Group #18018420 — subgroups

Subgroups — C₁₉×#12461 #18018420

Order 4864.

188 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2252	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2183	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1676	C₂	1	2	yes	maximal
4	C₁₉×#1372	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1365	C₂	1	2	yes	maximal
6	C₁₉×#500	C₂²	1	2	yes	—
7	C₁₉×#477	—	2	2	no	—
8	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#366	—	2	1	no	—
10	C₁₉×#366	—	2	1	no	—
11	C₁₉×C₄⋊C₁₆	—	2	1	no	—
12	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₁₉×#346	—	2	1	no	—
14	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#335	C₂²	1	2	yes	—
16	C₁₉×#333	—	2	2	no	—
17	C₁₉×C₄⋊Q₈	—	2	2	no	—
18	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₁₆×C₁₉	—	2	1	no	—
20	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
22	C₁₉×#107	—	2	2	no	—
23	C₁₉×#107	—	2	2	no	—
24	C₁₉×#107	—	4	2	no	—
25	C₁₉×C₄⋊C₈	—	2	1	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
28	C₁₉×#103	—	4	2	no	—
29	C₄×C₈×C₁₉	—	2	1	no	—
30	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×Q₈×C₁₉	—	4	2	no	—
32	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
37	C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄⋊C₄×C₁₉	—	4	2	no	—
39	C₄⋊C₄×C₁₉	—	4	2	no	—
40	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
41	C₄²×C₁₉	—	2	1	no	—
42	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₁₆×C₁₉	—	2	1	no	—
44	C₁₆×C₁₉	—	4	1	no	—
45	C₁₆×C₁₉	Q₁₆	1	2	yes	—
46	#12461	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	Q₈×C₁₉	—	2	2	no	—
48	Q₈×C₁₉	—	16	2	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	8	2	no	—
52	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
55	C₈×C₁₉	—	2	1	no	—
56	C₈×C₁₉	—	4	1	no	—
57	C₈×C₁₉	—	8	2	no	—
58	C₈×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
59	C₈×C₁₉	#137	1	1	yes	characteristic
60	#2252	C₂×C₁₉	1	1	yes	characteristic
61	#2183	C₂×C₁₉	1	1	yes	characteristic
62	#1676	C₂×C₁₉	1	2	yes	—
63	#1372	C₂×C₁₉	1	1	yes	characteristic
64	#1365	C₂×C₁₉	1	2	yes	—
65	C₂²×C₁₉	#466	1	1	yes	characteristic
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	—	4	1	no	—
69	C₄×C₁₉	—	16	2	no	—
70	C₄×C₁₉	#462	1	1	yes	characteristic
71	C₄×C₁₉	#473	1	1	yes	characteristic
72	C₄×C₁₉	#510	1	2	yes	—
73	#500	C₂²×C₁₉	1	2	yes	—
74	#477	—	2	2	no	—
75	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
76	#366	—	2	1	no	—
77	#366	—	2	1	no	—
78	C₄⋊C₁₆	—	2	1	no	—
79	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
80	#346	—	2	1	no	—
81	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
82	#335	C₂²×C₁₉	1	2	yes	—
83	#333	—	2	2	no	—
84	C₂×C₁₉	#1674	1	1	yes	characteristic
85	C₂×C₁₉	#2219	1	1	yes	characteristic
86	C₂×C₁₉	#2221	1	1	yes	characteristic
87	C₄⋊Q₈	—	2	2	no	—
88	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
89	C₂×C₁₆	—	2	1	no	—
90	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
91	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
92	#107	—	2	2	no	—
93	#107	—	2	2	no	—
94	#107	—	4	2	no	—
95	C₄⋊C₈	—	2	1	no	—
96	C₄⋊C₈	—	2	2	no	—
97	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
98	#103	—	4	2	no	—
99	C₄×C₈	—	2	1	no	—
100	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
101	C₁₉	#12461	1	1	yes	characteristic, direct product factor, Sylow
102	C₂×Q₈	—	4	2	no	—
103	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	4	2	no	—
106	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
107	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	4	2	no	—
110	C₄⋊C₄	—	4	2	no	—
111	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
112	C₄²	—	2	1	no	—
113	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
114	C₁₆	—	2	1	no	—
115	C₁₆	—	4	1	no	—
116	C₁₆	Q₁₆×C₁₉	1	2	yes	—
117	Q₈	—	2	2	no	—
118	Q₈	—	16	2	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	8	2	no	—
122	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
123	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
124	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	4	1	no	—
127	C₈	—	8	2	no	—
128	C₈	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
129	C₈	C₁₉×#137	1	1	yes	characteristic
130	C₂²	C₁₉×#466	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	16	2	no	—
135	C₄	C₁₉×#462	1	1	yes	characteristic
136	C₄	C₁₉×#473	1	1	yes	characteristic
137	C₄	C₁₉×#510	1	2	yes	—
138	C₂	C₁₉×#1674	1	1	yes	characteristic
139	C₂	C₁₉×#2219	1	1	yes	characteristic
140	C₂	C₁₉×#2221	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2252

C₂

yes

maximal, characteristic

C₁₉×#2183

C₂

yes

maximal, characteristic

C₁₉×#1676

C₂

yes

maximal

C₁₉×#1372

C₂

yes

maximal, characteristic

C₁₉×#1365

C₂

yes

maximal

C₁₉×#500

C₂²

yes

—

C₁₉×#477

—

C₈×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#366

—

C₁₉×#366

—

C₁₉×C₄⋊C₁₆

—

C₁₉×C₄⋊C₁₆

C₂²

yes

characteristic

C₁₉×#346

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

C₂²

yes

—

C₁₉×#333

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

#41

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

Q₁₆

yes

—

#12461

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₁₆

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

#2183

C₂×C₁₉

yes

characteristic

#1676

C₂×C₁₉

yes

—

#1372

C₂×C₁₉

yes

characteristic

#1365

C₂×C₁₉

yes

—

C₂²×C₁₉

#466

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#500

C₂²×C₁₉

yes

—

#477

—

C₈×Q₈

C₂²×C₁₉

yes

characteristic

#366

—

#366

—

C₄⋊C₁₆

—

C₄⋊C₁₆

C₂²×C₁₉

yes

characteristic

#346

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

#335

C₂²×C₁₉

yes

—

#333

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄×Q₈

D₄×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

—

—

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

D₄×C₁₉

yes

characteristic

#103

—

C₄×C₈

—

100

C₄×C₈

C₂³×C₁₉

yes

characteristic

101

C₁₉

#12461

yes

characteristic, direct product factor, Sylow

102

C₂×Q₈

—

103

C₂×Q₈

D₈×C₁₉

yes

characteristic

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

107

C₂×C₈

#41×C₁₉

yes

characteristic

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

D₈×C₁₉

yes

characteristic

112

C₄²

—

113

C₄²

C₂×D₄×C₁₉

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₁₆

Q₁₆×C₁₉

yes

—

117

Q₈

—

118

Q₈

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₁₉×#121

yes

characteristic

123

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

124

C₂×C₄

C₁₉×#135

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

C₂×Q₁₆×C₁₉

yes

characteristic

129

C₈

C₁₉×#137

yes

characteristic

130

C₂²

C₁₉×#466

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

C₁₉×#462

yes

characteristic

136

C₄

C₁₉×#473

yes

characteristic

137

C₄

C₁₉×#510

yes

—

138

C₂

C₁₉×#1674

yes

characteristic

139

C₂

C₁₉×#2219

yes

characteristic

140

C₂

C₁₉×#2221

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

#466

commutator, Frattini, cosocle

C₄×C₈

C₂³×C₁₉

LCS

G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

N	H ≅ G/N	type
46. #12461	C₁₉	direct (N × H)
101. C₁₉	#12461	direct (N × H)

H ≅ G/N

type

46. #12461

C₁₉

direct (N × H)

101. C₁₉

#12461

direct (N × H)

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

subgroup	index
C₁₉×#2252	2
C₁₉×#2183	2
C₁₉×#1676	2
C₁₉×#1372	2
C₁₉×#1365	2
#12461	19

subgroup

index

C₁₉×#2252

C₁₉×#2183

C₁₉×#1676

C₁₉×#1372

C₁₉×#1365

#12461

Subgroups — C₁₉×#12461 #18018420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12461 #18018420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12461 #18018420