Group #14560064 — subgroups

Subgroups — C₁₉×#2207 #14560064

Order 2432.

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

normal subgroups only

This group has 174 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×SD₃₂	C₂	1	2	yes	maximal, complemented
2	C₁₉×#493	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×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×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×D₈×C₁₉	—	2	1	no	—
8	C₂×D₈×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#127	—	2	1	no	—
10	C₄×Q₈×C₁₉	—	2	1	no	—
11	C₁₉×SD₃₂	—	2	4	no	—
12	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₁₉×#103	—	2	1	no	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×Q₈×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	Q₁₆×C₁₉	—	2	1	no	—
21	Q₁₆×C₁₉	D₄	1	2	yes	complemented
22	D₈×C₁₉	—	2	2	no	—
23	D₈×C₁₉	—	2	2	no	—
24	D₈×C₁₉	—	4	2	no	—
25	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	4	1	no	—
29	C₄²×C₁₉	—	4	1	no	—
30	C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₁₆×C₁₉	—	2	2	no	—
32	C₂³×C₁₉	—	4	2	no	—
33	Q₈×C₁₉	—	2	2	no	—
34	Q₈×C₁₉	—	4	1	no	—
35	D₄×C₁₉	—	4	2	no	—
36	D₄×C₁₉	—	4	2	no	—
37	D₄×C₁₉	—	8	2	no	—
38	D₄×C₁₉	—	8	2	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₁₉	—	2	1	no	—
45	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₈×C₁₉	#41	1	1	yes	characteristic
47	#2207	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₁₉	—	8	2	no	—
49	C₂²×C₁₉	—	8	2	no	—
50	C₂²×C₁₉	—	8	2	no	—
51	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	—	4	2	no	—
54	C₄×C₁₉	—	8	1	no	—
55	C₄×C₁₉	SD₃₂	1	2	yes	complemented
56	C₄×C₁₉	#121	1	1	yes	characteristic
57	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
58	C₂×SD₃₂	C₂×C₁₉	1	2	yes	complemented
59	#493	C₂×C₁₉	1	1	yes	characteristic
60	C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
61	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
62	#357	C₂×C₁₉	1	2	yes	complemented
63	C₂×C₁₉	—	16	2	no	—
64	C₂×C₁₉	#459	1	1	yes	characteristic
65	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
66	C₂×C₁₉	#509	1	1	yes	characteristic
67	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
68	C₂×D₈	—	2	1	no	—
69	C₂×D₈	C₂²×C₁₉	1	2	yes	—
70	#127	—	2	1	no	—
71	C₄×Q₈	—	2	1	no	—
72	SD₃₂	—	2	4	no	—
73	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
74	#107	C₂²×C₁₉	1	1	yes	characteristic
75	#103	—	2	1	no	—
76	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
77	C₁₉	#2207	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×Q₈	—	2	1	no	—
79	C₂×D₄	—	2	2	no	—
80	C₂×D₄	—	4	1	no	—
81	C₂×D₄	—	4	1	no	—
82	Q₁₆	—	2	1	no	—
83	Q₁₆	D₄×C₁₉	1	2	yes	complemented
84	D₈	—	2	2	no	—
85	D₈	—	2	2	no	—
86	D₈	—	4	2	no	—
87	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
88	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
89	C₄⋊C₄	—	2	1	no	—
90	C₄⋊C₄	—	4	1	no	—
91	C₄²	—	4	1	no	—
92	C₄²	D₄×C₁₉	1	1	yes	characteristic
93	C₁₆	—	2	2	no	—
94	C₂³	—	4	2	no	—
95	Q₈	—	2	2	no	—
96	Q₈	—	4	1	no	—
97	D₄	—	4	2	no	—
98	D₄	—	4	2	no	—
99	D₄	—	8	2	no	—
100	D₄	—	8	2	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
104	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
105	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
108	C₈	#41×C₁₉	1	1	yes	characteristic
109	C₂²	—	8	2	no	—
110	C₂²	—	8	2	no	—
111	C₂²	—	8	2	no	—
112	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	4	2	no	—
115	C₄	—	8	1	no	—
116	C₄	C₁₉×SD₃₂	1	2	yes	complemented
117	C₄	C₁₉×#121	1	1	yes	characteristic
118	C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
119	C₂	—	16	2	no	—
120	C₂	C₁₉×#459	1	1	yes	characteristic
121	C₂	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
122	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×SD₃₂

C₂

yes

maximal, complemented

C₁₉×#493

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

—

C₁₉×#127

—

C₄×Q₈×C₁₉

—

C₁₉×SD₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

D₄

yes

complemented

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×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

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

SD₃₂

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×SD₃₂

C₂×C₁₉

yes

complemented

#493

C₂×C₁₉

yes

characteristic

C₄×Q₁₆

C₂×C₁₉

yes

characteristic, complemented

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

#357

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂×D₈

—

C₂×D₈

C₂²×C₁₉

yes

—

#127

—

C₄×Q₈

—

SD₃₂

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

C₂²×C₁₉

yes

characteristic

#103

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2207

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

Q₁₆

D₄×C₁₉

yes

complemented

D₈

—

D₈

—

D₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

D₈×C₁₉

yes

characteristic

104

C₂×C₄

D₈×C₁₉

yes

characteristic

105

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

106

C₈

—

107

C₈

C₂×D₄×C₁₉

yes

characteristic

108

C₈

#41×C₁₉

yes

characteristic

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×D₈×C₁₉

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

C₁₉×SD₃₂

yes

complemented

117

C₄

C₁₉×#121

yes

characteristic

118

C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

119

C₂

—

120

C₂

C₁₉×#459

yes

characteristic

121

C₂

C₂×C₁₉×SD₃₂

yes

characteristic

122

C₂

C₁₉×#509

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#493	C₂
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

prime radical

C₁₉×#493

C₂

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×SD₃₂	C₂	semidirect
3. C₄×Q₁₆×C₁₉	C₂	semidirect
4. C₁₉×C₄⋊C₁₆	C₂	semidirect
5. C₁₉×#357	C₂	semidirect
21. Q₁₆×C₁₉	D₄	semidirect
47. #2207	C₁₉	direct (N × H)
55. C₄×C₁₉	SD₃₂	semidirect
58. C₂×SD₃₂	C₂×C₁₉	semidirect
60. C₄×Q₁₆	C₂×C₁₉	semidirect
61. C₄⋊C₁₆	C₂×C₁₉	semidirect
62. #357	C₂×C₁₉	semidirect
77. C₁₉	#2207	direct (N × H)
83. Q₁₆	D₄×C₁₉	semidirect
116. C₄	C₁₉×SD₃₂	semidirect

H ≅ G/N

type

1. C₂×C₁₉×SD₃₂

C₂

semidirect

3. C₄×Q₁₆×C₁₉

C₂

semidirect

4. C₁₉×C₄⋊C₁₆

C₂

semidirect

5. C₁₉×#357

C₂

semidirect

21. Q₁₆×C₁₉

D₄

semidirect

47. #2207

C₁₉

direct (N × H)

55. C₄×C₁₉

SD₃₂

semidirect

58. C₂×SD₃₂

C₂×C₁₉

semidirect

60. C₄×Q₁₆

C₂×C₁₉

semidirect

61. C₄⋊C₁₆

C₂×C₁₉

semidirect

62. #357

C₂×C₁₉

semidirect

77. C₁₉

#2207

direct (N × H)

83. Q₁₆

D₄×C₁₉

semidirect

116. C₄

C₁₉×SD₃₂

semidirect

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

subgroup	index
C₂×C₁₉×SD₃₂	2
C₁₉×#493	2
C₄×Q₁₆×C₁₉	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#357	2
#2207	19

subgroup

index

C₂×C₁₉×SD₃₂

C₁₉×#493

C₄×Q₁₆×C₁₉

C₁₉×C₄⋊C₁₆

C₁₉×#357

#2207

Subgroups — C₁₉×#2207 #14560064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2207 #14560064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2207 #14560064