Group #14571014 — subgroups

Subgroups — #14571014

Order 2432.

520 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 125 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	2	yes	maximal, complemented
2	#11926456	C₂	1	3	yes	maximal, complemented
3	#11926424	C₂	1	6	yes	maximal, complemented
4	#11926405	C₂	1	3	yes	maximal, complemented
5	C₁₉×#392	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	C₂²	1	3	yes	—
7	C₂³×Dic₁₉	C₂²	1	3	yes	—
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
11	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
12	C₁₉×#95	C₂²	1	1	yes	characteristic
13	C₁₉⋊#95	C₂²	1	3	yes	—
14	C₁₉⋊#95	C₂²	1	6	yes	—
15	C₁₉⋊#95	C₂²	1	6	yes	—
16	C₂⁴×C₁₉	C₂³	1	3	yes	—
17	C₂×D₄×C₁₉	—	2	12	no	—
18	C₂×D₄×C₁₉	—	4	3	no	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
21	C₂²×Dic₁₉	—	2	6	no	—
22	C₂²×Dic₁₉	—	4	3	no	—
23	C₂²×Dic₁₉	—	4	3	no	—
24	C₂²×Dic₁₉	C₂³	1	2	yes	—
25	C₂²×Dic₁₉	C₂³	1	6	yes	—
26	C₂×Dic₃₈	—	4	3	no	—
27	C₂²⋊C₄×C₁₉	—	4	3	no	—
28	C₂²⋊Dic₁₉	—	4	6	no	—
29	C₂²⋊Dic₁₉	—	4	3	no	—
30	C₂³×C₁₉	—	2	6	no	—
31	C₂³×C₁₉	—	2	3	no	—
32	C₂³×C₁₉	—	2	6	no	—
33	C₂³×C₁₉	—	2	3	no	—
34	C₂³×C₁₉	#41	1	6	yes	—
35	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
36	D₄×C₁₉	—	4	12	no	—
37	C₂×C₄×C₁₉	—	2	6	no	—
38	C₂×C₄×C₁₉	—	2	3	no	—
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×Dic₁₉	—	2	6	no	—
41	C₂×Dic₁₉	—	2	6	no	—
42	C₂×Dic₁₉	—	2	6	no	—
43	C₂×Dic₁₉	—	2	6	no	—
44	C₂×Dic₁₉	—	4	12	no	—
45	Dic₃₈	—	4	4	no	—
46	#2760	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	—	2	6	no	—
48	C₂²×C₁₉	—	2	12	no	—
49	C₂²×C₁₉	—	4	6	no	—
50	C₂²×C₁₉	—	4	3	no	—
51	C₂²×C₁₉	—	4	3	no	—
52	C₂²×C₁₉	C₂×#41	1	3	yes	—
53	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
54	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
55	C₄×C₁₉	—	4	3	no	—
56	C₄×C₁₉	—	4	1	no	—
57	Dic₁₉	—	4	6	no	—
58	Dic₁₉	—	4	2	no	—
59	#401	—	19	2	no	—
60	#393	—	19	3	no	—
61	#392	D₁₉	1	1	yes	characteristic
62	#386	—	19	6	no	—
63	#381	—	19	3	no	—
64	C₂×C₁₉	—	4	6	no	—
65	C₂×C₁₉	#538	1	3	yes	—
66	C₂×C₁₉	#551	1	3	yes	—
67	C₂×C₁₉	#560	1	1	yes	characteristic
68	C₂²×Q₈	—	19	1	no	—
69	C₂²×D₄	C₂×D₁₉	1	3	yes	—
70	C₂³×C₄	—	19	3	no	—
71	C₂×C₂²⋊C₄	—	19	3	no	—
72	C₂×C₂²⋊C₄	—	19	6	no	—
73	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
74	#95	—	19	3	no	—
75	#95	—	19	6	no	—
76	#95	—	19	6	no	—
77	#95	C₂×D₁₉	1	1	yes	characteristic
78	C₁₉	#2760	1	1	yes	characteristic, complemented, Sylow
79	C₂⁴	C₂²×D₁₉	1	3	yes	—
80	C₂×Q₈	—	76	3	no	—
81	C₂×D₄	—	2	12	no	—
82	C₂×D₄	—	4	3	no	—
83	C₂²×C₄	—	19	6	no	—
84	C₂²×C₄	—	19	2	no	—
85	C₂²×C₄	—	38	6	no	—
86	C₂²×C₄	—	76	3	no	—
87	C₂²×C₄	—	76	3	no	—
88	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
89	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
90	C₂²⋊C₄	—	4	3	no	—
91	C₂²⋊C₄	—	76	6	no	—
92	C₂²⋊C₄	—	76	3	no	—
93	C₂³	—	2	6	no	—
94	C₂³	—	2	3	no	—
95	C₂³	—	2	6	no	—
96	C₂³	—	2	3	no	—
97	C₂³	#64543	1	6	yes	—
98	C₂³	C₂³×D₁₉	1	1	yes	characteristic
99	Q₈	—	76	4	no	—
100	D₄	—	4	12	no	—
101	C₂×C₄	—	2	6	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	38	6	no	—
105	C₂×C₄	—	38	6	no	—
106	C₂×C₄	—	38	6	no	—
107	C₂×C₄	—	38	6	no	—
108	C₂×C₄	—	76	12	no	—
109	C₂²	—	2	6	no	—
110	C₂²	—	2	12	no	—
111	C₂²	—	4	6	no	—
112	C₂²	—	4	3	no	—
113	C₂²	—	4	3	no	—
114	C₂²	C₂×#64543	1	3	yes	—
115	C₂²	#10597430	1	3	yes	—
116	C₂²	#10597435	1	1	yes	characteristic
117	C₄	—	4	3	no	—
118	C₄	—	4	1	no	—
119	C₄	—	76	6	no	—
120	C₄	—	76	2	no	—
121	C₂	—	4	6	no	—
122	C₂	#11927131	1	3	yes	—
123	C₂	#11927225	1	3	yes	—
124	C₂	#11927281	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉⋊#401

C₂

yes

maximal, complemented

#11926456

C₂

yes

maximal, complemented

#11926424

C₂

yes

maximal, complemented

#11926405

C₂

yes

maximal, complemented

C₁₉×#392

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

—

C₂³×Dic₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2760

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#401

—

#393

—

#392

D₁₉

yes

characteristic

#386

—

#381

—

C₂×C₁₉

—

C₂×C₁₉

#538

yes

—

C₂×C₁₉

#551

yes

—

C₂×C₁₉

#560

yes

characteristic

C₂²×Q₈

—

C₂²×D₄

C₂×D₁₉

yes

—

C₂³×C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

—

—

—

C₂×D₁₉

yes

characteristic

C₁₉

#2760

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

#64543

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

100

D₄

—

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

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂×#64543

yes

—

115

C₂²

#10597430

yes

—

116

C₂²

#10597435

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₂

—

122

C₂

#11927131

yes

—

123

C₂

#11927225

yes

—

124

C₂

#11927281

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting, prime radical	C₁₉×#392	C₂
hypercenter	#392	D₁₉
hypocenter	C₁₉	#2760
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #392

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting, prime radical

C₁₉×#392

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #392

N	H ≅ G/N	type
1. C₁₉⋊#401	C₂	semidirect
2. #11926456	C₂	semidirect
3. #11926424	C₂	semidirect
4. #11926405	C₂	semidirect
78. C₁₉	#2760	semidirect

H ≅ G/N

type

1. C₁₉⋊#401

C₂

semidirect

2. #11926456

C₂

semidirect

3. #11926424

C₂

semidirect

4. #11926405

C₂

semidirect

78. C₁₉

#2760

semidirect

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

subgroup	index
C₁₉⋊#401	2
#11926456	2
#11926424	2
#11926405	2
C₁₉×#392	2
#2760	19

subgroup

index

C₁₉⋊#401

C₁₉×#392

Subgroups — #14571014

Conjugacy classes of subgroups

Complements

Maximal subgroups