Group #14566821 — subgroups

Subgroups — #14566821

Order 2432.

408 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 213 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	#11926443	C₂	1	4	yes	maximal
2	#11926430	C₂	1	4	yes	maximal
3	#11926430	C₂	1	4	yes	maximal
4	#11926410	C₂	1	2	yes	maximal
5	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#125	C₄	1	8	yes	complemented
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
14	C₁₉⋊#95	C₂²	1	4	yes	—
15	C₁₉⋊#95	C₂²	1	4	yes	—
16	C₁₉⋊#95	C₂²	1	4	yes	—
17	C₁₉⋊#95	C₂²	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
21	C₂²×Dic₁₉	C₂³	1	4	yes	—
22	C₂²×Dic₁₉	C₂³	1	4	yes	—
23	C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
24	C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
25	C₄²×C₁₉	C₂×C₄	1	4	yes	—
26	C₄⋊Dic₁₉	—	4	2	no	—
27	C₄⋊Dic₁₉	—	4	4	no	—
28	C₄⋊Dic₁₉	—	4	2	no	—
29	C₄×Dic₁₉	—	4	4	no	—
30	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	4	no	—
32	C₂×C₄×C₁₉	—	2	2	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
39	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
40	C₂×Dic₁₉	—	2	4	no	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	—	2	4	no	—
43	C₂×Dic₁₉	—	2	4	no	—
44	C₂×Dic₁₉	—	2	4	no	—
45	C₂×Dic₁₉	—	2	4	no	—
46	#2382	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
48	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
49	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
50	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
51	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
52	C₄×C₁₉	—	2	2	no	—
53	C₄×C₁₉	—	2	8	no	—
54	C₄×C₁₉	—	2	4	no	—
55	Dic₁₉	—	4	4	no	—
56	Dic₁₉	—	4	4	no	—
57	C₂×#125	D₁₉	1	1	yes	characteristic
58	#389	—	19	4	no	—
59	#387	—	19	4	no	—
60	#387	—	19	4	no	—
61	#382	—	19	2	no	—
62	C₂×C₁₉	#519	1	1	yes	characteristic
63	C₂×C₁₉	#520	1	2	yes	—
64	C₂×C₁₉	#562	1	1	yes	characteristic
65	C₂×C₁₉	#563	1	2	yes	—
66	C₂×C₁₉	#564	1	1	yes	characteristic
67	#125	Dic₁₉	1	8	yes	complemented
68	C₂×C₄⋊C₄	—	19	2	no	—
69	C₂×C₄⋊C₄	—	19	2	no	—
70	C₂×C₄⋊C₄	—	19	4	no	—
71	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
72	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
73	C₂×C₄²	—	19	4	no	—
74	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
75	#95	—	19	4	no	—
76	#95	—	19	4	no	—
77	#95	—	19	4	no	—
78	#95	—	19	4	no	—
79	C₁₉	#2382	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₄	—	19	4	no	—
81	C₂²×C₄	—	19	4	no	—
82	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
83	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
84	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
85	C₄⋊C₄	—	76	4	no	—
86	C₄⋊C₄	—	76	2	no	—
87	C₄⋊C₄	—	76	2	no	—
88	C₄⋊C₄	C₂×Dic₁₉	1	8	yes	—
89	C₄⋊C₄	C₂×Dic₁₉	1	16	yes	—
90	C₄²	—	76	4	no	—
91	C₄²	C₂×Dic₁₉	1	4	yes	—
92	C₂³	C₂³×D₁₉	1	1	yes	characteristic
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	38	4	no	—
100	C₂×C₄	—	38	4	no	—
101	C₂×C₄	—	38	4	no	—
102	C₂×C₄	—	38	4	no	—
103	C₂×C₄	—	38	4	no	—
104	C₂×C₄	—	38	4	no	—
105	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
106	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
107	C₂×C₄	C₂²×Dic₁₉	1	8	yes	—
108	C₂²	#10597433	1	1	yes	characteristic
109	C₂²	#10597433	1	1	yes	characteristic
110	C₂²	#10597435	1	2	yes	—
111	C₂²	#10597436	1	2	yes	—
112	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	2	8	no	—
115	C₄	—	2	4	no	—
116	C₄	—	76	4	no	—
117	C₄	—	76	4	no	—
118	C₂	#11927022	1	1	yes	characteristic
119	C₂	#11927027	1	2	yes	—
120	C₂	#11927292	1	1	yes	characteristic
121	C₂	#11927298	1	2	yes	—
122	C₂	C₁₉⋊#564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926443

C₂

yes

maximal

#11926430

C₂

yes

maximal

#11926430

C₂

yes

maximal

#11926410

C₂

yes

maximal

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

C₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2382

—

maximal, Sylow

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

D₁₉

yes

—

—

—

—

C₂×C₁₉

#519

yes

characteristic

C₂×C₁₉

#520

yes

—

C₂×C₁₉

#562

yes

characteristic

C₂×C₁₉

#563

yes

—

C₂×C₁₉

#564

yes

characteristic

#125

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₁₉

#2382

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄²

—

C₄²

C₂×Dic₁₉

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂²×Dic₁₉

yes

—

106

C₂×C₄

C₂²×Dic₁₉

yes

—

107

C₂×C₄

C₂²×Dic₁₉

yes

—

108

C₂²

#10597433

yes

characteristic

109

C₂²

#10597433

yes

characteristic

110

C₂²

#10597435

yes

—

111

C₂²

#10597436

yes

—

112

C₂²

C₂³×Dic₁₉

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₂

#11927022

yes

characteristic

119

C₂

#11927027

yes

—

120

C₂

#11927292

yes

characteristic

121

C₂

#11927298

yes

—

122

C₂

C₁₉⋊#564

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Fitting	C₂×C₁₉×#125	C₂
socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#2382
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator

C₂²×C₁₉

C₂³×C₄

Fitting

C₂×C₁₉×#125

C₂

socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
6. C₁₉×#125	C₄	semidirect
67. #125	Dic₁₉	semidirect
79. C₁₉	#2382	semidirect

H ≅ G/N

type

6. C₁₉×#125

C₄

semidirect

67. #125

Dic₁₉

semidirect

79. C₁₉

#2382

semidirect

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

subgroup	index
#11926443	2
#11926430	2
#11926410	2
C₂×C₁₉×#125	2
#2382	19

subgroup

index

C₂×C₁₉×#125

Subgroups — #14566821

Conjugacy classes of subgroups

Complements

Maximal subgroups