Group #14559552 — subgroups

Subgroups — C₁₉×#1695 #14559552

Order 2432.

154 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 68 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×#476	C₂	1	2	yes	maximal
3	C₁₉×#436	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#333	C₂	1	2	yes	maximal, complemented
6	C₂×M₁₆×C₁₉	—	2	1	no	—
7	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	—	2	1	no	—
11	C₁₉×#106	—	2	2	no	—
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₁₉×#102	—	2	2	no	—
15	C₁₉×C₂²⋊C₈	—	2	1	no	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	M₁₆×C₁₉	—	4	2	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×C₁₉	—	2	1	no	—
31	Q₈×C₁₉	—	8	2	no	—
32	D₄×C₁₉	—	2	2	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
40	C₈×C₁₉	—	2	1	no	—
41	C₈×C₁₉	—	4	1	no	—
42	C₈×C₁₉	—	4	2	no	—
43	C₈×C₁₉	SD₁₆	1	2	yes	—
44	#1695	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₁₉	—	4	1	no	—
46	C₂²×C₁₉	—	4	1	no	—
47	C₂²×C₁₉	—	4	1	no	—
48	C₂²×C₁₉	#121	1	1	yes	characteristic
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	4	1	no	—
51	C₄×C₁₉	—	8	2	no	—
52	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
53	C₄×C₁₉	#137	1	1	yes	characteristic
54	C₄×C₁₉	#137	1	2	yes	—
55	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
56	#476	C₂×C₁₉	1	2	yes	—
57	#436	C₂×C₁₉	1	1	yes	characteristic
58	#334	C₂×C₁₉	1	1	yes	characteristic, complemented
59	#333	C₂×C₁₉	1	2	yes	complemented
60	C₂×C₁₉	—	8	1	no	—
61	C₂×C₁₉	#461	1	1	yes	characteristic
62	C₂×C₁₉	#470	1	1	yes	characteristic
63	C₂×C₁₉	#472	1	1	yes	characteristic
64	C₂×M₁₆	—	2	1	no	—
65	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
66	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
67	#107	—	2	1	no	—
68	#107	—	2	1	no	—
69	#106	—	2	2	no	—
70	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
71	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
72	#102	—	2	2	no	—
73	C₂²⋊C₈	—	2	1	no	—
74	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
75	C₁₉	#1695	1	1	yes	characteristic, direct product factor, Sylow
76	C₂×Q₈	—	2	2	no	—
77	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
78	C₂²×C₄	—	2	1	no	—
79	M₁₆	—	4	2	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
83	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
84	C₄⋊C₄	—	2	2	no	—
85	C₄⋊C₄	—	2	2	no	—
86	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
87	C₂²⋊C₄	—	2	1	no	—
88	C₄²	C₂³×C₁₉	1	1	yes	characteristic
89	C₂³	—	2	1	no	—
90	Q₈	—	8	2	no	—
91	D₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
97	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
98	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	1	no	—
101	C₈	—	4	2	no	—
102	C₈	SD₁₆×C₁₉	1	2	yes	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	1	no	—
105	C₂²	—	4	1	no	—
106	C₂²	C₁₉×#121	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	4	1	no	—
109	C₄	—	8	2	no	—
110	C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
111	C₄	C₁₉×#137	1	1	yes	characteristic
112	C₄	C₁₉×#137	1	2	yes	—
113	C₂	—	8	1	no	—
114	C₂	C₁₉×#461	1	1	yes	characteristic
115	C₂	C₁₉×#470	1	1	yes	characteristic
116	C₂	C₁₉×#472	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic, complemented

C₁₉×#476

C₂

yes

maximal

C₁₉×#436

C₂

yes

maximal, characteristic

C₁₉×#334

C₂

yes

maximal, characteristic, complemented

C₁₉×#333

C₂

yes

maximal, complemented

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#102

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

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

#41

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₁₆

yes

—

#1695

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#500

C₂×C₁₉

yes

characteristic, complemented

#476

C₂×C₁₉

yes

—

#436

C₂×C₁₉

yes

characteristic

#334

C₂×C₁₉

yes

characteristic, complemented

#333

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₄⋊Q₈

C₂²×C₁₉

yes

—

C₄×D₄

C₂²×C₁₉

yes

—

—

—

C₄⋊C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₂²×C₁₉

yes

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#1695

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

D₄×C₁₉

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂³×C₁₉

yes

characteristic

C₂³

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

#41×C₁₉

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₈

SD₁₆×C₁₉

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₁₉×#121

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

C₂×SD₁₆×C₁₉

yes

characteristic

111

C₄

C₁₉×#137

yes

characteristic

112

C₄

C₁₉×#137

yes

—

113

C₂

—

114

C₂

C₁₉×#461

yes

characteristic

115

C₂

C₁₉×#470

yes

characteristic

116

C₂

C₁₉×#472

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#121

commutator, Frattini, cosocle

C₄²

C₂³×C₁₉

prime radical

C₂×D₄×C₁₉

D₄

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#500	C₂	semidirect
4. C₁₉×#334	C₂	semidirect
5. C₁₉×#333	C₂	semidirect
44. #1695	C₁₉	direct (N × H)
55. #500	C₂×C₁₉	semidirect
58. #334	C₂×C₁₉	semidirect
59. #333	C₂×C₁₉	semidirect
75. C₁₉	#1695	direct (N × H)

H ≅ G/N

type

1. C₁₉×#500

C₂

semidirect

4. C₁₉×#334

C₂

semidirect

5. C₁₉×#333

C₂

semidirect

44. #1695

C₁₉

direct (N × H)

55. #500

C₂×C₁₉

semidirect

58. #334

C₂×C₁₉

semidirect

59. #333

C₂×C₁₉

semidirect

75. C₁₉

#1695

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×#476	2
C₁₉×#436	2
C₁₉×#334	2
C₁₉×#333	2
#1695	19

subgroup

index

C₁₉×#500

C₁₉×#476

C₁₉×#436

C₁₉×#334

C₁₉×#333

#1695

Subgroups — C₁₉×#1695 #14559552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1695 #14559552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1695 #14559552