Group #14565059 — subgroups

Subgroups — #14565059

Order 2432.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#11926401	C₂	1	2	yes	maximal
3	#11926307	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926306	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₁₉×#107	—	2	2	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	(C₂×D₁₉)⋊C₈	—	2	2	no	—
15	C₂³×D₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	—	2	2	no	—
19	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄×D₁₉	—	2	1	no	—
21	C₂×C₄×D₁₉	—	2	2	no	—
22	C₂×C₄×D₁₉	—	2	1	no	—
23	C₂×C₄×D₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	D₄	1	2	yes	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	(C₂×D₁₉)⋊C₄	—	4	4	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	1	no	—
32	C₂×C₁₉⋊C₈	—	2	2	no	—
33	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×D₁₉	—	2	1	no	—
35	C₂²×D₁₉	—	2	2	no	—
36	C₂²×D₁₉	—	2	1	no	—
37	C₂²×D₁₉	—	2	2	no	—
38	C₂²×D₁₉	D₈	1	2	yes	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	2	yes	—
46	C₂×Dic₁₉	—	2	1	no	—
47	C₂×Dic₁₉	—	2	2	no	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₄×D₁₉	—	4	1	no	—
52	C₄×D₁₉	—	4	1	no	—
53	C₄×D₁₉	—	4	2	no	—
54	C₈×C₁₉	—	2	2	no	—
55	C₁₉⋊C₈	—	4	1	no	—
56	#2075	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	#121	1	1	yes	characteristic
58	C₂²×C₁₉	#123	1	2	yes	—
59	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
60	C₂²×C₁₉	#135	1	1	yes	characteristic
61	C₂²×C₁₉	#137	1	2	yes	—
62	C₂×D₁₉	—	2	2	no	—
63	C₂×D₁₉	—	2	4	no	—
64	C₂×D₁₉	—	4	1	no	—
65	C₂×D₁₉	—	4	1	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₄×C₁₉	—	8	2	no	—
68	C₄×C₁₉	#123	1	1	yes	characteristic
69	C₄×C₁₉	#124	1	1	yes	characteristic
70	C₄×C₁₉	#126	1	2	yes	—
71	Dic₁₉	—	4	1	no	—
72	Dic₁₉	—	8	2	no	—
73	C₂×#107	D₁₉	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₈	—	19	1	no	—
75	#380	—	19	2	no	—
76	#340	—	19	1	no	—
77	#340	—	19	2	no	—
78	C₂×C₁₉	#397	1	1	yes	characteristic
79	C₂×C₁₉	#466	1	1	yes	characteristic
80	C₂×C₁₉	#470	1	1	yes	characteristic
81	C₂×C₁₉	#480	1	2	yes	—
82	C₂×C₁₉	#485	1	2	yes	—
83	D₁₉	—	4	2	no	—
84	C₂³×C₄	—	19	1	no	—
85	C₂²×C₈	—	19	1	no	—
86	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
89	C₂×C₂²⋊C₄	—	38	2	no	—
90	#107	—	2	2	no	—
91	C₂²⋊C₈	—	38	2	no	—
92	#95	—	38	2	no	—
93	C₁₉	#2075	1	1	yes	characteristic, complemented, Sylow
94	C₂⁴	—	19	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	19	1	no	—
97	C₂²×C₄	—	38	2	no	—
98	C₂²×C₄	—	38	1	no	—
99	C₂²×C₄	—	38	2	no	—
100	C₂²×C₄	—	38	1	no	—
101	C₂²×C₄	—	38	2	no	—
102	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	38	2	no	—
105	C₂×C₈	—	38	1	no	—
106	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	38	2	no	—
110	C₄⋊C₄	—	38	2	no	—
111	C₂²⋊C₄	—	76	4	no	—
112	C₂³	—	19	2	no	—
113	C₂³	—	38	1	no	—
114	C₂³	—	38	2	no	—
115	C₂³	—	38	1	no	—
116	C₂³	—	38	2	no	—
117	C₂³	D₄×D₁₉	1	1	yes	characteristic
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	38	1	no	—
122	C₂×C₄	—	38	2	no	—
123	C₂×C₄	—	76	1	no	—
124	C₂×C₄	—	76	2	no	—
125	C₂×C₄	—	76	1	no	—
126	C₂×C₄	—	76	2	no	—
127	C₂×C₄	—	76	2	no	—
128	C₂×C₄	—	76	2	no	—
129	C₂×C₄	#64541	1	2	yes	—
130	C₂×C₄	#64543	1	1	yes	characteristic
131	C₂×C₄	#64545	1	2	yes	—
132	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	76	1	no	—
135	C₂²	—	38	4	no	—
136	C₂²	—	38	2	no	—
137	C₂²	—	76	1	no	—
138	C₂²	—	76	2	no	—
139	C₂²	—	76	1	no	—
140	C₂²	#10597340	1	2	yes	—
141	C₂²	D₈×D₁₉	1	1	yes	characteristic
142	C₂²	#10597358	1	1	yes	characteristic
143	C₂²	#10597364	1	2	yes	—
144	C₂²	#10597384	1	1	yes	characteristic
145	C₄	—	8	2	no	—
146	C₄	—	76	1	no	—
147	C₄	—	152	2	no	—
148	C₄	#10597344	1	2	yes	—
149	C₄	#10597375	1	1	yes	characteristic
150	C₄	#10597393	1	1	yes	characteristic
151	C₂	—	76	2	no	—
152	C₂	#11926470	1	1	yes	characteristic
153	C₂	#11926777	1	1	yes	characteristic
154	C₂	#11926799	1	1	yes	characteristic
155	C₂	#11926859	1	2	yes	—
156	C₂	#11926887	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal, characteristic

#11926401

C₂

yes

maximal

#11926307

C₂

yes

maximal, characteristic, complemented

#11926306

C₂

yes

maximal, complemented

C₂×C₁₉×#107

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉⋊#95

—

(C₂×D₁₉)⋊C₈

—

C₂³×D₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

D₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×D₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#107

D₁₉

yes

characteristic, complemented

C₂×C₂²⋊C₈

—

#380

—

#340

—

#340

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#485

yes

—

D₁₉

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

#107

—

C₂²⋊C₈

—

#95

—

C₁₉

#2075

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₁₉

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂²⋊D₁₉

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

D₄×D₁₉

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#64541

yes

—

130

C₂×C₄

#64543

yes

characteristic

131

C₂×C₄

#64545

yes

—

132

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

133

C₈

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

#10597340

yes

—

141

C₂²

D₈×D₁₉

yes

characteristic

142

C₂²

#10597358

yes

characteristic

143

C₂²

#10597364

yes

—

144

C₂²

#10597384

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

152

—

148

C₄

#10597344

yes

—

149

C₄

#10597375

yes

characteristic

150

C₄

#10597393

yes

characteristic

151

C₂

—

152

C₂

#11926470

yes

characteristic

153

C₂

#11926777

yes

characteristic

154

C₂

#11926799

yes

characteristic

155

C₂

#11926859

yes

—

156

C₂

#11926887

yes

—

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#107	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂³×D₁₉	D₄
hypercenter	C₂×#107	D₁₉
hypocenter	C₁₉	#2075
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#107

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂³×D₁₉

D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
3. #11926307	C₂	semidirect
4. #11926306	C₂	semidirect
5. C₂×C₁₉×#107	C₂	semidirect
73. C₂×#107	D₁₉	semidirect
93. C₁₉	#2075	semidirect

H ≅ G/N

type

3. #11926307

C₂

semidirect

4. #11926306

C₂

semidirect

5. C₂×C₁₉×#107

C₂

semidirect

73. C₂×#107

D₁₉

semidirect

93. C₁₉

#2075

semidirect

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

subgroup	index
C₂×(C₂×D₁₉)⋊C₈	2
#11926401	2
#11926307	2
#11926306	2
C₂×C₁₉×#107	2
#2075	19

subgroup

index

C₂×(C₂×D₁₉)⋊C₈

C₂×C₁₉×#107

Subgroups — #14565059

Conjugacy classes of subgroups

Complements

Maximal subgroups