Group #18017374 — subgroups

Subgroups — C₁₉×#11415 #18017374

Order 4864.

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

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 158 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×#2163	C₂	1	2	yes	maximal
2	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1313	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊C₁₆	C₄	1	4	yes	—
8	C₁₉×C₂²⋊C₁₆	C₄	1	4	yes	—
9	C₁₉×#346	C₂²	1	4	yes	—
10	C₁₉×#322	C₄	1	2	yes	—
11	C₁₉×#322	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₉	—	2	1	no	—
13	C₂²×C₈×C₁₉	—	2	1	no	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	C₂×C₄	1	8	yes	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₄×C₈×C₁₉	—	2	1	no	—
19	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	4	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	C₄²	1	2	yes	—
33	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
34	C₄²×C₁₉	C₄²	1	1	yes	characteristic
35	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
36	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
37	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₁₆×C₁₉	—	2	8	no	—
39	#11415	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂³×C₁₉	#97	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
50	C₈×C₁₉	—	2	2	no	—
51	C₈×C₁₉	—	4	2	no	—
52	C₈×C₁₉	—	4	2	no	—
53	C₈×C₁₉	#131	1	4	yes	—
54	#2163	C₂×C₁₉	1	2	yes	—
55	C₂×#322	C₂×C₁₉	1	1	yes	characteristic
56	#1313	C₂×C₁₉	1	4	yes	complemented
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	#347	1	2	yes	—
60	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	#347	1	2	yes	—
66	C₄×C₁₉	#405	1	2	yes	—
67	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
68	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
70	C₄⋊C₁₆	C₄×C₁₉	1	4	yes	—
71	C₂²⋊C₁₆	C₄×C₁₉	1	4	yes	—
72	#346	C₂²×C₁₉	1	4	yes	—
73	#322	C₄×C₁₉	1	2	yes	—
74	#322	C₂²×C₁₉	1	2	yes	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	#1452	1	1	yes	characteristic
77	C₂×C₁₉	C₂×#347	1	1	yes	characteristic
78	C₂×C₁₉	C₂×#347	1	1	yes	characteristic
79	C₂²×C₈	—	2	1	no	—
80	C₂²×C₈	—	2	1	no	—
81	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
82	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
83	C₂×C₁₆	C₂×C₄×C₁₉	1	8	yes	—
84	C₄×C₈	—	2	1	no	—
85	C₄×C₈	—	2	1	no	—
86	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
87	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
88	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
89	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
90	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
91	C₁₉	#11415	1	1	yes	characteristic, direct product factor, Sylow
92	C₂²×C₄	C₄²×C₁₉	1	1	yes	characteristic
93	C₂²×C₄	M₁₆×C₁₉	1	1	yes	characteristic
94	C₂²×C₄	M₁₆×C₁₉	1	1	yes	characteristic
95	C₂×C₈	—	2	4	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	4	2	no	—
99	C₂×C₈	—	4	2	no	—
100	C₂×C₈	C₄²×C₁₉	1	2	yes	—
101	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
102	C₄²	C₄²×C₁₉	1	1	yes	characteristic
103	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
104	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
105	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
106	C₁₆	—	2	8	no	—
107	C₂³	C₁₉×#97	1	1	yes	characteristic
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	C₁₉×#97	1	1	yes	characteristic
112	C₂×C₄	C₁₉×#97	1	1	yes	characteristic
113	C₂×C₄	C₁₉×#97	1	1	yes	characteristic
114	C₂×C₄	C₂×C₄²×C₁₉	1	1	yes	characteristic
115	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
116	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	4	2	no	—
120	C₈	C₁₉×#131	1	4	yes	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	C₁₉×#347	1	2	yes	—
124	C₂²	C₂×C₁₉×#97	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	2	1	no	—
129	C₄	C₁₉×#347	1	2	yes	—
130	C₄	C₁₉×#405	1	2	yes	—
131	C₂	—	2	2	no	—
132	C₂	C₁₉×#1452	1	1	yes	characteristic
133	C₂	C₂×C₁₉×#347	1	1	yes	characteristic
134	C₂	C₂×C₁₉×#347	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2163

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₁₉×#1313

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

C₄

yes

—

C₁₉×C₂²⋊C₁₆

C₄

yes

—

C₁₉×#346

C₂²

yes

—

C₁₉×#322

C₄

yes

—

C₁₉×#322

C₂²

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₁₆×C₁₉

—

#11415

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#131

yes

—

#2163

C₂×C₁₉

yes

—

C₂×#322

C₂×C₁₉

yes

characteristic

#1313

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#347

yes

—

C₂²×C₁₉

C₂×#97

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#347

yes

—

C₄×C₁₉

#405

yes

—

C₂×C₄×C₈

C₄×C₁₉

yes

characteristic

C₂×C₄×C₈

C₄×C₁₉

yes

characteristic

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₁₆

C₄×C₁₉

yes

—

C₂²⋊C₁₆

C₄×C₁₉

yes

—

#346

C₂²×C₁₉

yes

—

#322

C₄×C₁₉

yes

—

#322

C₂²×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×C₄×C₁₉

yes

—

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂×C₄×C₁₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

C₄×C₈

C₂³×C₁₉

yes

characteristic

C₁₉

#11415

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₄²×C₁₉

yes

characteristic

C₂²×C₄

M₁₆×C₁₉

yes

characteristic

C₂²×C₄

M₁₆×C₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

C₄²×C₁₉

yes

—

101

C₂×C₈

C₂²×C₄×C₁₉

yes

—

102

C₄²

C₄²×C₁₉

yes

characteristic

103

C₄²

M₁₆×C₁₉

yes

characteristic

104

C₄²

M₁₆×C₁₉

yes

characteristic

105

C₄²

C₂²×C₄×C₁₉

yes

characteristic

106

C₁₆

—

107

C₂³

C₁₉×#97

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₁₉×#97

yes

characteristic

112

C₂×C₄

C₁₉×#97

yes

characteristic

113

C₂×C₄

C₁₉×#97

yes

characteristic

114

C₂×C₄

C₂×C₄²×C₁₉

yes

characteristic

115

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

116

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

C₁₉×#131

yes

—

121

C₂²

—

122

C₂²

—

123

C₂²

C₁₉×#347

yes

—

124

C₂²

C₂×C₁₉×#97

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

C₁₉×#347

yes

—

130

C₄

C₁₉×#405

yes

—

131

C₂

—

132

C₂

C₁₉×#1452

yes

characteristic

133

C₂

C₂×C₁₉×#347

yes

characteristic

134

C₂

C₂×C₁₉×#347

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#97
prime radical	C₂³×C₁₉	#97
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

C₂×C₄²

commutator

C₂×C₄

C₂×C₄²×C₁₉

Frattini, cosocle

C₄×C₈

C₂³×C₁₉

socle

C₂²×C₁₉

C₂×#97

C₂³×C₁₉

G ▷ C₂×C₄ ▷ C₁

C₁ ◁ C₂×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1313	C₂	semidirect
39. #11415	C₁₉	direct (N × H)
56. #1313	C₂×C₁₉	semidirect
91. C₁₉	#11415	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1313

C₂

semidirect

39. #11415

C₁₉

direct (N × H)

56. #1313

C₂×C₁₉

semidirect

91. C₁₉

#11415

direct (N × H)

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

subgroup	index
C₁₉×#2163	2
C₂×C₁₉×#322	2
C₁₉×#1313	2
#11415	19

subgroup

index

C₁₉×#2163

C₂×C₁₉×#322

C₁₉×#1313

#11415

Subgroups — C₁₉×#11415 #18017374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11415 #18017374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11415 #18017374