Group #14563409 — subgroups

Subgroups — #14563409

Order 2432.

384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₉	C₂	1	2	yes	maximal, complemented
3	C₄×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926298	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₂²⋊Dic₁₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	—	2	4	no	—
11	C₂²×C₁₉⋊C₈	C₄	1	4	yes	complemented
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₁₉×C₂²⋊C₈	C₄	1	4	yes	complemented
15	C₁₉⋊#95	C₄	1	2	yes	—
16	C₈×Dic₁₉	—	2	4	no	—
17	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²⋊Dic₁₉	C₈	1	8	yes	complemented
29	C₄×Dic₁₉	—	2	2	no	—
30	C₄×Dic₁₉	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂×C₁₉⋊C₈	—	2	8	no	—
33	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
34	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
35	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
36	C₂³×C₁₉	—	2	2	no	—
37	C₂³×C₁₉	—	2	2	no	—
38	C₂³×C₁₉	C₄²	1	2	yes	—
39	C₂³×C₁₉	C₂×C₈	1	4	yes	—
40	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	C₄²	1	2	yes	—
46	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	#41	1	2	yes	—
50	C₂×Dic₁₉	—	2	4	no	—
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	C₂×C₈	1	8	yes	complemented
53	C₈×C₁₉	—	2	4	no	—
54	C₁₉⋊C₈	—	2	2	no	—
55	C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	complemented
56	C₈×C₂²⋊C₄	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	2	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	—	2	8	no	—
60	C₂²×C₁₉	C₄×C₈	1	4	yes	complemented
61	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
62	C₂²×C₁₉	C₄×D₄	1	2	yes	—
63	C₂²×C₁₉	C₂²×C₈	1	2	yes	—
64	C₂²×C₁₉	#131	1	2	yes	—
65	C₄×C₁₉	—	2	2	no	—
66	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₄×C₁₉	#117	1	1	yes	characteristic
68	C₄×C₁₉	C₄×D₄	1	2	yes	—
69	Dic₁₉	—	2	8	no	—
70	C₂³×C₈	—	19	1	no	—
71	C₂×C₂²⋊C₈	D₁₉	1	1	yes	characteristic
72	C₂×C₄×C₈	—	19	2	no	—
73	C₄×C₂²⋊C₄	—	19	1	no	—
74	#336	—	19	2	no	—
75	C₂×C₁₉	—	2	4	no	—
76	C₂×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
78	C₂×C₁₉	#405	1	1	yes	characteristic
79	C₂×C₁₉	C₈×D₄	1	4	yes	—
80	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
81	C₂²×C₈	—	19	1	no	—
82	C₂²×C₈	—	19	4	no	—
83	C₂²×C₈	—	19	1	no	—
84	C₂²×C₈	—	38	4	no	—
85	C₂²×C₈	C₂×D₁₉	1	2	yes	—
86	C₂×C₂²⋊C₄	—	19	2	no	—
87	C₂×C₄²	—	19	2	no	—
88	C₂²⋊C₈	Dic₁₉	1	4	yes	complemented
89	C₄×C₈	—	38	4	no	—
90	#95	—	19	2	no	—
91	C₁₉	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	C₄×D₁₉	1	1	yes	characteristic
93	C₂²×C₄	—	2	2	no	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	—	19	4	no	—
96	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
97	C₂²×C₄	C₄×D₁₉	1	2	yes	—
98	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
99	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	—	19	2	no	—
103	C₂×C₈	—	19	4	no	—
104	C₂×C₈	—	19	2	no	—
105	C₂×C₈	—	38	8	no	—
106	C₂×C₈	—	38	2	no	—
107	C₂×C₈	C₂×Dic₁₉	1	4	yes	—
108	C₂²⋊C₄	—	19	8	no	—
109	C₄²	—	38	2	no	—
110	C₄²	—	38	2	no	—
111	C₂³	—	2	2	no	—
112	C₂³	—	2	2	no	—
113	C₂³	C₈×D₁₉	1	4	yes	—
114	C₂³	C₄×Dic₁₉	1	2	yes	—
115	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	19	8	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	38	4	no	—
123	C₂×C₄	C₄×Dic₁₉	1	2	yes	—
124	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
125	C₂×C₄	D₄×D₁₉	1	2	yes	—
126	C₂×C₄	#64543	1	2	yes	—
127	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
128	C₈	—	2	4	no	—
129	C₈	—	19	4	no	—
130	C₈	—	38	2	no	—
131	C₂²	—	2	8	no	—
132	C₂²	—	2	2	no	—
133	C₂²	—	2	2	no	—
134	C₂²	C₈×Dic₁₉	1	4	yes	complemented
135	C₂²	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
136	C₂²	C₂×C₈×D₁₉	1	2	yes	—
137	C₂²	#10597353	1	2	yes	—
138	C₂²	C₂×C₄×Dic₁₉	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	38	8	no	—
141	C₄	#10597323	1	1	yes	characteristic
142	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
143	C₄	D₄×Dic₁₉	1	2	yes	—
144	C₂	—	2	4	no	—
145	C₂	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
146	C₂	C₂×C₈×Dic₁₉	1	1	yes	characteristic
147	C₂	#11926502	1	1	yes	characteristic
148	C₂	(C₂²⋊D₁₉)⋊C₈	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×C₈×Dic₁₉

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₁₉

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, complemented

C₂×C₁₉×C₂²⋊C₈

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₄

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₄

yes

complemented

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₈

C₄

yes

complemented

C₁₉⋊#95

C₄

yes

—

C₈×Dic₁₉

—

C₂⁴×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

C₈

yes

complemented

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄²

yes

—

C₂³×C₁₉

C₂×C₈

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×C₈

yes

complemented

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

complemented

C₈×C₂²⋊C₄

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₈

yes

complemented

C₂²×C₁₉

C₂×C₄²

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

C₂²×C₈

yes

—

C₂²×C₁₉

#131

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

—

Dic₁₉

—

C₂³×C₈

—

C₂×C₂²⋊C₈

D₁₉

yes

characteristic

C₂×C₄×C₈

—

C₄×C₂²⋊C₄

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

C₂×C₁₉

C₂×C₄×C₈

yes

characteristic

C₂×C₁₉

#405

yes

characteristic

C₂×C₁₉

C₈×D₄

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

Dic₁₉

yes

complemented

C₄×C₈

—

#95

—

C₁₉

C₈×C₂²⋊C₄

yes

characteristic, complemented, Sylow

C₂⁴

C₄×D₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂×Dic₁₉

yes

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₂³

—

112

C₂³

—

113

C₂³

C₈×D₁₉

yes

—

114

C₂³

C₄×Dic₁₉

yes

—

115

C₂³

C₂×C₄×D₁₉

yes

characteristic

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₄×Dic₁₉

yes

—

124

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

125

C₂×C₄

D₄×D₁₉

yes

—

126

C₂×C₄

#64543

yes

—

127

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₈×Dic₁₉

yes

complemented

135

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

—

136

C₂²

C₂×C₈×D₁₉

yes

—

137

C₂²

#10597353

yes

—

138

C₂²

C₂×C₄×Dic₁₉

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

#10597323

yes

characteristic

142

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

143

C₄

D₄×Dic₁₉

yes

—

144

C₂

—

145

C₂

C₂²⋊C₄×Dic₁₉

yes

characteristic

146

C₂

C₂×C₈×Dic₁₉

yes

characteristic

147

C₂

#11926502

yes

characteristic

148

C₂

(C₂²⋊D₁₉)⋊C₈

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator	C₂×C₁₉	C₂×C₄×C₈
Fitting	C₂×C₁₉×C₂²⋊C₈	C₂
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₂²⋊C₈	D₁₉
hypocenter	C₁₉	C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator

C₂×C₁₉

C₂×C₄×C₈

Fitting

C₂×C₁₉×C₂²⋊C₈

C₂

socle

C₂³×C₁₉

C₂²×C₄

prime radical

C₂⁴×C₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₂²⋊C₈

D₁₉

hypocenter

C₁₉

C₈×C₂²⋊C₄

LCS

G ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
2. C₂×C₈×Dic₁₉	C₂	semidirect
4. #11926298	C₂	semidirect
11. C₂²×C₁₉⋊C₈	C₄	semidirect
14. C₁₉×C₂²⋊C₈	C₄	semidirect
28. C₂²⋊Dic₁₉	C₈	semidirect
52. C₂×Dic₁₉	C₂×C₈	semidirect
55. C₁₉⋊C₈	C₂²⋊C₄	semidirect
60. C₂²×C₁₉	C₄×C₈	semidirect
88. C₂²⋊C₈	Dic₁₉	semidirect
91. C₁₉	C₈×C₂²⋊C₄	semidirect
134. C₂²	C₈×Dic₁₉	semidirect

H ≅ G/N

type

2. C₂×C₈×Dic₁₉

C₂

semidirect

4. #11926298

C₂

semidirect

11. C₂²×C₁₉⋊C₈

C₄

semidirect

14. C₁₉×C₂²⋊C₈

C₄

semidirect

28. C₂²⋊Dic₁₉

C₈

semidirect

52. C₂×Dic₁₉

C₂×C₈

semidirect

55. C₁₉⋊C₈

C₂²⋊C₄

semidirect

60. C₂²×C₁₉

C₄×C₈

semidirect

88. C₂²⋊C₈

Dic₁₉

semidirect

91. C₁₉

C₈×C₂²⋊C₄

semidirect

134. C₂²

C₈×Dic₁₉

semidirect

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

subgroup	index
C₂³×C₁₉⋊C₈	2
C₂×C₈×Dic₁₉	2
C₄×C₂²⋊Dic₁₉	2
#11926298	2
C₂×C₁₉×C₂²⋊C₈	2
C₈×C₂²⋊C₄	19

subgroup

index

C₂³×C₁₉⋊C₈

C₂×C₈×Dic₁₉

C₄×C₂²⋊Dic₁₉

#11926298

C₂×C₁₉×C₂²⋊C₈

C₈×C₂²⋊C₄

Subgroups — #14563409

Conjugacy classes of subgroups

Complements

Maximal subgroups