Group #18019653 — subgroups

Subgroups — C₁₉×#13694 #18019653

Order 4864.

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

normal subgroups only

This group has 214 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×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2215	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1423	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1415	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×D₁₆	C₂²	1	2	yes	—
7	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#466	—	2	2	no	—
9	C₁₉×D₃₂	—	2	2	no	—
10	C₂×C₁₉×C₃₂	—	2	2	no	—
11	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
13	C₁₉×#366	C₂²	1	2	yes	—
14	C₁₉×#357	—	2	2	no	—
15	C₂×D₈×C₁₉	—	2	2	no	—
16	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₁₉×#121	—	4	2	no	—
18	C₁₉×D₁₆	—	2	2	no	—
19	C₁₉×D₁₆	—	2	2	no	—
20	C₂×C₁₆×C₁₉	—	2	1	no	—
21	C₂×C₁₆×C₁₉	—	2	1	no	—
22	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×#107	—	2	2	no	—
25	C₁₉×#102	—	4	2	no	—
26	C₁₉×C₃₂	—	2	1	no	—
27	C₁₉×C₃₂	D₄	1	2	yes	complemented
28	C₂×D₄×C₁₉	—	4	2	no	—
29	C₂×D₄×C₁₉	—	8	2	no	—
30	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
31	D₈×C₁₉	—	4	2	no	—
32	D₈×C₁₉	—	4	2	no	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₄⋊C₄×C₁₉	—	4	2	no	—
38	C₂²⋊C₄×C₁₉	—	8	2	no	—
39	C₁₆×C₁₉	—	2	1	no	—
40	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₁₆×C₁₉	#41	1	1	yes	characteristic
42	#13694	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂³×C₁₉	—	8	2	no	—
44	C₂³×C₁₉	D₁₆	1	1	yes	characteristic
45	D₄×C₁₉	—	8	2	no	—
46	D₄×C₁₉	—	8	2	no	—
47	D₄×C₁₉	—	16	4	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	8	2	no	—
51	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	#121	1	1	yes	characteristic
55	C₈×C₁₉	#135	1	1	yes	characteristic
56	C₂×D₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
57	C₂²×C₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
58	#2215	C₂×C₁₉	1	2	yes	complemented
59	#1423	C₂×C₁₉	1	1	yes	characteristic, complemented
60	#1415	C₂×C₁₉	1	2	yes	complemented
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	—	16	2	no	—
64	C₂²×C₁₉	—	16	2	no	—
65	C₂²×C₁₉	—	16	2	no	—
66	C₂²×C₁₉	D₃₂	1	2	yes	complemented
67	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	16	2	no	—
70	C₄×C₁₉	#466	1	1	yes	characteristic
71	C₄×C₁₉	#508	1	1	yes	characteristic
72	C₂×D₁₆	C₂²×C₁₉	1	2	yes	—
73	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
74	#466	—	2	2	no	—
75	D₃₂	—	2	2	no	—
76	C₂×C₃₂	—	2	2	no	—
77	C₂×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
78	C₂×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
79	#366	C₂²×C₁₉	1	2	yes	—
80	#357	—	2	2	no	—
81	C₂×C₁₉	—	2	2	no	—
82	C₂×C₁₉	—	32	2	no	—
83	C₂×C₁₉	#2215	1	1	yes	characteristic
84	C₂×C₁₉	C₂×D₃₂	1	1	yes	characteristic
85	C₂×C₁₉	#2262	1	1	yes	characteristic
86	C₂×D₈	—	2	2	no	—
87	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
88	#121	—	4	2	no	—
89	D₁₆	—	2	2	no	—
90	D₁₆	—	2	2	no	—
91	C₂×C₁₆	—	2	1	no	—
92	C₂×C₁₆	—	2	1	no	—
93	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
94	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
95	#107	—	2	2	no	—
96	#102	—	4	2	no	—
97	C₃₂	—	2	1	no	—
98	C₃₂	D₄×C₁₉	1	2	yes	complemented
99	C₁₉	#13694	1	1	yes	characteristic, direct product factor, Sylow
100	C₂×D₄	—	4	2	no	—
101	C₂×D₄	—	8	2	no	—
102	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
103	D₈	—	4	2	no	—
104	D₈	—	4	2	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
108	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
109	C₄⋊C₄	—	4	2	no	—
110	C₂²⋊C₄	—	8	2	no	—
111	C₁₆	—	2	1	no	—
112	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
113	C₁₆	#41×C₁₉	1	1	yes	characteristic
114	C₂³	—	8	2	no	—
115	C₂³	C₁₉×D₁₆	1	1	yes	characteristic
116	D₄	—	8	2	no	—
117	D₄	—	8	2	no	—
118	D₄	—	16	4	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	8	2	no	—
122	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
123	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
124	C₈	—	2	1	no	—
125	C₈	C₁₉×#121	1	1	yes	characteristic
126	C₈	C₁₉×#135	1	1	yes	characteristic
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	—	16	2	no	—
130	C₂²	—	16	2	no	—
131	C₂²	—	16	2	no	—
132	C₂²	C₁₉×D₃₂	1	2	yes	complemented
133	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	16	2	no	—
136	C₄	C₁₉×#466	1	1	yes	characteristic
137	C₄	C₁₉×#508	1	1	yes	characteristic
138	C₂	—	2	2	no	—
139	C₂	—	32	2	no	—
140	C₂	C₁₉×#2215	1	1	yes	characteristic
141	C₂	C₂×C₁₉×D₃₂	1	1	yes	characteristic
142	C₂	C₁₉×#2262	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×D₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₉×C₃₂

C₂

yes

maximal, characteristic, complemented

C₁₉×#2215

C₂

yes

maximal, complemented

C₁₉×#1423

C₂

yes

maximal, characteristic, complemented

C₁₉×#1415

C₂

yes

maximal, complemented

C₂×C₁₉×D₁₆

C₂²

yes

—

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#466

—

C₁₉×D₃₂

—

C₂×C₁₉×C₃₂

—

C₂×C₁₉×C₃₂

C₂²

yes

characteristic

C₂×C₁₉×C₃₂

C₂²

yes

characteristic

C₁₉×#366

C₂²

yes

—

C₁₉×#357

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×#121

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#102

—

C₁₉×C₃₂

—

C₁₉×C₃₂

D₄

yes

complemented

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×D₄

yes

C₁₆×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

D₁₆

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×D₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₃₂

C₂×C₁₉

yes

characteristic, complemented

#2215

C₂×C₁₉

yes

complemented

#1423

C₂×C₁₉

yes

characteristic, complemented

#1415

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

D₃₂

yes

complemented

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₆

C₂²×C₁₉

yes

—

C₂²×C₁₆

C₂²×C₁₉

yes

characteristic

#466

—

D₃₂

—

C₂×C₃₂

—

C₂×C₃₂

C₂²×C₁₉

yes

characteristic

C₂×C₃₂

C₂²×C₁₉

yes

characteristic

#366

C₂²×C₁₉

yes

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2215

yes

characteristic

C₂×C₁₉

C₂×D₃₂

yes

characteristic

C₂×C₁₉

#2262

yes

characteristic

C₂×D₈

—

C₂²×C₈

D₄×C₁₉

yes

characteristic

#121

—

D₁₆

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

#107

—

#102

—

C₃₂

—

C₃₂

D₄×C₁₉

yes

complemented

C₁₉

#13694

yes

characteristic, direct product factor, Sylow

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

D₈×C₁₉

yes

characteristic

103

D₈

—

104

D₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

D₈×C₁₉

yes

characteristic

108

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₁₆

—

112

C₁₆

C₂×D₄×C₁₉

yes

characteristic

113

C₁₆

#41×C₁₉

yes

characteristic

114

C₂³

—

115

C₂³

C₁₉×D₁₆

yes

characteristic

116

D₄

—

117

D₄

—

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₁₉×D₁₆

yes

characteristic

123

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

124

C₈

—

125

C₈

C₁₉×#121

yes

characteristic

126

C₈

C₁₉×#135

yes

characteristic

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₁₉×D₃₂

yes

complemented

133

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

C₁₉×#466

yes

characteristic

137

C₄

C₁₉×#508

yes

characteristic

138

C₂

—

139

C₂

—

140

C₂

C₁₉×#2215

yes

characteristic

141

C₂

C₂×C₁₉×D₃₂

yes

characteristic

142

C₂

C₁₉×#2262

yes

characteristic

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

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
1. C₂×C₁₉×D₃₂	C₂	semidirect
2. C₂²×C₁₉×C₃₂	C₂	semidirect
3. C₁₉×#2215	C₂	semidirect
4. C₁₉×#1423	C₂	semidirect
5. C₁₉×#1415	C₂	semidirect
27. C₁₉×C₃₂	D₄	semidirect
42. #13694	C₁₉	direct (N × H)
56. C₂×D₃₂	C₂×C₁₉	semidirect
57. C₂²×C₃₂	C₂×C₁₉	semidirect
58. #2215	C₂×C₁₉	semidirect
59. #1423	C₂×C₁₉	semidirect
60. #1415	C₂×C₁₉	semidirect
66. C₂²×C₁₉	D₃₂	semidirect
98. C₃₂	D₄×C₁₉	semidirect
99. C₁₉	#13694	direct (N × H)
132. C₂²	C₁₉×D₃₂	semidirect

H ≅ G/N

type

1. C₂×C₁₉×D₃₂

C₂

semidirect

2. C₂²×C₁₉×C₃₂

C₂

semidirect

3. C₁₉×#2215

C₂

semidirect

4. C₁₉×#1423

C₂

semidirect

5. C₁₉×#1415

C₂

semidirect

27. C₁₉×C₃₂

D₄

semidirect

42. #13694

C₁₉

direct (N × H)

56. C₂×D₃₂

C₂×C₁₉

semidirect

57. C₂²×C₃₂

C₂×C₁₉

semidirect

58. #2215

C₂×C₁₉

semidirect

59. #1423

C₂×C₁₉

semidirect

60. #1415

C₂×C₁₉

semidirect

66. C₂²×C₁₉

D₃₂

semidirect

98. C₃₂

D₄×C₁₉

semidirect

99. C₁₉

#13694

direct (N × H)

132. C₂²

C₁₉×D₃₂

semidirect

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

subgroup	index
C₂×C₁₉×D₃₂	2
C₂²×C₁₉×C₃₂	2
C₁₉×#2215	2
C₁₉×#1423	2
C₁₉×#1415	2
#13694	19

subgroup

index

C₂×C₁₉×D₃₂

C₂²×C₁₉×C₃₂

C₁₉×#2215

C₁₉×#1423

C₁₉×#1415

#13694

Subgroups — C₁₉×#13694 #18019653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13694 #18019653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13694 #18019653