Group #14564180 — subgroups

Subgroups — #14564180

Order 2432.

340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 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	#11927311	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927108	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597280	C₂	1	2	yes	maximal, complemented
4	#11926315	C₂	1	2	yes	maximal, complemented
5	C₁₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₇₆	C₂²	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
9	#10597394	—	2	4	no	—
10	#10597393	—	2	1	no	—
11	#10597386	—	2	1	no	—
12	#10597383	C₄	1	4	yes	—
13	#10597376	—	2	2	no	—
14	#10597372	C₂²	1	1	yes	characteristic
15	C₂×#64520	—	2	2	no	—
16	C₂×#64520	C₂²	1	2	yes	—
17	C₁₉×#101	—	2	1	no	—
18	C₁₉×#100	—	2	1	no	—
19	#10597280	—	2	4	no	—
20	C₂³×D₁₉	C₂×C₄	1	2	yes	—
21	#41×C₁₉	—	2	2	no	—
22	#41×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	D₄	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₂²⋊D₁₉	—	2	4	no	—
29	C₂×D₇₆	—	2	1	no	—
30	C₂×D₇₆	—	2	1	no	—
31	C₂×D₇₆	—	2	2	no	—
32	C₂×D₇₆	—	2	2	no	—
33	M₁₆×C₁₉	—	2	2	no	—
34	M₁₆×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	(C₂×D₁₉)⋊C₄	—	2	4	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄×Dic₁₉	—	2	1	no	—
40	#64520	—	2	4	no	—
41	#64520	—	2	2	no	—
42	#64520	D₄	1	4	yes	complemented
43	C₂×C₁₉⋊C₈	—	2	4	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×D₁₉	—	2	2	no	—
48	C₂²×D₁₉	—	2	4	no	—
49	C₂²×D₁₉	—	8	2	no	—
50	Q₈×C₁₉	—	2	2	no	—
51	D₄×C₁₉	—	2	4	no	—
52	D₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	2	yes	—
60	C₂²⋊D₁₉	—	8	4	no	—
61	C₂×Dic₁₉	—	2	2	no	—
62	D₇₆	—	4	1	no	—
63	D₇₆	—	4	2	no	—
64	D₇₆	—	4	1	no	—
65	C₈×C₁₉	—	4	2	no	—
66	C₁₉⋊C₈	—	2	4	no	—
67	#1914	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	—	4	1	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₁₉	C₄×D₄	1	2	yes	—
73	C₂×D₁₉	—	4	4	no	—
74	C₂×D₁₉	—	4	2	no	—
75	C₂×D₁₉	—	8	4	no	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	#120	1	1	yes	characteristic
78	C₄×C₁₉	#121	1	2	yes	—
79	C₄×C₁₉	#123	1	1	yes	characteristic
80	Dic₁₉	—	4	2	no	—
81	#568	—	19	1	no	—
82	#535	—	19	1	no	—
83	#413	D₁₉	1	1	yes	characteristic, complemented
84	C₂×#100	—	19	2	no	—
85	#344	—	19	2	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	2	2	no	—
88	C₂×C₁₉	—	4	2	no	—
89	C₂×C₁₉	#386	1	1	yes	characteristic
90	D₁₉	—	8	2	no	—
91	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
92	C₂²×D₄	—	19	1	no	—
93	#131	—	38	4	no	—
94	C₂×M₁₆	—	19	2	no	—
95	C₂×M₁₆	—	38	2	no	—
96	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
97	#127	—	38	1	no	—
98	#124	—	38	1	no	—
99	#121	—	38	2	no	—
100	#120	—	19	4	no	—
101	#117	—	19	1	no	—
102	#101	—	2	1	no	—
103	#100	—	2	1	no	—
104	#100	—	38	4	no	—
105	C₁₉	#1914	1	1	yes	characteristic, complemented, Sylow
106	C₂⁴	—	19	2	no	—
107	#41	—	2	2	no	—
108	#41	—	2	2	no	—
109	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×D₄	—	38	4	no	—
111	C₂×D₄	—	38	1	no	—
112	C₂×D₄	—	38	2	no	—
113	C₂×D₄	—	38	2	no	—
114	C₂×D₄	—	38	1	no	—
115	C₂×D₄	C₄×D₁₉	1	2	yes	—
116	C₂×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
117	C₂²×C₄	D₇₆	1	2	yes	—
118	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
119	M₁₆	—	2	2	no	—
120	M₁₆	—	2	2	no	—
121	M₁₆	—	19	4	no	—
122	M₁₆	—	38	4	no	—
123	M₁₆	—	38	2	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	38	4	no	—
126	C₂×C₈	—	38	2	no	—
127	C₄⋊C₄	—	38	1	no	—
128	C₂²⋊C₄	—	19	2	no	—
129	C₂²⋊C₄	—	38	4	no	—
130	C₄²	—	38	1	no	—
131	C₂³	—	38	2	no	—
132	C₂³	—	38	4	no	—
133	C₂³	—	152	2	no	—
134	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
135	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
136	Q₈	—	2	2	no	—
137	D₄	—	2	4	no	—
138	D₄	—	2	2	no	—
139	D₄	—	76	2	no	—
140	D₄	—	76	1	no	—
141	D₄	—	76	1	no	—
142	D₄	—	152	4	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	38	2	no	—
146	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
147	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
148	C₂×C₄	D₄×D₁₉	1	2	yes	—
149	C₂×C₄	#64543	1	2	yes	—
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	C₈	—	4	2	no	—
152	C₈	—	38	4	no	—
153	C₂²	—	2	2	no	—
154	C₂²	—	4	1	no	—
155	C₂²	—	4	2	no	—
156	C₂²	—	76	4	no	—
157	C₂²	—	76	2	no	—
158	C₂²	—	152	4	no	—
159	C₂²	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
160	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
161	C₄	—	2	2	no	—
162	C₄	—	76	2	no	—
163	C₄	#10597328	1	1	yes	characteristic
164	C₄	#10597332	1	1	yes	characteristic
165	C₄	#10597385	1	2	yes	—
166	C₂	—	2	1	no	—
167	C₂	—	2	2	no	—
168	C₂	—	4	2	no	—
169	C₂	—	152	2	no	—
170	C₂	#11926421	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927311

C₂

yes

maximal, characteristic, complemented

#11927108

C₂

yes

maximal, characteristic

C₂×#10597280

C₂

yes

maximal, complemented

#11926315

C₂

yes

maximal, complemented

C₁₉×#413

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

—

—

—

C₄

yes

—

#10597376

—

#10597372

C₂²

yes

characteristic

C₂×#64520

—

C₂×#64520

C₂²

yes

—

C₁₉×#101

—

C₁₉×#100

—

#10597280

—

C₂³×D₁₉

C₂×C₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

C₂×C₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

#64520

D₄

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1914

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#123

yes

characteristic

Dic₁₉

—

#568

—

#535

—

#413

D₁₉

yes

characteristic, complemented

C₂×#100

—

#344

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#386

yes

characteristic

D₁₉

—

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

#127

—

#124

—

#121

—

100

#120

—

101

#117

—

102

#101

—

103

#100

—

104

#100

—

105

C₁₉

#1914

yes

characteristic, complemented, Sylow

106

C₂⁴

—

107

#41

—

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

C₄×D₁₉

yes

—

116

C₂×D₄

C₂²⋊D₁₉

yes

characteristic

117

C₂²×C₄

D₇₆

yes

—

118

C₂²×C₄

C₂²×D₁₉

yes

characteristic

119

M₁₆

—

120

M₁₆

—

121

M₁₆

—

122

M₁₆

—

123

M₁₆

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₄⋊C₄

—

128

C₂²⋊C₄

—

129

C₂²⋊C₄

—

130

C₄²

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

152

—

134

C₂³

(C₂×D₁₉)⋊C₄

yes

—

135

C₂³

C₂×C₄×D₁₉

yes

characteristic

136

Q₈

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

D₄

—

142

D₄

—

152

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

147

C₂×C₄

C₂×D₇₆

yes

characteristic

148

C₂×C₄

D₄×D₁₉

yes

—

149

C₂×C₄

#64543

yes

—

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

151

C₈

—

152

C₈

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

152

—

159

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

—

160

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

#10597328

yes

characteristic

164

C₄

#10597332

yes

characteristic

165

C₄

#10597385

yes

—

166

C₂

—

167

C₂

—

168

C₂

—

169

C₂

—

152

—

170

C₂

#11926421

yes

characteristic

	subgroup	G/H
center	C₂	#11926421
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#413	C₂
socle	C₂×C₁₉	#386
prime radical	#11927108	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#413	D₁₉
hypocenter	C₁₉	#1914
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #413

subgroup

G/H

center

C₂

#11926421

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#413

C₂

C₂×C₁₉

C₂

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #413

N	H ≅ G/N	type
1. #11927311	C₂	semidirect
3. C₂×#10597280	C₂	semidirect
4. #11926315	C₂	semidirect
5. C₁₉×#413	C₂	semidirect
42. #64520	D₄	semidirect
83. #413	D₁₉	semidirect
105. C₁₉	#1914	semidirect

H ≅ G/N

type

1. #11927311

C₂

semidirect

3. C₂×#10597280

C₂

semidirect

4. #11926315

C₂

semidirect

5. C₁₉×#413

C₂

semidirect

42. #64520

D₄

semidirect

83. #413

D₁₉

semidirect

105. C₁₉

#1914

semidirect

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

subgroup	index
#11927311	2
#11927108	2
C₂×#10597280	2
#11926315	2
C₁₉×#413	2
#1914	19

subgroup

index

C₁₉×#413

Subgroups — #14564180

Conjugacy classes of subgroups

Complements

Maximal subgroups