Group #14559550 — subgroups

Subgroups — C₁₉×#1693 #14559550

Order 2432.

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

normal subgroups only

This group has 166 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	C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#461	C₂	1	2	yes	maximal
3	C₁₉×#436	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#332	C₂	1	2	yes	maximal, complemented
6	C₂×SD₁₆×C₁₉	—	2	2	no	—
7	C₂×M₁₆×C₁₉	—	2	1	no	—
8	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#107	—	2	1	no	—
11	C₁₉×#107	—	2	1	no	—
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₁₉×#103	—	2	2	no	—
15	C₁₉×C₂²⋊C₈	—	2	1	no	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	SD₁₆×C₁₉	—	4	4	no	—
21	M₁₆×C₁₉	—	4	2	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×C₁₉	—	2	1	no	—
32	Q₈×C₁₉	—	4	2	no	—
33	Q₈×C₁₉	—	4	2	no	—
34	D₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₈×C₁₉	—	2	1	no	—
43	C₈×C₁₉	—	4	1	no	—
44	C₈×C₁₉	—	4	2	no	—
45	C₈×C₁₉	SD₁₆	1	2	yes	complemented
46	#1693	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₁₉	—	4	1	no	—
48	C₂²×C₁₉	—	4	1	no	—
49	C₂²×C₁₉	—	4	1	no	—
50	C₂²×C₁₉	#121	1	1	yes	characteristic
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	4	1	no	—
53	C₄×C₁₉	—	8	2	no	—
54	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
55	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
56	C₄×C₁₉	#137	1	1	yes	characteristic
57	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
58	#461	C₂×C₁₉	1	2	yes	—
59	#436	C₂×C₁₉	1	1	yes	characteristic
60	#334	C₂×C₁₉	1	1	yes	characteristic, complemented
61	#332	C₂×C₁₉	1	2	yes	complemented
62	C₂×C₁₉	—	8	1	no	—
63	C₂×C₁₉	#461	1	1	yes	characteristic
64	C₂×C₁₉	#469	1	1	yes	characteristic
65	C₂×C₁₉	#473	1	1	yes	characteristic
66	C₂×SD₁₆	—	2	2	no	—
67	C₂×M₁₆	—	2	1	no	—
68	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
69	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
70	#107	—	2	1	no	—
71	#107	—	2	1	no	—
72	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
73	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
74	#103	—	2	2	no	—
75	C₂²⋊C₈	—	2	1	no	—
76	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
77	C₁₉	#1693	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×Q₈	—	2	2	no	—
79	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
80	C₂²×C₄	—	2	1	no	—
81	SD₁₆	—	4	4	no	—
82	M₁₆	—	4	2	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
86	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
90	C₂²⋊C₄	—	2	1	no	—
91	C₄²	C₂³×C₁₉	1	1	yes	characteristic
92	C₂³	—	2	1	no	—
93	Q₈	—	4	2	no	—
94	Q₈	—	4	2	no	—
95	D₄	—	2	2	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
101	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
102	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	4	1	no	—
105	C₈	—	4	2	no	—
106	C₈	SD₁₆×C₁₉	1	2	yes	complemented
107	C₂²	—	4	1	no	—
108	C₂²	—	4	1	no	—
109	C₂²	—	4	1	no	—
110	C₂²	C₁₉×#121	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	4	1	no	—
113	C₄	—	8	2	no	—
114	C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
115	C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
116	C₄	C₁₉×#137	1	1	yes	characteristic
117	C₂	—	8	1	no	—
118	C₂	C₁₉×#461	1	1	yes	characteristic
119	C₂	C₁₉×#469	1	1	yes	characteristic
120	C₂	C₁₉×#473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic, complemented

C₁₉×#461

C₂

yes

maximal

C₁₉×#436

C₂

yes

maximal, characteristic

C₁₉×#334

C₂

yes

maximal, characteristic, complemented

C₁₉×#332

C₂

yes

maximal, complemented

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#103

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₁₆

yes

complemented

#1693

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

characteristic

#500

C₂×C₁₉

yes

characteristic, complemented

#461

C₂×C₁₉

yes

—

#436

C₂×C₁₉

yes

characteristic

#334

C₂×C₁₉

yes

characteristic, complemented

#332

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×SD₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

C₂²×C₁₉

yes

—

C₄×D₄

C₂²×C₁₉

yes

characteristic

#107

—

#107

—

C₄⋊C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₂²×C₁₉

yes

—

#103

—

C₂²⋊C₈

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#1693

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

D₄×C₁₉

yes

characteristic

C₂²×C₄

—

SD₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂³×C₁₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

101

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

102

C₂×C₄

#41×C₁₉

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

SD₁₆×C₁₉

yes

complemented

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

C₁₉×#121

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

C₂×SD₁₆×C₁₉

yes

characteristic

115

C₄

C₁₉×AGL(1,ℤ/8)

yes

—

116

C₄

C₁₉×#137

yes

characteristic

117

C₂

—

118

C₂

C₁₉×#461

yes

characteristic

119

C₂

C₁₉×#469

yes

characteristic

120

C₂

C₁₉×#473

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#121

commutator, Frattini, cosocle

C₄²

C₂³×C₁₉

prime radical

C₂×D₄×C₁₉

D₄

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#500	C₂	semidirect
4. C₁₉×#334	C₂	semidirect
5. C₁₉×#332	C₂	semidirect
45. C₈×C₁₉	SD₁₆	semidirect
46. #1693	C₁₉	direct (N × H)
57. #500	C₂×C₁₉	semidirect
60. #334	C₂×C₁₉	semidirect
61. #332	C₂×C₁₉	semidirect
77. C₁₉	#1693	direct (N × H)
106. C₈	SD₁₆×C₁₉	semidirect

H ≅ G/N

type

1. C₁₉×#500

C₂

semidirect

4. C₁₉×#334

C₂

semidirect

5. C₁₉×#332

C₂

semidirect

45. C₈×C₁₉

SD₁₆

semidirect

46. #1693

C₁₉

direct (N × H)

57. #500

C₂×C₁₉

semidirect

60. #334

C₂×C₁₉

semidirect

61. #332

C₂×C₁₉

semidirect

77. C₁₉

#1693

direct (N × H)

106. C₈

SD₁₆×C₁₉

semidirect

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

subgroup	index
C₁₉×#500	2
C₁₉×#461	2
C₁₉×#436	2
C₁₉×#334	2
C₁₉×#332	2
#1693	19

subgroup

index

C₁₉×#500

C₁₉×#461

C₁₉×#436

C₁₉×#334

C₁₉×#332

#1693

Subgroups — C₁₉×#1693 #14559550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1693 #14559550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1693 #14559550