Group #14560086 — subgroups

Subgroups — C₁₉×#2229 #14560086

Order 2432.

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

normal subgroups only

This group has 124 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×#499	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#367	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#366	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#358	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#358	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#125	—	2	1	no	—
10	C₄×Q₈×C₁₉	—	2	1	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₁₉×#107	C₂²	1	1	yes	characteristic
15	C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₁₉×#106	—	2	1	no	—
17	C₁₉×#103	—	2	1	no	—
18	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	Q₁₆×C₁₉	—	2	1	no	—
21	Q₁₆×C₁₉	Q₈	1	2	yes	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₄⋊C₄×C₁₉	—	4	1	no	—
28	C₄⋊C₄×C₁₉	—	4	1	no	—
29	C₄⋊C₄×C₁₉	—	4	1	no	—
30	C₄²×C₁₉	—	4	1	no	—
31	C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₁₆×C₁₉	—	2	1	no	—
33	C₁₆×C₁₉	—	2	1	no	—
34	Q₈×C₁₉	—	2	2	no	—
35	Q₈×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₁₉	#41	1	1	yes	characteristic
46	#2229	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	4	2	no	—
51	C₄×C₁₉	—	8	1	no	—
52	C₄×C₁₉	—	8	1	no	—
53	C₄×C₁₉	—	8	1	no	—
54	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₄×C₁₉	#137	1	1	yes	characteristic
56	#499	C₂×C₁₉	1	1	yes	characteristic
57	C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
58	#367	C₂×C₁₉	1	1	yes	characteristic
59	#366	C₂×C₁₉	1	1	yes	characteristic
60	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
61	#358	C₂×C₁₉	1	1	yes	characteristic
62	#358	C₂×C₁₉	1	1	yes	characteristic
63	C₂×C₁₉	#474	1	1	yes	characteristic
64	C₂×C₁₉	#508	1	1	yes	characteristic
65	C₂×C₁₉	#510	1	1	yes	characteristic
66	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
67	#125	—	2	1	no	—
68	C₄×Q₈	—	2	1	no	—
69	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
70	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
71	#107	C₂²×C₁₉	1	1	yes	characteristic
72	#107	C₂²×C₁₉	1	1	yes	characteristic
73	#107	C₂²×C₁₉	1	1	yes	characteristic
74	#106	—	2	1	no	—
75	#103	—	2	1	no	—
76	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
77	C₁₉	#2229	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×Q₈	—	2	1	no	—
79	Q₁₆	—	2	1	no	—
80	Q₁₆	Q₈×C₁₉	1	2	yes	—
81	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
82	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	2	1	no	—
85	C₄⋊C₄	—	2	1	no	—
86	C₄⋊C₄	—	4	1	no	—
87	C₄⋊C₄	—	4	1	no	—
88	C₄⋊C₄	—	4	1	no	—
89	C₄²	—	4	1	no	—
90	C₄²	D₄×C₁₉	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	2	1	no	—
93	Q₈	—	2	2	no	—
94	Q₈	—	4	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
100	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
101	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
104	C₈	#41×C₁₉	1	1	yes	characteristic
105	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	8	1	no	—
111	C₄	—	8	1	no	—
112	C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
113	C₄	C₁₉×#137	1	1	yes	characteristic
114	C₂	C₁₉×#474	1	1	yes	characteristic
115	C₂	C₁₉×#508	1	1	yes	characteristic
116	C₂	C₁₉×#510	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#499

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#367

C₂

yes

maximal, characteristic

C₁₉×#366

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₁₉×#358

C₂

yes

maximal, characteristic

C₁₉×#358

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#125

—

C₄×Q₈×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#106

—

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×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

—

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₄×Q₁₆

C₂×C₁₉

yes

characteristic

#367

C₂×C₁₉

yes

characteristic

#366

C₂×C₁₉

yes

characteristic

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic

#358

C₂×C₁₉

yes

characteristic

#358

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

#125

—

C₄×Q₈

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

characteristic

#106

—

#103

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2229

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

Q₈×C₁₉

yes

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

100

C₂×C₄

D₈×C₁₉

yes

characteristic

101

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

102

C₈

—

103

C₈

C₂×Q₈×C₁₉

yes

characteristic

104

C₈

#41×C₁₉

yes

characteristic

105

C₂²

C₂×D₈×C₁₉

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

113

C₄

C₁₉×#137

yes

characteristic

114

C₂

C₁₉×#474

yes

characteristic

115

C₂

C₁₉×#508

yes

characteristic

116

C₂

C₁₉×#510

yes

characteristic

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

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
46. #2229	C₁₉	direct (N × H)
77. C₁₉	#2229	direct (N × H)

H ≅ G/N

type

46. #2229

C₁₉

direct (N × H)

77. C₁₉

#2229

direct (N × H)

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

subgroup	index
C₁₉×#499	2
C₄×Q₁₆×C₁₉	2
C₁₉×#367	2
C₁₉×#366	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#358	2
#2229	19

subgroup

index

C₁₉×#499

C₄×Q₁₆×C₁₉

C₁₉×#367

C₁₉×#366

C₁₉×C₄⋊C₁₆

C₁₉×#358

#2229

Subgroups — C₁₉×#2229 #14560086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2229 #14560086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2229 #14560086