Group #14571703 — subgroups

Subgroups — #14571703

Order 2432.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₂×#10597316	C₂	1	2	yes	maximal
2	#11926484	C₂	1	4	yes	maximal
3	#11926476	C₂	1	4	yes	maximal
4	#11926474	C₂	1	4	yes	maximal
5	C₁₉×#382	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
11	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
13	#10597316	—	2	8	no	—
14	C₁₉×#95	C₂²	1	4	yes	—
15	C₁₉⋊#95	C₂²	1	8	yes	—
16	C₁₉⋊#95	C₂²	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
20	C₂²×Dic₁₉	C₂³	1	4	yes	—
21	C₂²×Dic₁₉	C₂³	1	4	yes	—
22	C₄⋊C₄×C₁₉	—	4	2	no	—
23	C₄²×C₁₉	D₄	1	4	yes	—
24	C₄⋊Dic₁₉	—	2	4	no	—
25	C₄⋊Dic₁₉	—	2	4	no	—
26	C₄⋊Dic₁₉	—	4	4	no	—
27	Dic₁₉⋊C₄	—	2	8	no	—
28	Dic₁₉⋊C₄	—	2	8	no	—
29	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	4	no	—
33	C₂×C₄×C₁₉	—	2	4	no	—
34	C₂×C₄×C₁₉	—	2	8	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₂×D₄	1	4	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	8	no	—
42	#2822	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
44	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
45	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
46	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
47	C₄×C₁₉	—	2	4	no	—
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	—	4	4	no	—
50	Dic₁₉	—	4	4	no	—
51	Dic₁₉	—	4	4	no	—
52	C₂×#125	—	19	2	no	—
53	#400	—	19	4	no	—
54	#398	—	19	4	no	—
55	#398	—	19	4	no	—
56	#382	D₁₉	1	1	yes	characteristic
57	C₂×C₁₉	#536	1	2	yes	—
58	C₂×C₁₉	#537	1	1	yes	characteristic
59	C₂×C₁₉	#563	1	2	yes	—
60	C₂×C₁₉	#564	1	2	yes	—
61	#125	—	38	8	no	—
62	C₂×C₄⋊C₄	—	19	4	no	—
63	C₂×C₄⋊C₄	—	19	2	no	—
64	C₂×C₄⋊C₄	—	19	4	no	—
65	C₂×C₄⋊C₄	—	19	2	no	—
66	C₂×C₄⋊C₄	—	19	4	no	—
67	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
68	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
69	#95	—	19	8	no	—
70	#95	—	19	4	no	—
71	#95	C₂×D₁₉	1	4	yes	—
72	C₁₉	#2822	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₄	—	19	4	no	—
74	C₂²×C₄	—	19	4	no	—
75	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
76	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
77	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	4	2	no	—
79	C₄⋊C₄	—	38	8	no	—
80	C₄⋊C₄	—	38	8	no	—
81	C₄⋊C₄	—	38	4	no	—
82	C₄⋊C₄	—	38	4	no	—
83	C₄⋊C₄	—	76	4	no	—
84	C₄²	D₇₆	1	4	yes	—
85	C₂³	C₂³×D₁₉	1	1	yes	characteristic
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	8	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	—	38	8	no	—
96	C₂×C₄	C₂×D₇₆	1	4	yes	—
97	C₂×C₄	C₂×D₇₆	1	2	yes	—
98	C₂²	C₂²×D₇₆	1	1	yes	characteristic
99	C₂²	#10597430	1	1	yes	characteristic
100	C₂²	#10597433	1	1	yes	characteristic
101	C₂²	#10597436	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	2	2	no	—
104	C₄	—	4	4	no	—
105	C₄	—	76	4	no	—
106	C₄	—	76	4	no	—
107	C₂	#11927120	1	2	yes	—
108	C₂	#11927125	1	1	yes	characteristic
109	C₂	#11927294	1	2	yes	—
110	C₂	C₁₉⋊#564	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal

#11926484

C₂

yes

maximal

#11926476

C₂

yes

maximal

#11926474

C₂

yes

maximal

C₁₉×#382

C₂

yes

maximal, characteristic

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×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597316

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2822

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#537

yes

characteristic

C₂×C₁₉

#563

yes

—

C₂×C₁₉

#564

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

—

C₁₉

#2822

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₇₆

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

C₂×D₇₆

yes

—

C₂×C₄

C₂×D₇₆

yes

—

C₂²

C₂²×D₇₆

yes

characteristic

C₂²

#10597430

yes

characteristic

100

C₂²

#10597433

yes

characteristic

101

C₂²

#10597436

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₂

#11927120

yes

—

108

C₂

#11927125

yes

characteristic

109

C₂

#11927294

yes

—

110

C₂

C₁₉⋊#564

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#382	C₂
hypercenter	#382	D₁₉
hypocenter	C₁₉	#2822
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#382

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
72. C₁₉	#2822	semidirect

H ≅ G/N

type

72. C₁₉

#2822

semidirect

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

subgroup	index
C₂×#10597316	2
#11926484	2
#11926476	2
#11926474	2
C₁₉×#382	2
#2822	19

subgroup

index

C₁₉×#382

Subgroups — #14571703

Conjugacy classes of subgroups

Complements

Maximal subgroups