Group #14560068 — subgroups

Subgroups — C₁₉×#2211 #14560068

Order 2432.

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

normal subgroups only

This group has 158 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×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#495	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₁₆×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
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×SD₁₆×C₁₉	—	2	1	no	—
11	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#124	—	2	1	no	—
13	C₄×Q₈×C₁₉	—	2	1	no	—
14	C₁₉×Q₃₂	—	2	2	no	—
15	C₁₉×SD₃₂	—	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×#103	—	2	1	no	—
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	Q₁₆×C₁₉	—	2	1	no	—
25	Q₁₆×C₁₉	—	2	1	no	—
26	Q₁₆×C₁₉	—	2	1	no	—
27	Q₁₆×C₁₉	D₄	1	2	yes	—
28	SD₁₆×C₁₉	—	4	2	no	—
29	D₈×C₁₉	—	2	1	no	—
30	D₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₂²⋊C₄×C₁₉	—	4	1	no	—
36	C₂²⋊C₄×C₁₉	—	4	1	no	—
37	C₄²×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	Q₈×C₁₉	—	2	2	no	—
43	Q₈×C₁₉	—	4	1	no	—
44	Q₈×C₁₉	—	4	1	no	—
45	Q₈×C₁₉	—	4	1	no	—
46	D₄×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
52	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₈×C₁₉	—	2	1	no	—
55	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₁₉	#41	1	1	yes	characteristic
57	#2211	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₁₉	—	8	1	no	—
59	C₂²×C₁₉	—	8	1	no	—
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	—	8	1	no	—
66	C₄×C₁₉	—	8	1	no	—
67	C₄×C₁₉	#121	1	1	yes	characteristic
68	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	C₂×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
70	C₂×SD₃₂	C₂×C₁₉	1	1	yes	characteristic
71	#495	C₂×C₁₉	1	1	yes	characteristic
72	C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
73	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
74	#358	C₂×C₁₉	1	1	yes	characteristic, complemented
75	#357	C₂×C₁₉	1	1	yes	characteristic
76	C₂×C₁₉	—	16	1	no	—
77	C₂×C₁₉	#459	1	1	yes	characteristic
78	C₂×C₁₉	#508	1	1	yes	characteristic
79	C₂×C₁₉	#510	1	1	yes	characteristic
80	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
81	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
82	C₂×SD₁₆	—	2	1	no	—
83	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
84	#124	—	2	1	no	—
85	C₄×Q₈	—	2	1	no	—
86	Q₃₂	—	2	2	no	—
87	SD₃₂	—	2	2	no	—
88	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
89	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
90	#107	C₂²×C₁₉	1	1	yes	characteristic
91	#103	—	2	1	no	—
92	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
93	C₁₉	#2211	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×D₄	—	2	1	no	—
97	Q₁₆	—	2	1	no	—
98	Q₁₆	—	2	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	D₄×C₁₉	1	2	yes	—
101	SD₁₆	—	4	2	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
105	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	4	1	no	—
108	C₂²⋊C₄	—	4	1	no	—
109	C₂²⋊C₄	—	4	1	no	—
110	C₄²	—	4	1	no	—
111	C₄²	D₄×C₁₉	1	1	yes	characteristic
112	C₁₆	—	2	1	no	—
113	C₁₆	—	2	1	no	—
114	C₂³	—	4	1	no	—
115	Q₈	—	2	2	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	4	1	no	—
119	D₄	—	4	1	no	—
120	D₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
125	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
126	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
127	C₈	—	2	1	no	—
128	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
129	C₈	#41×C₁₉	1	1	yes	characteristic
130	C₂²	—	8	1	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	4	2	no	—
137	C₄	—	8	1	no	—
138	C₄	—	8	1	no	—
139	C₄	C₁₉×#121	1	1	yes	characteristic
140	C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂	—	16	1	no	—
142	C₂	C₁₉×#459	1	1	yes	characteristic
143	C₂	C₁₉×#508	1	1	yes	characteristic
144	C₂	C₁₉×#510	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×SD₃₂

C₂

yes

maximal, characteristic

C₁₉×#495

C₂

yes

maximal, characteristic

C₄×Q₁₆×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

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×SD₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

D₄

yes

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂×SD₃₂

C₂×C₁₉

yes

characteristic

#495

C₂×C₁₉

yes

characteristic

C₄×Q₁₆

C₂×C₁₉

yes

characteristic, complemented

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

#358

C₂×C₁₉

yes

characteristic, complemented

#357

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂²×C₁₉

yes

characteristic

#124

—

C₄×Q₈

—

Q₃₂

—

SD₃₂

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

characteristic

#103

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2211

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

100

Q₁₆

D₄×C₁₉

yes

—

101

SD₁₆

—

102

D₈

—

103

D₈

—

104

C₂×C₈

D₄×C₁₉

yes

characteristic

105

C₂×C₈

C₂³×C₁₉

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

D₄×C₁₉

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₂³

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

D₈×C₁₉

yes

characteristic

125

C₂×C₄

D₈×C₁₉

yes

characteristic

126

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

127

C₈

—

128

C₈

C₂×D₄×C₁₉

yes

characteristic

129

C₈

#41×C₁₉

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₂×D₈×C₁₉

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

C₁₉×#121

yes

characteristic

140

C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

141

C₂

—

142

C₂

C₁₉×#459

yes

characteristic

143

C₂

C₁₉×#508

yes

characteristic

144

C₂

C₁₉×#510

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×D₈×C₁₉	C₂²
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×D₈×C₁₉

C₂²

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×Q₃₂	C₂	semidirect
4. C₄×Q₁₆×C₁₉	C₂	semidirect
5. C₁₉×C₄⋊C₁₆	C₂	semidirect
6. C₁₉×#358	C₂	semidirect
57. #2211	C₁₉	direct (N × H)
69. C₂×Q₃₂	C₂×C₁₉	semidirect
72. C₄×Q₁₆	C₂×C₁₉	semidirect
73. C₄⋊C₁₆	C₂×C₁₉	semidirect
74. #358	C₂×C₁₉	semidirect
93. C₁₉	#2211	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×Q₃₂

C₂

semidirect

4. C₄×Q₁₆×C₁₉

C₂

semidirect

5. C₁₉×C₄⋊C₁₆

C₂

semidirect

6. C₁₉×#358

C₂

semidirect

57. #2211

C₁₉

direct (N × H)

69. C₂×Q₃₂

C₂×C₁₉

semidirect

72. C₄×Q₁₆

C₂×C₁₉

semidirect

73. C₄⋊C₁₆

C₂×C₁₉

semidirect

74. #358

C₂×C₁₉

semidirect

93. C₁₉

#2211

direct (N × H)

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

subgroup	index
C₂×C₁₉×Q₃₂	2
C₂×C₁₉×SD₃₂	2
C₁₉×#495	2
C₄×Q₁₆×C₁₉	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#358	2
C₁₉×#357	2
#2211	19

subgroup

index

C₂×C₁₉×Q₃₂

C₂×C₁₉×SD₃₂

C₁₉×#495

C₄×Q₁₆×C₁₉

C₁₉×C₄⋊C₁₆

C₁₉×#358

C₁₉×#357

#2211

Subgroups — C₁₉×#2211 #14560068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2211 #14560068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2211 #14560068