Group #14560067 — subgroups

Subgroups — C₁₉×#2210 #14560067

Order 2432.

170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×SD₁₆×C₁₉	—	2	1	no	—
10	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#124	—	2	1	no	—
13	C₄×D₄×C₁₉	—	2	1	no	—
14	C₁₉×SD₃₂	—	2	2	no	—
15	C₁₉×D₁₆	—	2	2	no	—
16	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₁₉×#102	—	2	1	no	—
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	—	4	1	no	—
25	Q₁₆×C₁₉	—	2	1	no	—
26	Q₁₆×C₁₉	—	2	1	no	—
27	SD₁₆×C₁₉	—	4	2	no	—
28	D₈×C₁₉	—	2	1	no	—
29	D₈×C₁₉	—	2	1	no	—
30	D₈×C₁₉	—	2	1	no	—
31	D₈×C₁₉	D₄	1	2	yes	—
32	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂²⋊C₄×C₁₉	—	4	1	no	—
36	C₂²⋊C₄×C₁₉	—	4	1	no	—
37	C₂²⋊C₄×C₁₉	—	4	1	no	—
38	C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₁₆×C₁₉	—	2	1	no	—
40	C₁₆×C₁₉	—	2	1	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	Q₈×C₁₉	—	4	1	no	—
44	Q₈×C₁₉	—	4	1	no	—
45	D₄×C₁₉	—	2	2	no	—
46	D₄×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	1	no	—
48	D₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	8	2	no	—
52	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₁₉	—	2	1	no	—
56	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₈×C₁₉	#41	1	1	yes	characteristic
58	#2210	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂²×C₁₉	—	4	2	no	—
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	—	8	1	no	—
62	C₂²×C₁₉	—	8	1	no	—
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	—	8	1	no	—
65	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	8	1	no	—
69	C₄×C₁₉	—	8	1	no	—
70	C₄×C₁₉	#121	1	1	yes	characteristic
71	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
72	C₂×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
73	C₂×D₁₆	C₂×C₁₉	1	1	yes	characteristic
74	#495	C₂×C₁₉	1	1	yes	characteristic, complemented
75	C₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
76	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
77	#358	C₂×C₁₉	1	1	yes	characteristic, complemented
78	#357	C₂×C₁₉	1	1	yes	characteristic, complemented
79	C₂×C₁₉	—	8	2	no	—
80	C₂×C₁₉	—	16	1	no	—
81	C₂×C₁₉	#459	1	1	yes	characteristic
82	C₂×C₁₉	#508	1	1	yes	characteristic
83	C₂×C₁₉	#509	1	1	yes	characteristic
84	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
85	C₂×SD₁₆	—	2	1	no	—
86	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
87	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
88	#124	—	2	1	no	—
89	C₄×D₄	—	2	1	no	—
90	SD₃₂	—	2	2	no	—
91	D₁₆	—	2	2	no	—
92	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
93	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
94	#107	C₂²×C₁₉	1	1	yes	characteristic
95	#102	—	2	1	no	—
96	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
97	C₁₉	#2210	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×Q₈	—	2	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂²×C₄	—	4	1	no	—
102	Q₁₆	—	2	1	no	—
103	Q₁₆	—	2	1	no	—
104	SD₁₆	—	4	2	no	—
105	D₈	—	2	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	D₄×C₁₉	1	2	yes	—
109	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
110	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
111	C₄⋊C₄	—	2	1	no	—
112	C₂²⋊C₄	—	4	1	no	—
113	C₂²⋊C₄	—	4	1	no	—
114	C₂²⋊C₄	—	4	1	no	—
115	C₄²	D₄×C₁₉	1	1	yes	characteristic
116	C₁₆	—	2	1	no	—
117	C₁₆	—	2	1	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	4	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	4	1	no	—
122	D₄	—	2	2	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	8	2	no	—
129	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
130	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
131	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
134	C₈	#41×C₁₉	1	1	yes	characteristic
135	C₂²	—	4	2	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	—	8	1	no	—
141	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	8	1	no	—
145	C₄	—	8	1	no	—
146	C₄	C₁₉×#121	1	1	yes	characteristic
147	C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂	—	8	2	no	—
149	C₂	—	16	1	no	—
150	C₂	C₁₉×#459	1	1	yes	characteristic
151	C₂	C₁₉×#508	1	1	yes	characteristic
152	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×SD₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₂

yes

maximal, characteristic

C₁₉×#495

C₂

yes

maximal, characteristic, complemented

C₄×D₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#358

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

C₄×D₄×C₁₉

—

C₁₉×SD₃₂

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×SD₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂×D₁₆

C₂×C₁₉

yes

characteristic

#495

C₂×C₁₉

yes

characteristic, complemented

C₄×D₈

C₂×C₁₉

yes

characteristic, complemented

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

#358

C₂×C₁₉

yes

characteristic, complemented

#357

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂²×C₁₉

yes

characteristic

C₂×D₈

C₂²×C₁₉

yes

characteristic

#124

—

C₄×D₄

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

characteristic

#102

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2210

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂²×C₄

—

102

Q₁₆

—

103

Q₁₆

—

104

SD₁₆

—

105

D₈

—

106

D₈

—

107

D₈

—

108

D₈

D₄×C₁₉

yes

—

109

C₂×C₈

D₄×C₁₉

yes

characteristic

110

C₂×C₈

C₂³×C₁₉

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

D₄×C₁₉

yes

characteristic

116

C₁₆

—

117

C₁₆

—

118

C₂³

—

119

C₂³

—

120

Q₈

—

121

Q₈

—

122

D₄

—

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

D₈×C₁₉

yes

characteristic

130

C₂×C₄

D₈×C₁₉

yes

characteristic

131

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

132

C₈

—

133

C₈

C₂×D₄×C₁₉

yes

characteristic

134

C₈

#41×C₁₉

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂×D₈×C₁₉

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

C₁₉×#121

yes

characteristic

147

C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

148

C₂

—

149

C₂

—

150

C₂

C₁₉×#459

yes

characteristic

151

C₂

C₁₉×#508

yes

characteristic

152

C₂

C₁₉×#509

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₂×C₁₉×D₁₆

C₂

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×SD₃₂	C₂	semidirect
3. C₁₉×#495	C₂	semidirect
4. C₄×D₈×C₁₉	C₂	semidirect
5. C₁₉×C₄⋊C₁₆	C₂	semidirect
6. C₁₉×#358	C₂	semidirect
7. C₁₉×#357	C₂	semidirect
58. #2210	C₁₉	direct (N × H)
72. C₂×SD₃₂	C₂×C₁₉	semidirect
74. #495	C₂×C₁₉	semidirect
75. C₄×D₈	C₂×C₁₉	semidirect
76. C₄⋊C₁₆	C₂×C₁₉	semidirect
77. #358	C₂×C₁₉	semidirect
78. #357	C₂×C₁₉	semidirect
97. C₁₉	#2210	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×SD₃₂

C₂

semidirect

3. C₁₉×#495

C₂

semidirect

4. C₄×D₈×C₁₉

C₂

semidirect

5. C₁₉×C₄⋊C₁₆

C₂

semidirect

6. C₁₉×#358

C₂

semidirect

7. C₁₉×#357

C₂

semidirect

58. #2210

C₁₉

direct (N × H)

72. C₂×SD₃₂

C₂×C₁₉

semidirect

74. #495

C₂×C₁₉

semidirect

75. C₄×D₈

C₂×C₁₉

semidirect

76. C₄⋊C₁₆

C₂×C₁₉

semidirect

77. #358

C₂×C₁₉

semidirect

78. #357

C₂×C₁₉

semidirect

97. C₁₉

#2210

direct (N × H)

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

subgroup	index
C₂×C₁₉×SD₃₂	2
C₂×C₁₉×D₁₆	2
C₁₉×#495	2
C₄×D₈×C₁₉	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#358	2
C₁₉×#357	2
#2210	19

subgroup

index

C₂×C₁₉×SD₃₂

C₂×C₁₉×D₁₆

C₁₉×#495

C₄×D₈×C₁₉

C₁₉×C₄⋊C₁₆

C₁₉×#358

C₁₉×#357

#2210

Subgroups — C₁₉×#2210 #14560067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2210 #14560067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2210 #14560067