Group #14560100 — subgroups

Subgroups — C₁₉×#2243 #14560100

Order 2432.

142 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 64 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×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#495	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#358	C₂	1	2	yes	maximal, complemented
4	C₁₉×#357	C₂	1	2	yes	maximal
5	C₁₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×SD₁₆×C₁₉	—	2	1	no	—
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	—	2	1	no	—
10	C₁₉×#124	—	2	1	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
12	C₁₉×#107	—	2	1	no	—
13	C₁₉×#107	C₂²	1	2	yes	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×Q₈×C₁₉	—	4	1	no	—
17	C₂×D₄×C₁₉	—	2	1	no	—
18	Q₁₆×C₁₉	—	2	2	no	—
19	SD₁₆×C₁₉	—	4	2	no	—
20	D₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	4	1	no	—
25	C₂²⋊C₄×C₁₉	—	4	1	no	—
26	C₂²⋊C₄×C₁₉	—	4	1	no	—
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₁₆×C₁₉	—	2	2	no	—
29	C₂³×C₁₉	—	4	1	no	—
30	Q₈×C₁₉	—	4	1	no	—
31	Q₈×C₁₉	—	4	1	no	—
32	Q₈×C₁₉	—	8	2	no	—
33	D₄×C₁₉	—	4	1	no	—
34	D₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₈×C₁₉	SD₁₆	1	2	yes	—
41	C₈×C₁₉	#41	1	2	yes	—
42	#2243	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₁₉	—	8	1	no	—
44	C₂²×C₁₉	—	8	1	no	—
45	C₂²×C₁₉	—	8	1	no	—
46	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	8	1	no	—
50	C₄×C₁₉	—	8	2	no	—
51	C₄×C₁₉	#124	1	1	yes	characteristic
52	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
53	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
54	#495	C₂×C₁₉	1	1	yes	characteristic
55	#358	C₂×C₁₉	1	2	yes	complemented
56	#357	C₂×C₁₉	1	2	yes	—
57	#346	C₂×C₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	16	1	no	—
59	C₂×C₁₉	#486	1	1	yes	characteristic
60	C₂×C₁₉	#509	1	1	yes	characteristic
61	C₂×C₁₉	#510	1	1	yes	characteristic
62	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
63	C₂×SD₁₆	—	2	1	no	—
64	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
65	C₄⋊Q₈	—	2	1	no	—
66	#124	—	2	1	no	—
67	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
68	#107	—	2	1	no	—
69	#107	C₂²×C₁₉	1	2	yes	—
70	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
71	C₁₉	#2243	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×Q₈	—	2	1	no	—
73	C₂×Q₈	—	4	1	no	—
74	C₂×D₄	—	2	1	no	—
75	Q₁₆	—	2	2	no	—
76	SD₁₆	—	4	2	no	—
77	D₈	—	2	2	no	—
78	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
79	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	4	1	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₂²⋊C₄	—	4	1	no	—
84	C₄²	D₄×C₁₉	1	1	yes	characteristic
85	C₁₆	—	2	2	no	—
86	C₂³	—	4	1	no	—
87	Q₈	—	4	1	no	—
88	Q₈	—	4	1	no	—
89	Q₈	—	8	2	no	—
90	D₄	—	4	1	no	—
91	D₄	—	4	1	no	—
92	C₂×C₄	—	4	1	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
95	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
96	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
97	C₈	SD₁₆×C₁₉	1	2	yes	—
98	C₈	#41×C₁₉	1	2	yes	—
99	C₂²	—	8	1	no	—
100	C₂²	—	8	1	no	—
101	C₂²	—	8	1	no	—
102	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	8	1	no	—
106	C₄	—	8	2	no	—
107	C₄	C₁₉×#124	1	1	yes	characteristic
108	C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
109	C₂	—	16	1	no	—
110	C₂	C₁₉×#486	1	1	yes	characteristic
111	C₂	C₁₉×#509	1	1	yes	characteristic
112	C₂	C₁₉×#510	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic, complemented

C₁₉×#495

C₂

yes

maximal, characteristic

C₁₉×#358

C₂

yes

maximal, complemented

C₁₉×#357

C₂

yes

maximal

C₁₉×#346

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#124

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

—

C₁₉×#107

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

SD₁₆

yes

—

C₈×C₁₉

#41

yes

—

#2243

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

#500

C₂×C₁₉

yes

characteristic, complemented

#495

C₂×C₁₉

yes

characteristic

#358

C₂×C₁₉

yes

complemented

#357

C₂×C₁₉

yes

—

#346

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂²×C₁₉

yes

characteristic

C₄⋊Q₈

—

#124

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

—

#107

C₂²×C₁₉

yes

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2243

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

SD₁₆×C₁₉

yes

—

C₈

#41×C₁₉

yes

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×D₈×C₁₉

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

C₁₉×#124

yes

characteristic

108

C₄

C₂×SD₁₆×C₁₉

yes

characteristic

109

C₂

—

110

C₂

C₁₉×#486

yes

characteristic

111

C₂

C₁₉×#509

yes

characteristic

112

C₂

C₁₉×#510

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×D₈×C₁₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₂×D₈×C₁₉

C₂²

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#500	C₂	semidirect
3. C₁₉×#358	C₂	semidirect
5. C₁₉×#346	C₂	semidirect
42. #2243	C₁₉	direct (N × H)
53. #500	C₂×C₁₉	semidirect
55. #358	C₂×C₁₉	semidirect
57. #346	C₂×C₁₉	semidirect
71. C₁₉	#2243	direct (N × H)

H ≅ G/N

type

1. C₁₉×#500

C₂

semidirect

3. C₁₉×#358

C₂

semidirect

5. C₁₉×#346

C₂

semidirect

42. #2243

C₁₉

direct (N × H)

53. #500

C₂×C₁₉

semidirect

55. #358

C₂×C₁₉

semidirect

57. #346

C₂×C₁₉

semidirect

71. C₁₉

#2243

direct (N × H)

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

subgroup	index
C₁₉×#500	2
C₁₉×#495	2
C₁₉×#358	2
C₁₉×#357	2
C₁₉×#346	2
#2243	19

subgroup

index

C₁₉×#500

C₁₉×#495

C₁₉×#358

C₁₉×#357

C₁₉×#346

#2243

Subgroups — C₁₉×#2243 #14560100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2243 #14560100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2243 #14560100