#11926340	2
C₁₉×#355	2
#2134	19

subgroup

index

C₁₉×#355

Subgroups — #14565325

Conjugacy classes of subgroups

Complements

Maximal subgroups