Group #14559946 — subgroups

Subgroups — C₁₉×#2089 #14559946

Order 2432.

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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×#428	C₂	1	2	yes	maximal
2	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#424	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#343	C₂	1	2	yes	maximal
5	C₁₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#107	—	2	2	no	—
12	C₁₉×#107	—	2	2	no	—
13	C₁₉×#106	—	2	2	no	—
14	C₁₉×C₄⋊C₈	—	2	2	no	—
15	C₂²×C₄×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	M₁₆×C₁₉	—	2	2	no	—
18	M₁₆×C₁₉	—	2	2	no	—
19	M₁₆×C₁₉	Q₈	1	4	yes	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	—	2	2	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	D₄	1	2	yes	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	—	2	1	no	—
30	C₂³×C₁₉	#41	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	8	2	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₁₉	#41	1	2	yes	—
39	C₈×C₁₉	—	2	4	no	—
40	C₈×C₁₉	—	2	2	no	—
41	C₈×C₁₉	—	4	1	no	—
42	#2089	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	#121	1	1	yes	characteristic
46	C₂²×C₁₉	#125	1	2	yes	—
47	C₄×C₁₉	—	4	1	no	—
48	C₄×C₁₉	—	4	1	no	—
49	C₄×C₁₉	—	8	2	no	—
50	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
51	C₄×C₁₉	#123	1	1	yes	characteristic
52	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
53	#428	C₂×C₁₉	1	2	yes	—
54	C₂×#107	C₂×C₁₉	1	1	yes	characteristic
55	#424	C₂×C₁₉	1	1	yes	characteristic
56	#343	C₂×C₁₉	1	2	yes	—
57	#341	C₂×C₁₉	1	1	yes	characteristic
58	C₂×C₁₉	—	2	2	no	—
59	C₂×C₁₉	#398	1	1	yes	characteristic
60	C₂×C₁₉	#472	1	1	yes	characteristic
61	C₂×C₁₉	#473	1	1	yes	characteristic
62	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
63	C₂×M₁₆	C₂²×C₁₉	1	2	yes	—
64	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
65	#117	C₂²×C₁₉	1	1	yes	characteristic
66	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
67	#107	—	2	2	no	—
68	#107	—	2	2	no	—
69	#106	—	2	2	no	—
70	C₄⋊C₈	—	2	2	no	—
71	C₁₉	#2089	1	1	yes	characteristic, direct product factor, Sylow
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	2	2	no	—
76	M₁₆	Q₈×C₁₉	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	D₄×C₁₉	1	2	yes	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
84	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
85	C₂²⋊C₄	—	2	1	no	—
86	C₄²	—	2	1	no	—
87	C₂³	#41×C₁₉	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	8	2	no	—
92	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
94	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
95	C₂×C₄	#41×C₁₉	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	4	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	C₁₉×#121	1	1	yes	characteristic
102	C₂²	C₁₉×#125	1	2	yes	—
103	C₄	—	4	1	no	—
104	C₄	—	4	1	no	—
105	C₄	—	8	2	no	—
106	C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
107	C₄	C₁₉×#123	1	1	yes	characteristic
108	C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	C₁₉×#398	1	1	yes	characteristic
111	C₂	C₁₉×#472	1	1	yes	characteristic
112	C₂	C₁₉×#473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#428

C₂

yes

maximal

C₂×C₁₉×#107

C₂

yes

maximal, characteristic

C₁₉×#424

C₂

yes

maximal, characteristic

C₁₉×#343

C₂

yes

maximal

C₁₉×#341

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2089

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#125

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#123

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

#428

C₂×C₁₉

yes

—

C₂×#107

C₂×C₁₉

yes

characteristic

#424

C₂×C₁₉

yes

characteristic

#343

C₂×C₁₉

yes

—

#341

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

C₂²×C₁₉

yes

characteristic

C₂×M₁₆

C₂²×C₁₉

yes

—

C₂²×C₈

C₂²×C₁₉

yes

characteristic

#117

C₂²×C₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₁₉

#2089

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₂³×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Q₈×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₂²⋊C₄

—

C₄²

—

C₂³

#41×C₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

C₂×Q₈×C₁₉

yes

—

C₂×C₄

#41×C₁₉

yes

—

C₈

—

C₈

—

C₈

—

C₂²

—

100

C₂²

—

101

C₂²

C₁₉×#121

yes

characteristic

102

C₂²

C₁₉×#125

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

C₁₉×C₂²⋊Q₈

yes

—

107

C₄

C₁₉×#123

yes

characteristic

108

C₄

C₁₉×C₄⋊Q₈

yes

characteristic

109

C₂

—

110

C₂

C₁₉×#398

yes

characteristic

111

C₂

C₁₉×#472

yes

characteristic

112

C₂

C₁₉×#473

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#121

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

C₂³×C₁₉

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
42. #2089	C₁₉	direct (N × H)
71. C₁₉	#2089	direct (N × H)

H ≅ G/N

type

42. #2089

C₁₉

direct (N × H)

71. C₁₉

#2089

direct (N × H)

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

subgroup	index
C₁₉×#428	2
C₂×C₁₉×#107	2
C₁₉×#424	2
C₁₉×#343	2
C₁₉×#341	2
#2089	19

subgroup

index

C₁₉×#428

C₂×C₁₉×#107

C₁₉×#424

C₁₉×#343

C₁₉×#341

#2089

Subgroups — C₁₉×#2089 #14559946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2089 #14559946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2089 #14559946