Group #14560063 — subgroups

Subgroups — C₁₉×#2206 #14560063

Order 2432.

186 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 68 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×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#357	C₂	1	2	yes	maximal, complemented
6	C₂×D₈×C₁₉	—	2	1	no	—
7	C₂×D₈×C₁₉	C₂²	1	2	yes	—
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#127	—	2	1	no	—
10	C₄×D₄×C₁₉	—	2	1	no	—
11	C₁₉×D₁₆	—	2	4	no	—
12	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₁₉×#102	—	2	1	no	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₁₉	—	2	1	no	—
17	C₂×D₄×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	—	4	1	no	—
19	C₂×D₄×C₁₉	—	4	1	no	—
20	C₂²×C₄×C₁₉	—	4	1	no	—
21	D₈×C₁₉	—	2	2	no	—
22	D₈×C₁₉	—	2	1	no	—
23	D₈×C₁₉	—	2	2	no	—
24	D₈×C₁₉	—	4	2	no	—
25	D₈×C₁₉	D₄	1	2	yes	complemented
26	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂²⋊C₄×C₁₉	—	4	1	no	—
30	C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₁₆×C₁₉	—	2	2	no	—
32	C₂³×C₁₉	—	4	1	no	—
33	C₂³×C₁₉	—	4	2	no	—
34	D₄×C₁₉	—	2	2	no	—
35	D₄×C₁₉	—	4	2	no	—
36	D₄×C₁₉	—	4	1	no	—
37	D₄×C₁₉	—	4	2	no	—
38	D₄×C₁₉	—	8	2	no	—
39	D₄×C₁₉	—	8	2	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	8	2	no	—
42	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
43	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₈×C₁₉	—	2	1	no	—
46	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₈×C₁₉	#41	1	1	yes	characteristic
48	#2206	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂²×C₁₉	—	4	2	no	—
50	C₂²×C₁₉	—	8	1	no	—
51	C₂²×C₁₉	—	8	1	no	—
52	C₂²×C₁₉	—	8	2	no	—
53	C₂²×C₁₉	—	8	2	no	—
54	C₂²×C₁₉	—	8	2	no	—
55	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	—	8	1	no	—
58	C₄×C₁₉	D₁₆	1	2	yes	complemented
59	C₄×C₁₉	#121	1	1	yes	characteristic
60	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂×D₁₆	C₂×C₁₉	1	2	yes	complemented
62	#493	C₂×C₁₉	1	1	yes	characteristic, complemented
63	C₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
64	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
65	#357	C₂×C₁₉	1	2	yes	complemented
66	C₂×C₁₉	—	8	2	no	—
67	C₂×C₁₉	—	16	2	no	—
68	C₂×C₁₉	#459	1	1	yes	characteristic
69	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
70	C₂×C₁₉	#509	1	1	yes	characteristic
71	C₂×D₈	—	2	1	no	—
72	C₂×D₈	C₂²×C₁₉	1	2	yes	—
73	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
74	#127	—	2	1	no	—
75	C₄×D₄	—	2	1	no	—
76	D₁₆	—	2	4	no	—
77	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
78	#107	C₂²×C₁₉	1	1	yes	characteristic
79	#102	—	2	1	no	—
80	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
81	C₁₉	#2206	1	1	yes	characteristic, direct product factor, Sylow
82	C₂×D₄	—	2	1	no	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	4	1	no	—
85	C₂×D₄	—	4	1	no	—
86	C₂²×C₄	—	4	1	no	—
87	D₈	—	2	2	no	—
88	D₈	—	2	1	no	—
89	D₈	—	2	2	no	—
90	D₈	—	4	2	no	—
91	D₈	D₄×C₁₉	1	2	yes	complemented
92	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
93	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
94	C₄⋊C₄	—	2	1	no	—
95	C₂²⋊C₄	—	4	1	no	—
96	C₄²	D₄×C₁₉	1	1	yes	characteristic
97	C₁₆	—	2	2	no	—
98	C₂³	—	4	1	no	—
99	C₂³	—	4	2	no	—
100	D₄	—	2	2	no	—
101	D₄	—	4	2	no	—
102	D₄	—	4	1	no	—
103	D₄	—	4	2	no	—
104	D₄	—	8	2	no	—
105	D₄	—	8	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	8	2	no	—
108	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
109	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
110	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
111	C₈	—	2	1	no	—
112	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
113	C₈	#41×C₁₉	1	1	yes	characteristic
114	C₂²	—	4	2	no	—
115	C₂²	—	8	1	no	—
116	C₂²	—	8	1	no	—
117	C₂²	—	8	2	no	—
118	C₂²	—	8	2	no	—
119	C₂²	—	8	2	no	—
120	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	8	1	no	—
123	C₄	C₁₉×D₁₆	1	2	yes	complemented
124	C₄	C₁₉×#121	1	1	yes	characteristic
125	C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
126	C₂	—	8	2	no	—
127	C₂	—	16	2	no	—
128	C₂	C₁₉×#459	1	1	yes	characteristic
129	C₂	C₂×C₁₉×D₁₆	1	1	yes	characteristic
130	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×D₁₆

C₂

yes

maximal, complemented

C₁₉×#493

C₂

yes

maximal, characteristic, complemented

C₄×D₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, complemented

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#127

—

C₄×D₄×C₁₉

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

D₄

yes

complemented

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₆

C₂×C₁₉

yes

complemented

#493

C₂×C₁₉

yes

characteristic, complemented

C₄×D₈

C₂×C₁₉

yes

characteristic, complemented

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

#357

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×D₁₆

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×D₈

—

C₂×D₈

C₂²×C₁₉

yes

—

C₂×D₈

C₂²×C₁₉

yes

characteristic

#127

—

C₄×D₄

—

D₁₆

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

C₂²×C₁₉

yes

characteristic

#102

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2206

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

D₈

—

D₈

—

D₈

D₄×C₁₉

yes

complemented

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

100

D₄

—

101

D₄

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

D₈×C₁₉

yes

characteristic

109

C₂×C₄

D₈×C₁₉

yes

characteristic

110

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

111

C₈

—

112

C₈

C₂×D₄×C₁₉

yes

characteristic

113

C₈

#41×C₁₉

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₂×D₈×C₁₉

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

C₁₉×D₁₆

yes

complemented

124

C₄

C₁₉×#121

yes

characteristic

125

C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

C₁₉×#459

yes

characteristic

129

C₂

C₂×C₁₉×D₁₆

yes

characteristic

130

C₂

C₁₉×#509

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
1. C₂×C₁₉×D₁₆	C₂	semidirect
2. C₁₉×#493	C₂	semidirect
3. C₄×D₈×C₁₉	C₂	semidirect
4. C₁₉×C₄⋊C₁₆	C₂	semidirect
5. C₁₉×#357	C₂	semidirect
25. D₈×C₁₉	D₄	semidirect
48. #2206	C₁₉	direct (N × H)
58. C₄×C₁₉	D₁₆	semidirect
61. C₂×D₁₆	C₂×C₁₉	semidirect
62. #493	C₂×C₁₉	semidirect
63. C₄×D₈	C₂×C₁₉	semidirect
64. C₄⋊C₁₆	C₂×C₁₉	semidirect
65. #357	C₂×C₁₉	semidirect
81. C₁₉	#2206	direct (N × H)
91. D₈	D₄×C₁₉	semidirect
123. C₄	C₁₉×D₁₆	semidirect

H ≅ G/N

type

1. C₂×C₁₉×D₁₆

C₂

semidirect

2. C₁₉×#493

C₂

semidirect

3. C₄×D₈×C₁₉

C₂

semidirect

4. C₁₉×C₄⋊C₁₆

C₂

semidirect

5. C₁₉×#357

C₂

semidirect

25. D₈×C₁₉

D₄

semidirect

48. #2206

C₁₉

direct (N × H)

58. C₄×C₁₉

D₁₆

semidirect

61. C₂×D₁₆

C₂×C₁₉

semidirect

62. #493

C₂×C₁₉

semidirect

63. C₄×D₈

C₂×C₁₉

semidirect

64. C₄⋊C₁₆

C₂×C₁₉

semidirect

65. #357

C₂×C₁₉

semidirect

81. C₁₉

#2206

direct (N × H)

91. D₈

D₄×C₁₉

semidirect

123. C₄

C₁₉×D₁₆

semidirect

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

subgroup	index
C₂×C₁₉×D₁₆	2
C₁₉×#493	2
C₄×D₈×C₁₉	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#357	2
#2206	19

subgroup

index

C₂×C₁₉×D₁₆

C₁₉×#493

C₄×D₈×C₁₉

C₁₉×C₄⋊C₁₆

C₁₉×#357

#2206

Subgroups — C₁₉×#2206 #14560063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2206 #14560063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2206 #14560063