Group #18013427 — subgroups

Subgroups — C₁₉×#7468 #18013427

Order 4864.

182 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 118 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×M₆₄	C₂	1	2	yes	maximal
2	C₂×C₁₉×#346	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×M₆₄	—	2	2	no	—
7	C₁₉×M₆₄	C₄	1	4	yes	complemented
8	C₂×C₁₉×C₃₂	—	2	2	no	—
9	C₁₉×#346	—	2	2	no	—
10	C₂²×C₈×C₁₉	C₈	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₈	1	1	yes	characteristic
13	C₂×C₁₆×C₁₉	—	2	1	no	—
14	C₂×C₁₆×C₁₉	—	2	1	no	—
15	C₂×C₁₆×C₁₉	C₈	1	2	yes	—
16	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
19	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
20	C₄×C₈×C₁₉	—	2	1	no	—
21	C₄×C₈×C₁₉	—	2	1	no	—
22	C₁₉×C₃₂	—	2	4	no	—
23	C₂²×C₄×C₁₉	C₁₆	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	C₁₆	1	2	yes	—
28	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
29	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
33	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₁₆×C₁₉	—	2	2	no	—
37	C₁₆×C₁₉	C₂²⋊C₄	1	2	yes	—
38	C₁₆×C₁₉	C₄⋊C₄	1	2	yes	—
39	#7468	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
48	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
49	C₈×C₁₉	—	2	2	no	—
50	C₈×C₁₉	#95	1	1	yes	characteristic
51	C₈×C₁₉	#97	1	1	yes	characteristic
52	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
53	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
54	C₂×M₆₄	C₂×C₁₉	1	2	yes	—
55	C₂×#346	C₂×C₁₉	1	1	yes	characteristic
56	C₂²×C₁₉	—	2	2	no	—
57	C₂²×C₁₉	C₄×C₁₆	1	1	yes	characteristic
58	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
59	C₂²×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
60	C₄×C₁₉	—	4	2	no	—
61	C₄×C₁₉	#336	1	1	yes	characteristic
62	C₄×C₁₉	#346	1	1	yes	characteristic
63	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
64	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
65	C₂²×C₁₆	C₄×C₁₉	1	1	yes	characteristic
66	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
67	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
68	M₆₄	—	2	2	no	—
69	M₆₄	C₄×C₁₉	1	4	yes	complemented
70	C₂×C₃₂	—	2	2	no	—
71	#346	—	2	2	no	—
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	—	2	1	no	—
74	C₂×C₁₉	#1374	1	1	yes	characteristic
75	C₂×C₁₉	#1400	1	2	yes	—
76	C₂²×C₈	C₈×C₁₉	1	1	yes	characteristic
77	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
78	C₂×C₄²	C₈×C₁₉	1	1	yes	characteristic
79	C₂×C₁₆	—	2	1	no	—
80	C₂×C₁₆	—	2	1	no	—
81	C₂×C₁₆	C₈×C₁₉	1	2	yes	—
82	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	—
83	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
84	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
85	C₂×C₁₆	Q₈×C₁₉	1	1	yes	characteristic
86	C₄×C₈	—	2	1	no	—
87	C₄×C₈	—	2	1	no	—
88	C₃₂	—	2	4	no	—
89	C₁₉	#7468	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²×C₄	C₁₆×C₁₉	1	2	yes	—
91	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
92	C₂×C₈	—	2	1	no	—
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	C₁₆×C₁₉	1	2	yes	—
95	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
96	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
97	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
98	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
99	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
100	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
101	C₄²	—	2	1	no	—
102	C₄²	—	2	1	no	—
103	C₁₆	—	2	2	no	—
104	C₁₆	C₂²⋊C₄×C₁₉	1	2	yes	—
105	C₁₆	C₄⋊C₄×C₁₉	1	2	yes	—
106	C₂³	C₂×C₁₆×C₁₉	1	1	yes	characteristic
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	C₄×C₈×C₁₉	1	1	yes	characteristic
110	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
111	C₂×C₄	C₁₉×C₄⋊C₈	1	1	yes	characteristic
112	C₂×C₄	C₂×C₁₆×C₁₉	1	1	yes	characteristic
113	C₂×C₄	C₁₉×M₃₂	1	1	yes	characteristic
114	C₂×C₄	C₁₉×M₃₂	1	1	yes	characteristic
115	C₈	—	2	2	no	—
116	C₈	C₁₉×#95	1	1	yes	characteristic
117	C₈	C₁₉×#97	1	1	yes	characteristic
118	C₈	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
119	C₈	C₁₉×C₄⋊C₈	1	1	yes	characteristic
120	C₂²	—	2	2	no	—
121	C₂²	C₄×C₁₆×C₁₉	1	1	yes	characteristic
122	C₂²	C₁₉×C₂²⋊C₁₆	1	1	yes	characteristic
123	C₂²	C₁₉×C₄⋊C₁₆	1	1	yes	characteristic
124	C₄	—	4	2	no	—
125	C₄	C₁₉×#336	1	1	yes	characteristic
126	C₄	C₁₉×#346	1	1	yes	characteristic
127	C₄	C₁₉×C₂²⋊C₁₆	1	1	yes	characteristic
128	C₄	C₁₉×C₄⋊C₁₆	1	1	yes	characteristic
129	C₂	—	2	1	no	—
130	C₂	—	2	1	no	—
131	C₂	C₁₉×#1374	1	1	yes	characteristic
132	C₂	C₁₉×#1400	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×M₆₄

C₂

yes

maximal

C₂×C₁₉×#346

C₂

yes

maximal, characteristic

C₂²×C₁₆×C₁₉

C₄

yes

characteristic

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×M₆₄

—

C₁₉×M₆₄

C₄

yes

complemented

C₂×C₁₉×C₃₂

—

C₁₉×#346

—

C₂²×C₈×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₈

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₈

yes

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

—

C₂×C₁₆×C₁₉

Q₈

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₁₉×C₃₂

—

C₂²×C₄×C₁₉

C₁₆

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₁₆

yes

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂²⋊C₄

yes

—

C₁₆×C₁₉

C₄⋊C₄

yes

—

#7468

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

C₄⋊C₈

yes

characteristic

C₂×M₆₄

C₂×C₁₉

yes

—

C₂×#346

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₁₆

yes

characteristic

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₂²×C₁₉

C₄⋊C₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₉

C₄⋊C₁₆

yes

characteristic

C₂²×C₁₆

C₄×C₁₉

yes

characteristic

C₂²×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₄×C₈

C₄×C₁₉

yes

characteristic

M₆₄

—

M₆₄

C₄×C₁₉

yes

complemented

C₂×C₃₂

—

#346

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1374

yes

characteristic

C₂×C₁₉

#1400

yes

—

C₂²×C₈

C₈×C₁₉

yes

characteristic

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂×C₄²

C₈×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₈×C₁₉

yes

—

C₂×C₁₆

C₂×C₄×C₁₉

yes

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

—

C₂×C₁₆

Q₈×C₁₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₁₉

#7468

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₁₆×C₁₉

yes

—

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₁₆×C₁₉

yes

—

C₂×C₈

C₄²×C₁₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₂×C₈×C₁₉

yes

characteristic

C₂×C₈

M₁₆×C₁₉

yes

characteristic

100

C₂×C₈

M₁₆×C₁₉

yes

characteristic

101

C₄²

—

102

C₄²

—

103

C₁₆

—

104

C₁₆

C₂²⋊C₄×C₁₉

yes

—

105

C₁₆

C₄⋊C₄×C₁₉

yes

—

106

C₂³

C₂×C₁₆×C₁₉

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄×C₈×C₁₉

yes

characteristic

110

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

111

C₂×C₄

C₁₉×C₄⋊C₈

yes

characteristic

112

C₂×C₄

C₂×C₁₆×C₁₉

yes

characteristic

113

C₂×C₄

C₁₉×M₃₂

yes

characteristic

114

C₂×C₄

C₁₉×M₃₂

yes

characteristic

115

C₈

—

116

C₈

C₁₉×#95

yes

characteristic

117

C₈

C₁₉×#97

yes

characteristic

118

C₈

C₁₉×C₂²⋊C₈

yes

characteristic

119

C₈

C₁₉×C₄⋊C₈

yes

characteristic

120

C₂²

—

121

C₂²

C₄×C₁₆×C₁₉

yes

characteristic

122

C₂²

C₁₉×C₂²⋊C₁₆

yes

characteristic

123

C₂²

C₁₉×C₄⋊C₁₆

yes

characteristic

124

C₄

—

125

C₄

C₁₉×#336

yes

characteristic

126

C₄

C₁₉×#346

yes

characteristic

127

C₄

C₁₉×C₂²⋊C₁₆

yes

characteristic

128

C₄

C₁₉×C₄⋊C₁₆

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

C₁₉×#1374

yes

characteristic

132

C₂

C₁₉×#1400

yes

—

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

subgroup

G/H

center

C₂×C₈×C₁₉

C₂²⋊C₄

commutator

C₂²

C₄×C₁₆×C₁₉

Frattini, cosocle

C₂²×C₁₆

C₂²×C₁₉

socle

C₂²×C₁₉

C₂²⋊C₁₆

prime radical

C₂³×C₁₉

C₂×C₁₆

LCS

G ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
7. C₁₉×M₆₄	C₄	semidirect
39. #7468	C₁₉	direct (N × H)
69. M₆₄	C₄×C₁₉	semidirect
89. C₁₉	#7468	direct (N × H)

H ≅ G/N

type

7. C₁₉×M₆₄

C₄

semidirect

39. #7468

C₁₉

direct (N × H)

69. M₆₄

C₄×C₁₉

semidirect

89. C₁₉

#7468

direct (N × H)

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

subgroup	index
C₂×C₁₉×M₆₄	2
C₂×C₁₉×#346	2
#7468	19

subgroup

index

C₂×C₁₉×M₆₄

C₂×C₁₉×#346

#7468

Subgroups — C₁₉×#7468 #18013427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7468 #18013427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7468 #18013427