Group #14565304 — subgroups

Subgroups — #14565304

Order 2432.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10597291	C₂	1	2	yes	maximal, complemented
2	#11926339	C₂	1	2	yes	maximal, complemented
3	#11926337	C₂	1	2	yes	maximal, complemented
4	C₁₉×#535	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₉	C₄	1	1	yes	characteristic, complemented
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#127	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₁₉×#124	C₄	1	1	yes	characteristic, complemented
10	C₁₉×#124	C₂²	1	1	yes	characteristic
11	C₁₉×#121	—	2	2	no	—
12	C₁₉×#120	—	2	2	no	—
13	C₁₉×#117	C₄	1	1	yes	characteristic, complemented
14	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
15	#10597291	—	2	2	no	—
16	#10597291	C₂²	1	4	yes	—
17	C₂⁴×C₁₉	D₄	1	2	yes	—
18	#41×C₁₉	—	4	2	no	—
19	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
20	C₂×D₄×C₁₉	—	2	1	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	2	2	no	—
23	C₂×D₄×C₁₉	—	4	2	no	—
24	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
26	C₂×D₄×C₁₉	D₄	1	2	yes	—
27	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	4	2	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂²⋊C₄×C₁₉	—	2	1	no	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
36	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
37	C₂²⋊Dic₁₉	—	2	4	no	—
38	C₂²⋊Dic₁₉	—	4	2	no	—
39	C₂³×C₁₉	—	2	2	no	—
40	C₂³×C₁₉	—	2	2	no	—
41	C₂³×C₁₉	—	2	1	no	—
42	C₂³×C₁₉	—	8	2	no	—
43	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
44	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂³×C₁₉	C₂×D₄	1	2	yes	—
46	Q₈×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	1	no	—
48	D₄×C₁₉	—	4	2	no	—
49	D₄×C₁₉	—	4	1	no	—
50	D₄×C₁₉	—	4	1	no	—
51	D₄×C₁₉	—	4	2	no	—
52	D₄×C₁₉	—	8	2	no	—
53	D₄×C₁₉	—	8	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×Dic₁₉	—	4	4	no	—
62	C₂×Dic₁₉	—	8	4	no	—
63	#2127	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	2	no	—
65	C₂²×C₁₉	—	2	2	no	—
66	C₂²×C₁₉	—	4	1	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	—	4	4	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	—	4	1	no	—
72	C₂²×C₁₉	—	8	2	no	—
73	C₂²×C₁₉	#99	1	2	yes	—
74	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	4	1	no	—
78	C₄×C₁₉	—	4	1	no	—
79	C₄×C₁₉	—	4	1	no	—
80	Dic₁₉	—	8	4	no	—
81	#535	D₁₉	1	1	yes	characteristic
82	C₂×#99	—	19	2	no	—
83	#354	—	19	2	no	—
84	#353	—	19	2	no	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	—	2	2	no	—
87	C₂×C₁₉	—	4	2	no	—
88	C₂×C₁₉	—	4	2	no	—
89	C₂×C₁₉	—	8	1	no	—
90	C₂×C₁₉	C₂×#99	1	1	yes	characteristic
91	C₂×#41	Dic₁₉	1	1	yes	characteristic, complemented
92	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
93	#127	Dic₁₉	1	1	yes	characteristic, complemented
94	#127	C₂×D₁₉	1	1	yes	characteristic
95	#124	Dic₁₉	1	1	yes	characteristic, complemented
96	#124	C₂×D₁₉	1	1	yes	characteristic
97	#121	—	2	2	no	—
98	#120	—	2	2	no	—
99	#117	Dic₁₉	1	1	yes	characteristic, complemented
100	C₂×C₂²⋊C₄	—	38	2	no	—
101	#99	—	19	4	no	—
102	#99	—	38	2	no	—
103	C₁₉	#2127	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	C₂²⋊D₁₉	1	2	yes	—
105	#41	—	4	2	no	—
106	C₂×Q₈	C₂×Dic₁₉	1	1	yes	characteristic, complemented
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	—	2	2	no	—
109	C₂×D₄	—	2	2	no	—
110	C₂×D₄	—	4	2	no	—
111	C₂×D₄	C₂×Dic₁₉	1	1	yes	characteristic
112	C₂×D₄	C₂×Dic₁₉	1	1	yes	characteristic, complemented
113	C₂×D₄	C₂²⋊D₁₉	1	2	yes	—
114	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
115	C₂²×C₄	—	2	1	no	—
116	C₂²×C₄	—	76	2	no	—
117	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
118	C₄⋊C₄	—	2	1	no	—
119	C₂²⋊C₄	—	2	2	no	—
120	C₂²⋊C₄	—	2	1	no	—
121	C₂²⋊C₄	—	2	2	no	—
122	C₂²⋊C₄	—	38	4	no	—
123	C₂²⋊C₄	—	76	2	no	—
124	C₄²	C₂×Dic₁₉	1	1	yes	characteristic, complemented
125	C₄²	C₂×Dic₁₉	1	1	yes	characteristic, complemented
126	C₂³	—	2	2	no	—
127	C₂³	—	2	2	no	—
128	C₂³	—	2	1	no	—
129	C₂³	—	8	2	no	—
130	C₂³	C₂²⋊Dic₁₉	1	2	yes	—
131	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
132	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
133	Q₈	—	4	1	no	—
134	D₄	—	4	1	no	—
135	D₄	—	4	2	no	—
136	D₄	—	4	1	no	—
137	D₄	—	4	1	no	—
138	D₄	—	4	2	no	—
139	D₄	—	8	2	no	—
140	D₄	—	8	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	—	76	4	no	—
147	C₂×C₄	—	152	4	no	—
148	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
149	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
150	C₂²	—	2	2	no	—
151	C₂²	—	2	2	no	—
152	C₂²	—	4	1	no	—
153	C₂²	—	4	2	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	4	no	—
156	C₂²	—	4	2	no	—
157	C₂²	—	4	1	no	—
158	C₂²	—	8	2	no	—
159	C₂²	#10597291	1	2	yes	—
160	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
161	C₄	—	2	1	no	—
162	C₄	—	2	1	no	—
163	C₄	—	4	1	no	—
164	C₄	—	4	1	no	—
165	C₄	—	4	1	no	—
166	C₄	—	152	4	no	—
167	C₂	—	2	1	no	—
168	C₂	—	2	2	no	—
169	C₂	—	4	2	no	—
170	C₂	—	4	2	no	—
171	C₂	—	8	1	no	—
172	C₂	C₂×#10597291	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597291

C₂

yes

maximal, complemented

#11926339

C₂

yes

maximal, complemented

#11926337

C₂

yes

maximal, complemented

C₁₉×#535

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₄

yes

characteristic, complemented

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#127

C₄

yes

characteristic, complemented

C₁₉×#127

C₂²

yes

characteristic

C₁₉×#124

C₄

yes

characteristic, complemented

C₁₉×#124

C₂²

yes

characteristic

C₁₉×#121

—

C₁₉×#120

—

C₁₉×#117

C₄

yes

characteristic, complemented

C₂×C₂²⋊Dic₁₉

—

#10597291

—

#10597291

C₂²

yes

—

C₂⁴×C₁₉

D₄

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic, complemented

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic, complemented

C₂×D₄×C₁₉

D₄

yes

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic, complemented

C₄²×C₁₉

C₂×C₄

yes

characteristic, complemented

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

Q₈×C₁₉

—

D₄×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

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2127

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#99

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#535

D₁₉

yes

characteristic

C₂×#99

—

#354

—

#353

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#99

yes

characteristic

C₂×#41

Dic₁₉

yes

characteristic, complemented

C₂²×D₄

C₂×D₁₉

yes

characteristic

#127

Dic₁₉

yes

characteristic, complemented

#127

C₂×D₁₉

yes

characteristic

#124

Dic₁₉

yes

characteristic, complemented

#124

C₂×D₁₉

yes

—

—

Dic₁₉

yes

characteristic, complemented

100

C₂×C₂²⋊C₄

—

101

#99

—

102

#99

—

103

C₁₉

#2127

yes

characteristic, complemented, Sylow

104

C₂⁴

C₂²⋊D₁₉

yes

—

105

#41

—

106

C₂×Q₈

C₂×Dic₁₉

yes

characteristic, complemented

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

C₂×Dic₁₉

yes

characteristic

112

C₂×D₄

C₂×Dic₁₉

yes

characteristic, complemented

113

C₂×D₄

C₂²⋊D₁₉

yes

—

114

C₂×D₄

C₂²×D₁₉

yes

characteristic

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

C₂×Dic₁₉

yes

characteristic, complemented

125

C₄²

C₂×Dic₁₉

yes

characteristic, complemented

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

C₂²⋊Dic₁₉

yes

—

131

C₂³

C₂²⋊Dic₁₉

yes

characteristic

132

C₂³

C₂×C₂²⋊D₁₉

yes

—

133

Q₈

—

134

D₄

—

135

D₄

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

152

—

148

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

149

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

#10597291

yes

—

160

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

152

—

167

C₂

—

168

C₂

—

169

C₂

—

170

C₂

—

171

C₂

—

172

C₂

C₂×#10597291

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#10597291
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂×D₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#535	C₂
socle	C₂×C₁₉	C₂×#99
cosocle	C₂×D₄×C₁₉	C₂³
hypercenter	#535	D₁₉
hypocenter	C₁₉	#2127
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×D₄ ◁ #535

subgroup

G/H

center

C₂

C₂×#10597291

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂×D₄

C₂²×D₁₉

Fitting, prime radical

C₁₉×#535

C₂

socle

C₂×C₁₉

C₂×#99

cosocle

C₂×D₄×C₁₉

C₂³

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×D₄ ◁ #535

N	H ≅ G/N	type
1. C₂×#10597291	C₂	semidirect
2. #11926339	C₂	semidirect
3. #11926337	C₂	semidirect
5. C₂×#41×C₁₉	C₄	semidirect
7. C₁₉×#127	C₄	semidirect
9. C₁₉×#124	C₄	semidirect
13. C₁₉×#117	C₄	semidirect
19. C₂×Q₈×C₁₉	C₂×C₄	semidirect
25. C₂×D₄×C₁₉	C₂×C₄	semidirect
35. C₄²×C₁₉	C₂×C₄	semidirect
36. C₄²×C₁₉	C₂×C₄	semidirect
91. C₂×#41	Dic₁₉	semidirect
93. #127	Dic₁₉	semidirect
95. #124	Dic₁₉	semidirect
99. #117	Dic₁₉	semidirect
103. C₁₉	#2127	semidirect
106. C₂×Q₈	C₂×Dic₁₉	semidirect
112. C₂×D₄	C₂×Dic₁₉	semidirect
124. C₄²	C₂×Dic₁₉	semidirect
125. C₄²	C₂×Dic₁₉	semidirect

H ≅ G/N

type

1. C₂×#10597291

C₂

semidirect

2. #11926339

C₂

semidirect

3. #11926337

C₂

semidirect

5. C₂×#41×C₁₉

C₄

semidirect

7. C₁₉×#127

C₄

semidirect

9. C₁₉×#124

C₄

semidirect

13. C₁₉×#117

C₄

semidirect

19. C₂×Q₈×C₁₉

C₂×C₄

semidirect

25. C₂×D₄×C₁₉

C₂×C₄

semidirect

35. C₄²×C₁₉

C₂×C₄

semidirect

36. C₄²×C₁₉

C₂×C₄

semidirect

91. C₂×#41

Dic₁₉

semidirect

93. #127

Dic₁₉

semidirect

95. #124

Dic₁₉

semidirect

99. #117

Dic₁₉

semidirect

103. C₁₉

#2127

semidirect

106. C₂×Q₈

C₂×Dic₁₉

semidirect

112. C₂×D₄

C₂×Dic₁₉

semidirect

124. C₄²

C₂×Dic₁₉

semidirect

125. C₄²

C₂×Dic₁₉

semidirect

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

subgroup	index
C₂×#10597291	2
#11926339	2
#11926337	2
C₁₉×#535	2
#2127	19

subgroup

index

C₁₉×#535

Subgroups — #14565304

Conjugacy classes of subgroups

Complements

Maximal subgroups