Group #14569588 — subgroups

Subgroups — #14569588

Order 2432.

462 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₁₉⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926485	C₂	1	3	yes	maximal, complemented
3	#11926473	C₂	1	3	yes	maximal, complemented
4	#11926468	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926423	C₂	1	3	yes	maximal
6	#11926417	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
11	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
12	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
15	C₁₉×#95	C₂²	1	1	yes	characteristic
16	C₁₉×#95	C₂²	1	3	yes	—
17	C₁₉⋊#95	C₂²	1	3	yes	—
18	C₁₉⋊#95	C₂²	1	3	yes	—
19	C₁₉⋊#95	C₂²	1	3	yes	—
20	C₁₉⋊#95	C₂²	1	3	yes	—
21	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×D₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	—	2	6	no	—
24	C₂²×C₄×C₁₉	—	4	3	no	—
25	C₂²×C₄×C₁₉	—	4	3	no	—
26	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
28	C₂×C₂²⋊D₁₉	—	2	6	no	—
29	C₂²×Dic₁₉	C₂³	1	3	yes	—
30	C₂²×Dic₁₉	C₂³	1	3	yes	—
31	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
32	C₂²⋊Dic₁₉	—	2	6	no	—
33	(C₂×D₁₉)⋊C₄	—	4	3	no	—
34	(C₂×D₁₉)⋊C₄	—	4	3	no	—
35	Dic₁₉⋊C₄	—	4	3	no	—
36	Dic₁₉⋊C₄	—	4	3	no	—
37	C₂³×C₁₉	—	2	3	no	—
38	C₂³×C₁₉	—	2	1	no	—
39	C₂³×C₁₉	#41	1	6	yes	—
40	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
41	C₂²×D₁₉	—	2	3	no	—
42	C₂²×D₁₉	—	2	3	no	—
43	C₂²×D₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	3	no	—
45	C₂×C₄×C₁₉	—	2	3	no	—
46	C₂×C₄×C₁₉	—	2	3	no	—
47	C₂×C₄×C₁₉	—	2	3	no	—
48	C₂×C₄×C₁₉	—	2	3	no	—
49	C₂×C₄×C₁₉	—	2	3	no	—
50	C₂×C₄×C₁₉	—	4	12	no	—
51	C₂²⋊D₁₉	—	4	4	no	—
52	C₂×Dic₁₉	—	2	3	no	—
53	C₂×Dic₁₉	—	2	3	no	—
54	C₂×Dic₁₉	—	2	3	no	—
55	C₂×Dic₁₉	—	2	3	no	—
56	C₂×Dic₁₉	—	2	3	no	—
57	C₂×Dic₁₉	—	2	3	no	—
58	C₂×Dic₁₉	—	2	3	no	—
59	#2643	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	2	6	no	—
61	C₂²×C₁₉	—	2	6	no	—
62	C₂²×C₁₉	#126	1	4	yes	—
63	C₂²×C₁₉	C₂×#41	1	3	yes	—
64	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
65	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
66	C₂×D₁₉	—	4	1	no	—
67	C₂×D₁₉	—	4	3	no	—
68	C₂×D₁₉	—	4	3	no	—
69	C₄×C₁₉	—	4	3	no	—
70	C₄×C₁₉	—	4	3	no	—
71	Dic₁₉	—	4	1	no	—
72	Dic₁₉	—	4	3	no	—
73	Dic₁₉	—	4	3	no	—
74	#401	—	19	1	no	—
75	#400	—	19	3	no	—
76	#397	—	19	3	no	—
77	#396	—	19	1	no	—
78	#386	—	19	3	no	—
79	#385	—	19	3	no	—
80	C₂×#95	D₁₉	1	1	yes	characteristic, complemented
81	C₂×C₁₉	—	2	4	no	—
82	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
83	C₂×C₁₉	#538	1	3	yes	—
84	C₂×C₁₉	#539	1	3	yes	—
85	D₁₉	—	8	1	no	—
86	C₂²×D₄	—	19	1	no	—
87	C₂³×C₄	C₂×D₁₉	1	3	yes	—
88	C₂×C₄⋊C₄	—	19	3	no	—
89	C₂×C₄⋊C₄	—	19	3	no	—
90	C₂×C₂²⋊C₄	—	19	3	no	—
91	C₂×C₂²⋊C₄	—	19	3	no	—
92	C₂×C₂²⋊C₄	—	19	3	no	—
93	#95	—	19	3	no	—
94	#95	—	19	3	no	—
95	#95	—	19	3	no	—
96	#95	—	19	3	no	—
97	#95	C₂×D₁₉	1	1	yes	characteristic
98	#95	C₂×D₁₉	1	3	yes	—
99	C₁₉	#2643	1	1	yes	characteristic, complemented, Sylow
100	C₂⁴	—	19	1	no	—
101	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
102	C₂×D₄	—	38	6	no	—
103	C₂²×C₄	—	2	6	no	—
104	C₂²×C₄	—	4	3	no	—
105	C₂²×C₄	—	4	3	no	—
106	C₂²×C₄	—	19	1	no	—
107	C₂²×C₄	—	19	3	no	—
108	C₂²×C₄	—	19	3	no	—
109	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
110	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
111	C₄⋊C₄	—	76	3	no	—
112	C₄⋊C₄	—	76	3	no	—
113	C₂²⋊C₄	—	38	6	no	—
114	C₂²⋊C₄	—	76	3	no	—
115	C₂²⋊C₄	—	76	3	no	—
116	C₂³	—	2	3	no	—
117	C₂³	—	2	1	no	—
118	C₂³	—	38	3	no	—
119	C₂³	—	38	3	no	—
120	C₂³	—	38	1	no	—
121	C₂³	#64541	1	6	yes	—
122	C₂³	C₂³×D₁₉	1	1	yes	characteristic
123	D₄	—	76	4	no	—
124	C₂×C₄	—	2	3	no	—
125	C₂×C₄	—	2	3	no	—
126	C₂×C₄	—	2	3	no	—
127	C₂×C₄	—	2	3	no	—
128	C₂×C₄	—	2	3	no	—
129	C₂×C₄	—	2	3	no	—
130	C₂×C₄	—	4	12	no	—
131	C₂×C₄	—	38	3	no	—
132	C₂×C₄	—	38	3	no	—
133	C₂×C₄	—	38	3	no	—
134	C₂×C₄	—	38	3	no	—
135	C₂×C₄	—	38	3	no	—
136	C₂×C₄	—	38	3	no	—
137	C₂×C₄	—	38	3	no	—
138	C₂²	—	2	6	no	—
139	C₂²	—	2	6	no	—
140	C₂²	—	76	1	no	—
141	C₂²	—	76	3	no	—
142	C₂²	—	76	3	no	—
143	C₂²	#10597322	1	4	yes	—
144	C₂²	C₂×#64541	1	3	yes	—
145	C₂²	#10597430	1	3	yes	—
146	C₂²	#10597433	1	1	yes	characteristic
147	C₄	—	4	3	no	—
148	C₄	—	4	3	no	—
149	C₄	—	76	1	no	—
150	C₄	—	76	3	no	—
151	C₄	—	76	3	no	—
152	C₂	—	2	4	no	—
153	C₂	—	152	1	no	—
154	C₂	C₂×#10597322	1	1	yes	characteristic
155	C₂	#11927132	1	3	yes	—
156	C₂	#11927141	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉⋊#401

C₂

yes

maximal, characteristic, complemented

#11926485

C₂

yes

maximal, complemented

#11926473

C₂

yes

maximal, complemented

#11926468

C₂

yes

maximal, characteristic, complemented

#11926423

C₂

yes

maximal

#11926417

C₂

yes

maximal, complemented

C₂×C₁₉×#95

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊D₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2643

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#126

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

C₂×#95

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₂×#126

yes

characteristic

C₂×C₁₉

#538

yes

—

C₂×C₁₉

#539

yes

—

D₁₉

—

C₂²×D₄

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

—

C₂×D₁₉

yes

characteristic

#95

C₂×D₁₉

yes

—

C₁₉

#2643

yes

characteristic, complemented, Sylow

100

C₂⁴

—

101

C₂⁴

C₂²×D₁₉

yes

characteristic

102

C₂×D₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂²×D₁₉

yes

—

110

C₂²×C₄

C₂²×D₁₉

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

#64541

yes

—

122

C₂³

C₂³×D₁₉

yes

characteristic

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#10597322

yes

—

144

C₂²

C₂×#64541

yes

—

145

C₂²

#10597430

yes

—

146

C₂²

#10597433

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₂

—

153

C₂

—

152

—

154

C₂

C₂×#10597322

yes

characteristic

155

C₂

#11927132

yes

—

156

C₂

#11927141

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#95	C₂
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	C₂×#95	D₁₉
hypocenter	C₁₉	#2643
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#95

C₂

prime radical

C₂²×C₂²⋊D₁₉

C₂²

hypercenter

C₂×#95

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
1. C₁₉⋊#401	C₂	semidirect
2. #11926485	C₂	semidirect
3. #11926473	C₂	semidirect
4. #11926468	C₂	semidirect
6. #11926417	C₂	semidirect
7. C₂×C₁₉×#95	C₂	semidirect
80. C₂×#95	D₁₉	semidirect
99. C₁₉	#2643	semidirect

H ≅ G/N

type

1. C₁₉⋊#401

C₂

semidirect

2. #11926485

C₂

semidirect

3. #11926473

C₂

semidirect

4. #11926468

C₂

semidirect

6. #11926417

C₂

semidirect

7. C₂×C₁₉×#95

C₂

semidirect

80. C₂×#95

D₁₉

semidirect

99. C₁₉

#2643

semidirect

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

subgroup	index
C₁₉⋊#401	2
#11926485	2
#11926473	2
#11926468	2
#11926423	2
#11926417	2
C₂×C₁₉×#95	2
#2643	19

subgroup

index

C₁₉⋊#401

C₂×C₁₉×#95

Subgroups — #14569588

Conjugacy classes of subgroups

Complements

Maximal subgroups