Group #14563390 — subgroups

Subgroups — #14563390

Order 2432.

200 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 105 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	#11926499	C₂	1	2	yes	maximal
2	C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
3	#11926301	C₂	1	1	yes	maximal, characteristic
4	#11926300	C₂	1	2	yes	maximal
5	C₁₉×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#117	C₂²	1	1	yes	characteristic
9	#10597372	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	2	yes	—
11	C₁₉×#97	C₄	1	2	yes	complemented
12	C₄×C₈×C₁₉	C₄	1	2	yes	complemented
13	#10597272	C₄	1	4	yes	complemented
14	C₈×Dic₁₉	C₄	1	4	yes	complemented
15	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	M₁₆×C₁₉	—	2	2	no	—
17	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₄²×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄×Dic₁₉	C₂×C₄	1	4	yes	—
28	#64520	—	2	2	no	—
29	#64520	—	2	2	no	—
30	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
31	C₂³×C₁₉	#41	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	2	no	—
33	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
34	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
36	C₂×C₄×C₁₉	#41	1	2	yes	—
37	C₂×Dic₁₉	—	2	4	no	—
38	C₈×C₁₉	—	2	2	no	—
39	C₈×C₁₉	C₄²	1	2	yes	—
40	C₈×C₁₉	C₄²	1	1	yes	characteristic
41	C₈×C₁₉	C₄²	1	1	yes	characteristic
42	C₁₉⋊C₈	—	2	4	no	—
43	#1747	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	4	1	no	—
45	C₂²×C₁₉	#117	1	2	yes	—
46	C₂²×C₁₉	#117	1	1	yes	characteristic
47	C₄×C₁₉	—	4	2	no	—
48	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
49	C₄×C₁₉	#117	1	2	yes	—
50	C₄×C₁₉	#117	1	1	yes	characteristic
51	Dic₁₉	—	4	4	no	—
52	#405	—	19	2	no	—
53	#405	D₁₉	1	1	yes	characteristic
54	#338	—	19	1	no	—
55	H(3,ℤ/4)	—	19	1	no	—
56	H(3,ℤ/4)	—	19	2	no	—
57	C₂×C₁₉	—	2	2	no	—
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	#376	1	1	yes	characteristic
60	C₂×M₁₆	—	19	2	no	—
61	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
62	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
63	#117	—	19	2	no	—
64	#117	C₂×D₁₉	1	1	yes	characteristic
65	#97	—	19	4	no	—
66	#97	Dic₁₉	1	2	yes	complemented
67	C₄×C₈	—	19	4	no	—
68	C₄×C₈	Dic₁₉	1	2	yes	complemented
69	C₁₉	#1747	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	38	2	no	—
73	M₁₆	—	38	2	no	—
74	C₂×C₈	—	19	4	no	—
75	C₂×C₈	C₄×D₁₉	1	2	yes	—
76	C₂×C₈	C₄×D₁₉	1	2	yes	—
77	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
78	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
80	C₄⋊C₄	—	2	1	no	—
81	C₄⋊C₄	—	38	2	no	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	—	38	2	no	—
84	C₄²	—	19	4	no	—
85	C₄²	C₂×Dic₁₉	1	2	yes	—
86	C₂³	#64541	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	38	4	no	—
89	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
90	C₂×C₄	#64541	1	1	yes	characteristic
91	C₂×C₄	#64541	1	2	yes	—
92	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	—	38	4	no	—
95	C₈	C₄×Dic₁₉	1	1	yes	characteristic
96	C₈	C₄×Dic₁₉	1	2	yes	—
97	C₈	C₄×Dic₁₉	1	1	yes	characteristic
98	C₂²	—	4	1	no	—
99	C₂²	#10597318	1	2	yes	—
100	C₂²	#10597372	1	1	yes	characteristic
101	C₄	—	4	2	no	—
102	C₄	—	76	4	no	—
103	C₄	#10597318	1	2	yes	—
104	C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
105	C₄	#10597372	1	1	yes	characteristic
106	C₂	—	2	1	no	—
107	C₂	—	2	2	no	—
108	C₂	#11926390	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926499

C₂

yes

maximal

C₁₉⋊#338

C₂

yes

maximal, characteristic

#11926301

C₂

yes

maximal, characteristic

#11926300

C₂

yes

maximal

C₁₉×#405

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597372

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₁₉×#97

C₄

yes

complemented

C₄×C₈×C₁₉

C₄

yes

complemented

#10597272

C₄

yes

complemented

C₈×Dic₁₉

C₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄²

yes

—

C₈×C₁₉

C₄²

yes

characteristic

C₈×C₁₉

C₄²

yes

characteristic

C₁₉⋊C₈

—

#1747

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#117

yes

—

C₂²×C₁₉

#117

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

#117

yes

—

C₄×C₁₉

#117

yes

characteristic

Dic₁₉

—

#405

—

#405

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#376

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

#117

C₂×D₁₉

yes

characteristic

#97

—

#97

Dic₁₉

yes

complemented

C₄×C₈

—

C₄×C₈

Dic₁₉

yes

complemented

C₁₉

#1747

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×Dic₁₉

yes

—

C₂³

#64541

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₉

yes

—

C₂×C₄

#64541

yes

characteristic

C₂×C₄

#64541

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

C₄×Dic₁₉

yes

characteristic

C₈

C₄×Dic₁₉

yes

—

C₈

C₄×Dic₁₉

yes

characteristic

C₂²

—

C₂²

#10597318

yes

—

100

C₂²

#10597372

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

#10597318

yes

—

104

C₄

C₂×C₄×Dic₁₉

yes

characteristic

105

C₄

#10597372

yes

characteristic

106

C₂

—

107

C₂

—

108

C₂

#11926390

yes

characteristic

	subgroup	G/H
center	C₈	C₄×Dic₁₉
commutator	C₄×C₁₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#405	C₂
socle	C₂×C₁₉	#376
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#405	D₁₉
hypocenter	C₁₉	#1747
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ #405

subgroup

G/H

center

C₈

C₄×Dic₁₉

commutator

C₄×C₁₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#405

C₂

C₂×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₈ ◁ #405

N	H ≅ G/N	type
11. C₁₉×#97	C₄	semidirect
12. C₄×C₈×C₁₉	C₄	semidirect
13. #10597272	C₄	semidirect
14. C₈×Dic₁₉	C₄	semidirect
66. #97	Dic₁₉	semidirect
68. C₄×C₈	Dic₁₉	semidirect
69. C₁₉	#1747	semidirect

H ≅ G/N

type

11. C₁₉×#97

C₄

semidirect

12. C₄×C₈×C₁₉

C₄

semidirect

13. #10597272

C₄

semidirect

14. C₈×Dic₁₉

C₄

semidirect

66. #97

Dic₁₉

semidirect

68. C₄×C₈

Dic₁₉

semidirect

69. C₁₉

#1747

semidirect

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

subgroup	index
#11926499	2
C₁₉⋊#338	2
#11926301	2
#11926300	2
C₁₉×#405	2
#1747	19

subgroup

index

C₁₉⋊#338

C₁₉×#405

Subgroups — #14563390

Conjugacy classes of subgroups

Complements

Maximal subgroups