Group #18019647 — subgroups

Subgroups — C₁₉×#13688 #18019647

Order 4864.

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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×Q₆₄	C₂	1	2	yes	maximal
2	C₁₉×#2247	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
4	C₁₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1416	C₂	1	2	yes	maximal
6	C₂×C₁₉×Q₃₂	—	2	1	no	—
7	C₂×C₁₉×Q₃₂	C₂²	1	2	yes	—
8	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
9	C₁₉×#494	—	2	1	no	—
10	C₄×Q₁₆×C₁₉	—	2	1	no	—
11	C₁₉×Q₆₄	—	2	4	no	—
12	C₂×C₁₉×C₃₂	C₂²	1	2	yes	—
13	C₁₉×#366	C₂²	1	1	yes	characteristic
14	C₁₉×#358	—	2	1	no	—
15	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₁₉	—	2	1	no	—
17	C₂×Q₁₆×C₁₉	—	2	2	no	—
18	C₂×Q₁₆×C₁₉	—	4	1	no	—
19	C₁₉×C₄⋊Q₈	—	4	1	no	—
20	C₄×Q₈×C₁₉	—	4	1	no	—
21	C₁₉×Q₃₂	—	2	2	no	—
22	C₁₉×Q₃₂	—	2	1	no	—
23	C₁₉×Q₃₂	—	2	2	no	—
24	C₁₉×Q₃₂	—	4	2	no	—
25	C₁₉×Q₃₂	D₄	1	2	yes	—
26	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
28	C₁₉×#107	—	2	1	no	—
29	C₁₉×#103	—	4	1	no	—
30	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₁₉×C₃₂	—	2	2	no	—
32	C₂×Q₈×C₁₉	—	4	1	no	—
33	C₂×Q₈×C₁₉	—	4	2	no	—
34	Q₁₆×C₁₉	—	2	2	no	—
35	Q₁₆×C₁₉	—	4	2	no	—
36	Q₁₆×C₁₉	—	4	1	no	—
37	Q₁₆×C₁₉	—	4	2	no	—
38	Q₁₆×C₁₉	—	8	2	no	—
39	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₄⋊C₄×C₁₉	—	4	1	no	—
42	C₄⋊C₄×C₁₉	—	8	1	no	—
43	C₄⋊C₄×C₁₉	—	8	1	no	—
44	C₄⋊C₄×C₁₉	—	8	1	no	—
45	C₄²×C₁₉	—	8	1	no	—
46	C₄²×C₁₉	D₈	1	1	yes	characteristic
47	C₁₆×C₁₉	—	2	1	no	—
48	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₁₆×C₁₉	#41	1	1	yes	characteristic
50	#13688	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	Q₈×C₁₉	—	4	2	no	—
52	Q₈×C₁₉	—	8	1	no	—
53	Q₈×C₁₉	—	8	2	no	—
54	Q₈×C₁₉	—	8	2	no	—
55	C₂×C₄×C₁₉	—	8	1	no	—
56	C₂×C₄×C₁₉	—	8	1	no	—
57	C₂×C₄×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	#121	1	1	yes	characteristic
63	C₈×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
64	C₂×Q₆₄	C₂×C₁₉	1	2	yes	—
65	#2247	C₂×C₁₉	1	1	yes	characteristic
66	C₄×Q₃₂	C₂×C₁₉	1	1	yes	characteristic
67	C₄⋊C₃₂	C₂×C₁₉	1	1	yes	characteristic
68	#1416	C₂×C₁₉	1	2	yes	—
69	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	8	2	no	—
72	C₄×C₁₉	—	16	2	no	—
73	C₄×C₁₉	—	16	1	no	—
74	C₄×C₁₉	Q₆₄	1	2	yes	complemented
75	C₄×C₁₉	#459	1	1	yes	characteristic
76	C₄×C₁₉	#509	1	1	yes	characteristic
77	C₂×Q₃₂	—	2	1	no	—
78	C₂×Q₃₂	C₂²×C₁₉	1	2	yes	—
79	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
80	#494	—	2	1	no	—
81	C₄×Q₁₆	—	2	1	no	—
82	Q₆₄	—	2	4	no	—
83	C₂×C₃₂	C₂²×C₁₉	1	2	yes	—
84	#366	C₂²×C₁₉	1	1	yes	characteristic
85	#358	—	2	1	no	—
86	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
87	C₂×C₁₉	#2206	1	1	yes	characteristic
88	C₂×C₁₉	C₂×Q₆₄	1	1	yes	characteristic
89	C₂×C₁₉	#2264	1	1	yes	characteristic
90	C₂×Q₁₆	—	2	1	no	—
91	C₂×Q₁₆	—	2	2	no	—
92	C₂×Q₁₆	—	4	1	no	—
93	C₄⋊Q₈	—	4	1	no	—
94	C₄×Q₈	—	4	1	no	—
95	Q₃₂	—	2	2	no	—
96	Q₃₂	—	2	1	no	—
97	Q₃₂	—	2	2	no	—
98	Q₃₂	—	4	2	no	—
99	Q₃₂	D₄×C₁₉	1	2	yes	—
100	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
101	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
102	#107	—	2	1	no	—
103	#103	—	4	1	no	—
104	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
105	C₃₂	—	2	2	no	—
106	C₁₉	#13688	1	1	yes	characteristic, direct product factor, Sylow
107	C₂×Q₈	—	4	1	no	—
108	C₂×Q₈	—	4	2	no	—
109	Q₁₆	—	2	2	no	—
110	Q₁₆	—	4	2	no	—
111	Q₁₆	—	4	1	no	—
112	Q₁₆	—	4	2	no	—
113	Q₁₆	—	8	2	no	—
114	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
115	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
116	C₄⋊C₄	—	4	1	no	—
117	C₄⋊C₄	—	8	1	no	—
118	C₄⋊C₄	—	8	1	no	—
119	C₄⋊C₄	—	8	1	no	—
120	C₄²	—	8	1	no	—
121	C₄²	D₈×C₁₉	1	1	yes	characteristic
122	C₁₆	—	2	1	no	—
123	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
124	C₁₆	#41×C₁₉	1	1	yes	characteristic
125	Q₈	—	4	2	no	—
126	Q₈	—	8	1	no	—
127	Q₈	—	8	2	no	—
128	Q₈	—	8	2	no	—
129	C₂×C₄	—	8	1	no	—
130	C₂×C₄	—	8	1	no	—
131	C₂×C₄	—	8	2	no	—
132	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
133	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
134	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
135	C₈	—	2	1	no	—
136	C₈	C₁₉×#121	1	1	yes	characteristic
137	C₈	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	8	2	no	—
141	C₄	—	16	2	no	—
142	C₄	—	16	1	no	—
143	C₄	C₁₉×Q₆₄	1	2	yes	complemented
144	C₄	C₁₉×#459	1	1	yes	characteristic
145	C₄	C₁₉×#509	1	1	yes	characteristic
146	C₂	C₁₉×#2206	1	1	yes	characteristic
147	C₂	C₂×C₁₉×Q₆₄	1	1	yes	characteristic
148	C₂	C₁₉×#2264	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×Q₆₄

C₂

yes

maximal

C₁₉×#2247

C₂

yes

maximal, characteristic

C₄×C₁₉×Q₃₂

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic

C₁₉×#1416

C₂

yes

maximal

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

C₂²

yes

—

C₂×C₁₉×Q₃₂

C₂²

yes

characteristic

C₁₉×#494

—

C₄×Q₁₆×C₁₉

—

C₁₉×Q₆₄

—

C₂×C₁₉×C₃₂

C₂²

yes

—

C₁₉×#366

C₂²

yes

characteristic

C₁₉×#358

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

D₄

yes

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×D₄

yes

C₁₆×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×Q₆₄

C₂×C₁₉

yes

—

#2247

C₂×C₁₉

yes

characteristic

C₄×Q₃₂

C₂×C₁₉

yes

characteristic

C₄⋊C₃₂

C₂×C₁₉

yes

characteristic

#1416

C₂×C₁₉

yes

—

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₆₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

—

C₂×Q₃₂

C₂²×C₁₉

yes

—

C₂×Q₃₂

C₂²×C₁₉

yes

characteristic

#494

—

C₄×Q₁₆

—

Q₆₄

—

C₂×C₃₂

C₂²×C₁₉

yes

—

#366

C₂²×C₁₉

yes

characteristic

#358

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

#2206

yes

characteristic

C₂×C₁₉

C₂×Q₆₄

yes

characteristic

C₂×C₁₉

#2264

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

Q₃₂

D₄×C₁₉

yes

—

100

C₂×C₁₆

D₄×C₁₉

yes

characteristic

101

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

102

#107

—

103

#103

—

104

C₄×C₈

D₄×C₁₉

yes

characteristic

105

C₃₂

—

106

C₁₉

#13688

yes

characteristic, direct product factor, Sylow

107

C₂×Q₈

—

108

C₂×Q₈

—

109

Q₁₆

—

110

Q₁₆

—

111

Q₁₆

—

112

Q₁₆

—

113

Q₁₆

—

114

C₂×C₈

D₈×C₁₉

yes

characteristic

115

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄²

—

121

C₄²

D₈×C₁₉

yes

characteristic

122

C₁₆

—

123

C₁₆

C₂×D₄×C₁₉

yes

characteristic

124

C₁₆

#41×C₁₉

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₁₉×D₁₆

yes

characteristic

133

C₂×C₄

C₁₉×D₁₆

yes

characteristic

134

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

135

C₈

—

136

C₈

C₁₉×#121

yes

characteristic

137

C₈

C₁₉×AGL(1,ℤ/8)

yes

characteristic

138

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

C₁₉×Q₆₄

yes

complemented

144

C₄

C₁₉×#459

yes

characteristic

145

C₄

C₁₉×#509

yes

characteristic

146

C₂

C₁₉×#2206

yes

characteristic

147

C₂

C₂×C₁₉×Q₆₄

yes

characteristic

148

C₂

C₁₉×#2264

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
50. #13688	C₁₉	direct (N × H)
74. C₄×C₁₉	Q₆₄	semidirect
106. C₁₉	#13688	direct (N × H)
143. C₄	C₁₉×Q₆₄	semidirect

H ≅ G/N

type

50. #13688

C₁₉

direct (N × H)

74. C₄×C₁₉

Q₆₄

semidirect

106. C₁₉

#13688

direct (N × H)

143. C₄

C₁₉×Q₆₄

semidirect

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

subgroup	index
C₂×C₁₉×Q₆₄	2
C₁₉×#2247	2
C₄×C₁₉×Q₃₂	2
C₁₉×C₄⋊C₃₂	2
C₁₉×#1416	2
#13688	19

subgroup

index

C₂×C₁₉×Q₆₄

C₁₉×#2247

C₄×C₁₉×Q₃₂

C₁₉×C₄⋊C₃₂

C₁₉×#1416

#13688

Subgroups — C₁₉×#13688 #18019647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13688 #18019647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13688 #18019647