Group #14566741 — subgroups

Subgroups — #14566741

Order 2432.

448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 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	#11926430	C₂	1	4	yes	maximal
2	#11926430	C₂	1	4	yes	maximal
3	C₄⋊C₄×Dic₁₉	C₂	1	4	yes	maximal
4	#11926390	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	4	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
11	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
13	C₁₉⋊#95	C₂²	1	2	yes	—
14	C₁₉⋊#95	C₂²	1	2	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	16	yes	—
24	C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
25	C₄²×C₁₉	C₂×C₄	1	4	yes	—
26	C₄⋊Dic₁₉	—	2	8	no	—
27	C₄×Dic₁₉	—	2	8	no	—
28	C₄×Dic₁₉	—	2	8	no	—
29	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	4	no	—
31	C₂×C₄×C₁₉	—	2	4	no	—
32	C₂×C₄×C₁₉	—	2	4	no	—
33	C₂×C₄×C₁₉	—	2	2	no	—
34	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
37	C₂×Dic₁₉	—	2	4	no	—
38	C₂×Dic₁₉	—	2	4	no	—
39	C₂×Dic₁₉	—	2	4	no	—
40	C₂×Dic₁₉	—	2	4	no	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	#41	1	8	yes	—
43	#2371	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
45	C₂²×C₁₉	C₂×#41	1	4	yes	—
46	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
47	C₄×C₁₉	—	2	4	no	—
48	C₄×C₁₉	—	2	8	no	—
49	C₄×C₁₉	—	2	2	no	—
50	Dic₁₉	—	2	8	no	—
51	Dic₁₉	—	4	4	no	—
52	C₂×#125	D₁₉	1	1	yes	characteristic
53	#387	—	19	4	no	—
54	#387	—	19	4	no	—
55	C₄×C₄⋊C₄	—	19	4	no	—
56	#376	—	19	2	no	—
57	C₂×C₁₉	C₄×#41	1	2	yes	—
58	C₂×C₁₉	#519	1	1	yes	characteristic
59	C₂×C₁₉	#552	1	4	yes	—
60	#125	Dic₁₉	1	8	yes	complemented
61	C₂×C₄⋊C₄	—	19	4	no	—
62	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
63	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
64	C₂×C₄²	—	19	4	no	—
65	C₂×C₄²	—	19	4	no	—
66	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
67	#95	—	19	2	no	—
68	#95	—	19	4	no	—
69	#95	—	19	2	no	—
70	#95	—	19	4	no	—
71	#95	—	19	4	no	—
72	C₁₉	#2371	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₄	—	19	4	no	—
74	C₂²×C₄	—	19	4	no	—
75	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
76	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
77	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
78	C₄⋊C₄	—	38	8	no	—
79	C₄⋊C₄	C₂×Dic₁₉	1	16	yes	—
80	C₄⋊C₄	C₂×Dic₁₉	1	8	yes	—
81	C₄²	—	38	8	no	—
82	C₄²	—	38	8	no	—
83	C₄²	C₂×Dic₁₉	1	4	yes	—
84	C₂³	C₂³×D₁₉	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	19	8	no	—
90	C₂×C₄	—	38	4	no	—
91	C₂×C₄	—	38	4	no	—
92	C₂×C₄	—	38	4	no	—
93	C₂×C₄	—	38	4	no	—
94	C₂×C₄	—	38	4	no	—
95	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
96	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
97	C₂×C₄	C₂²×Dic₁₉	1	8	yes	—
98	C₂²	#10597433	1	2	yes	—
99	C₂²	#41×D₁₉	1	4	yes	—
100	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	2	2	no	—
104	C₄	—	38	8	no	—
105	C₄	—	76	4	no	—
106	C₂	#41×Dic₁₉	1	2	yes	—
107	C₂	#11927022	1	1	yes	characteristic
108	C₂	#11927226	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926430

C₂

yes

maximal

#11926430

C₂

yes

maximal

C₄⋊C₄×Dic₁₉

C₂

yes

maximal

#11926390

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

—

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

—

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

—

C₂³×C₁₉

C₂⁴

yes

characteristic

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

#41

yes

—

#2371

—

maximal, Sylow

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

D₁₉

yes

characteristic

#387

—

#387

—

C₄×C₄⋊C₄

—

#376

—

C₂×C₁₉

C₄×#41

yes

—

C₂×C₁₉

#519

yes

characteristic

C₂×C₁₉

#552

yes

—

#125

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

—

C₁₉

#2371

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

C₂×Dic₁₉

yes

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄²

—

C₄²

—

C₄²

C₂×Dic₁₉

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂²

#10597433

yes

—

C₂²

#41×D₁₉

yes

—

100

C₂²

C₂³×Dic₁₉

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₂

#41×Dic₁₉

yes

—

107

C₂

#11927022

yes

characteristic

108

C₂

#11927226

yes

—

	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	#2371
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
60. #125	Dic₁₉	semidirect
72. C₁₉	#2371	semidirect

H ≅ G/N

type

6. C₁₉×#125

C₄

semidirect

60. #125

Dic₁₉

semidirect

72. C₁₉

#2371

semidirect

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

subgroup	index
#11926430	2
C₄⋊C₄×Dic₁₉	2
#11926390	2
C₂×C₁₉×#125	2
#2371	19

subgroup

index

#11926430

C₄⋊C₄×Dic₁₉

#11926390

C₂×C₁₉×#125

#2371

Subgroups — #14566741

Conjugacy classes of subgroups

Complements

Maximal subgroups