Group #14560090 — subgroups

Subgroups — C₁₉×#2233 #14560090

Order 2432.

150 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 64 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×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#367	C₂	1	2	yes	maximal, complemented
4	C₁₉×#357	C₂	1	2	yes	maximal, complemented
5	C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#121	—	2	1	no	—
9	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#107	—	2	1	no	—
12	C₁₉×#107	C₂²	1	2	yes	—
13	C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₁₉×#102	—	2	1	no	—
15	C₂×D₄×C₁₉	—	2	1	no	—
16	C₂×D₄×C₁₉	—	4	1	no	—
17	C₂²×C₄×C₁₉	—	4	1	no	—
18	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
19	D₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	4	1	no	—
26	C₂²⋊C₄×C₁₉	—	4	1	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	—	4	1	no	—
29	C₂³×C₁₉	D₈	1	1	yes	characteristic
30	D₄×C₁₉	—	4	1	no	—
31	D₄×C₁₉	—	4	1	no	—
32	D₄×C₁₉	—	8	2	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	—	8	2	no	—
38	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₈×C₁₉	—	2	1	no	—
41	C₈×C₁₉	#41	1	2	yes	—
42	#2233	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	8	1	no	—
46	C₂²×C₁₉	—	8	1	no	—
47	C₂²×C₁₉	—	8	1	no	—
48	C₂²×C₁₉	SD₃₂	1	2	yes	—
49	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	—	8	1	no	—
52	C₄×C₁₉	—	8	2	no	—
53	C₄×C₁₉	#123	1	1	yes	characteristic
54	C₄×C₁₉	#137	1	1	yes	characteristic
55	#466	C₂×C₁₉	1	1	yes	characteristic
56	C₂×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
57	#367	C₂×C₁₉	1	2	yes	complemented
58	#357	C₂×C₁₉	1	2	yes	complemented
59	C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
60	C₂×C₁₉	—	2	2	no	—
61	C₂×C₁₉	—	16	1	no	—
62	C₂×C₁₉	#480	1	1	yes	characteristic
63	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
64	C₂×C₁₉	#509	1	1	yes	characteristic
65	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
66	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
67	#121	—	2	1	no	—
68	C₂×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
70	#107	—	2	1	no	—
71	#107	C₂²×C₁₉	1	2	yes	—
72	#107	C₂²×C₁₉	1	1	yes	characteristic
73	#102	—	2	1	no	—
74	C₁₉	#2233	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×D₄	—	2	1	no	—
76	C₂×D₄	—	4	1	no	—
77	C₂²×C₄	—	4	1	no	—
78	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
79	D₈	—	2	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
82	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	2	2	no	—
85	C₄⋊C₄	—	4	1	no	—
86	C₂²⋊C₄	—	4	1	no	—
87	C₁₆	—	2	2	no	—
88	C₂³	—	4	1	no	—
89	C₂³	D₈×C₁₉	1	1	yes	characteristic
90	D₄	—	4	1	no	—
91	D₄	—	4	1	no	—
92	D₄	—	8	2	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	8	2	no	—
98	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
99	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
100	C₈	—	2	1	no	—
101	C₈	#41×C₁₉	1	2	yes	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	—	8	1	no	—
105	C₂²	—	8	1	no	—
106	C₂²	—	8	1	no	—
107	C₂²	C₁₉×SD₃₂	1	2	yes	—
108	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	8	1	no	—
111	C₄	—	8	2	no	—
112	C₄	C₁₉×#123	1	1	yes	characteristic
113	C₄	C₁₉×#137	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	—	16	1	no	—
116	C₂	C₁₉×#480	1	1	yes	characteristic
117	C₂	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
118	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#466

C₂

yes

maximal, characteristic

C₂×C₁₉×#107

C₂

yes

maximal, characteristic, complemented

C₁₉×#367

C₂

yes

maximal, complemented

C₁₉×#357

C₂

yes

maximal, complemented

C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#121

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

—

C₁₉×#107

C₂²

yes

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₁₆×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

D₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

#41

yes

—

#2233

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

SD₃₂

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₂×#107

C₂×C₁₉

yes

characteristic, complemented

#367

C₂×C₁₉

yes

complemented

#357

C₂×C₁₉

yes

complemented

C₂²⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#480

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×D₈

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

#121

—

C₂×C₄⋊C₄

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

—

#107

C₂²×C₁₉

yes

—

#107

C₂²×C₁₉

yes

characteristic

#102

—

C₁₉

#2233

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₁₉

yes

characteristic

D₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

D₈×C₁₉

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

100

C₈

—

101

C₈

#41×C₁₉

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₁₉×SD₃₂

yes

—

108

C₂²

C₂×D₈×C₁₉

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

C₁₉×#123

yes

characteristic

113

C₄

C₁₉×#137

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

C₁₉×#480

yes

characteristic

117

C₂

C₂×C₁₉×SD₃₂

yes

characteristic

118

C₂

C₁₉×#509

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₁₉×#466

C₂

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
2. C₂×C₁₉×#107	C₂	semidirect
3. C₁₉×#367	C₂	semidirect
4. C₁₉×#357	C₂	semidirect
5. C₁₉×C₂²⋊C₁₆	C₂	semidirect
42. #2233	C₁₉	direct (N × H)
56. C₂×#107	C₂×C₁₉	semidirect
57. #367	C₂×C₁₉	semidirect
58. #357	C₂×C₁₉	semidirect
59. C₂²⋊C₁₆	C₂×C₁₉	semidirect
74. C₁₉	#2233	direct (N × H)

H ≅ G/N

type

2. C₂×C₁₉×#107

C₂

semidirect

3. C₁₉×#367

C₂

semidirect

4. C₁₉×#357

C₂

semidirect

5. C₁₉×C₂²⋊C₁₆

C₂

semidirect

42. #2233

C₁₉

direct (N × H)

56. C₂×#107

C₂×C₁₉

semidirect

57. #367

C₂×C₁₉

semidirect

58. #357

C₂×C₁₉

semidirect

59. C₂²⋊C₁₆

C₂×C₁₉

semidirect

74. C₁₉

#2233

direct (N × H)

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

subgroup	index
C₁₉×#466	2
C₂×C₁₉×#107	2
C₁₉×#367	2
C₁₉×#357	2
C₁₉×C₂²⋊C₁₆	2
#2233	19

subgroup

index

C₁₉×#466

C₂×C₁₉×#107

C₁₉×#367

C₁₉×#357

C₁₉×C₂²⋊C₁₆

#2233

Subgroups — C₁₉×#2233 #14560090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2233 #14560090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2233 #14560090