Group #14569602 — subgroups

Subgroups — #14569602

Order 2432.

352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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⋊#401	C₂	1	1	yes	maximal, characteristic
2	#11926486	C₂	1	3	yes	maximal
3	#11926484	C₂	1	3	yes	maximal
4	#11926448	C₂	1	3	yes	maximal
5	#11926441	C₂	1	3	yes	maximal
6	#11926389	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#401	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
10	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
12	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
13	C₁₉×#95	C₂²	1	1	yes	characteristic
14	C₁₉×#95	C₂²	1	3	yes	—
15	C₁₉×#95	C₂²	1	3	yes	—
16	C₁₉⋊#95	C₂²	1	3	yes	—
17	C₁₉⋊#95	C₂²	1	3	yes	—
18	C₁₉⋊#95	C₂²	1	3	yes	—
19	C₁₉⋊#95	C₂²	1	3	yes	—
20	C₁₉⋊#95	C₂²	1	3	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	C₂³	1	3	yes	—
26	C₂²×Dic₁₉	C₂³	1	3	yes	—
27	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₈	—	2	6	no	—
29	C₄⋊Dic₁₉	—	4	3	no	—
30	Dic₁₉⋊C₄	—	2	6	no	—
31	Dic₁₉⋊C₄	—	4	3	no	—
32	C₄×Dic₁₉	—	2	6	no	—
33	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	3	no	—
35	C₂×C₄×C₁₉	—	2	3	no	—
36	C₂×C₄×C₁₉	—	2	3	no	—
37	C₂×C₄×C₁₉	—	2	3	no	—
38	C₂×C₄×C₁₉	—	2	6	no	—
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×Dic₁₉	—	2	3	no	—
41	C₂×Dic₁₉	—	2	3	no	—
42	C₂×Dic₁₉	—	2	3	no	—
43	C₂×Dic₁₉	—	2	3	no	—
44	C₂×Dic₁₉	—	2	3	no	—
45	C₂×Dic₁₉	—	2	3	no	—
46	C₂×Dic₁₉	—	2	3	no	—
47	C₂×Dic₁₉	#41	1	6	yes	—
48	Dic₃₈	—	4	4	no	—
49	#2645	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	C₂×#41	1	3	yes	—
51	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
52	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
53	C₄×C₁₉	—	4	1	no	—
54	C₄×C₁₉	—	4	3	no	—
55	C₄×C₁₉	—	4	3	no	—
56	Dic₁₉	—	4	1	no	—
57	Dic₁₉	—	4	3	no	—
58	Dic₁₉	—	4	3	no	—
59	Dic₁₉	#126	1	4	yes	—
60	#401	—	19	1	no	—
61	#401	D₁₉	1	1	yes	characteristic
62	#400	—	19	3	no	—
63	#400	—	19	3	no	—
64	#391	—	19	3	no	—
65	#389	—	19	3	no	—
66	#376	—	19	1	no	—
67	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
68	C₂×C₁₉	#541	1	3	yes	—
69	C₂×C₁₉	#542	1	3	yes	—
70	C₂²×Q₈	—	19	1	no	—
71	C₂×C₄⋊C₄	—	19	3	no	—
72	C₂×C₄⋊C₄	—	19	3	no	—
73	C₂×C₄⋊C₄	—	19	3	no	—
74	C₂×C₄²	—	19	3	no	—
75	#95	—	19	3	no	—
76	#95	—	19	3	no	—
77	#95	—	19	3	no	—
78	#95	—	19	3	no	—
79	#95	—	19	3	no	—
80	#95	C₂×D₁₉	1	1	yes	characteristic
81	#95	C₂×D₁₉	1	3	yes	—
82	#95	C₂×D₁₉	1	3	yes	—
83	C₁₉	#2645	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₈	—	38	6	no	—
85	C₂²×C₄	—	19	1	no	—
86	C₂²×C₄	—	19	1	no	—
87	C₂²×C₄	—	19	3	no	—
88	C₂²×C₄	—	19	3	no	—
89	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
92	C₄⋊C₄	—	38	6	no	—
93	C₄⋊C₄	—	76	3	no	—
94	C₄⋊C₄	—	76	3	no	—
95	C₄²	—	38	6	no	—
96	C₂³	C₂³×D₁₉	1	1	yes	characteristic
97	Q₈	—	76	4	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	2	6	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	19	6	no	—
105	C₂×C₄	—	38	3	no	—
106	C₂×C₄	—	38	3	no	—
107	C₂×C₄	—	38	3	no	—
108	C₂×C₄	—	38	3	no	—
109	C₂×C₄	—	38	3	no	—
110	C₂×C₄	—	38	3	no	—
111	C₂×C₄	—	38	3	no	—
112	C₂²	#41×D₁₉	1	3	yes	—
113	C₂²	#10597435	1	1	yes	characteristic
114	C₂²	#10597436	1	3	yes	—
115	C₄	—	4	1	no	—
116	C₄	—	4	3	no	—
117	C₄	—	4	3	no	—
118	C₄	—	19	4	no	—
119	C₄	—	76	1	no	—
120	C₄	—	76	3	no	—
121	C₄	—	76	3	no	—
122	C₂	#126×D₁₉	1	1	yes	characteristic
123	C₂	#11927151	1	3	yes	—
124	C₂	#11927160	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉⋊#401

C₂

yes

maximal, characteristic

#11926486

C₂

yes

maximal

#11926484

C₂

yes

maximal

#11926448

C₂

yes

maximal

#11926441

C₂

yes

maximal

#11926389

C₂

yes

maximal, characteristic

C₁₉×#401

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉×#95

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

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

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

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×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

Dic₃₈

—

#2645

—

maximal, Sylow

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#126

yes

—

#401

—

#401

D₁₉

yes

—

—

—

—

—

C₂×C₁₉

C₂×#126

yes

characteristic

C₂×C₁₉

#541

yes

—

C₂×C₁₉

#542

yes

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

—

—

C₂×D₁₉

yes

characteristic

#95

C₂×D₁₉

yes

—

#95

C₂×D₁₉

yes

—

C₁₉

#2645

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂²

#41×D₁₉

yes

—

113

C₂²

#10597435

yes

characteristic

114

C₂²

#10597436

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₂

#126×D₁₉

yes

characteristic

123

C₂

#11927151

yes

—

124

C₂

#11927160

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#401	C₂
hypercenter	#401	D₁₉
hypocenter	C₁₉	#2645
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#401

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
83. C₁₉	#2645	semidirect

H ≅ G/N

type

83. C₁₉

#2645

semidirect

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

subgroup	index
C₁₉⋊#401	2
#11926486	2
#11926484	2
#11926448	2
#11926441	2
#11926389	2
C₁₉×#401	2
#2645	19

subgroup

index

C₁₉⋊#401

C₁₉×#401

Subgroups — #14569602

Conjugacy classes of subgroups

Complements

Maximal subgroups