Group #14560071 — subgroups

Subgroups — C₁₉×#2214 #14560071

Order 2432.

150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 60 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×#510	C₂	1	2	yes	maximal
2	C₁₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#443	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#362	C₂	1	2	yes	maximal, complemented
6	C₁₉×#135	C₂²	1	1	yes	characteristic
7	C₂×Q₁₆×C₁₉	—	2	1	no	—
8	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#131	—	2	1	no	—
10	C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₁₉×Q₃₂	—	2	2	no	—
12	C₁₉×SD₃₂	—	2	2	no	—
13	C₁₉×M₃₂	C₂²	1	2	yes	—
14	C₁₉×#108	C₂²	1	1	yes	characteristic
15	C₁₉×#104	—	2	1	no	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	#41×C₁₉	—	2	1	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	Q₁₆×C₁₉	—	2	2	no	—
20	Q₁₆×C₁₉	—	2	2	no	—
21	Q₁₆×C₁₉	—	4	1	no	—
22	Q₁₆×C₁₉	—	4	1	no	—
23	Q₁₆×C₁₉	D₄	1	1	yes	characteristic
24	SD₁₆×C₁₉	—	2	1	no	—
25	D₈×C₁₉	D₄	1	1	yes	characteristic
26	M₁₆×C₁₉	—	2	1	no	—
27	M₁₆×C₁₉	—	4	1	no	—
28	C₂×C₈×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₁₉	—	4	2	no	—
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₁₆×C₁₉	—	2	2	no	—
34	Q₈×C₁₉	—	2	1	no	—
35	Q₈×C₁₉	—	4	2	no	—
36	Q₈×C₁₉	—	4	2	no	—
37	D₄×C₁₉	—	2	1	no	—
38	D₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₈×C₁₉	—	4	1	no	—
44	C₈×C₁₉	D₈	1	1	yes	characteristic
45	C₈×C₁₉	D₈	1	1	yes	characteristic
46	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₈×C₁₉	#41	1	1	yes	characteristic
48	#2214	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂²×C₁₉	—	4	1	no	—
50	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
51	C₄×C₁₉	—	2	2	no	—
52	C₄×C₁₉	—	4	1	no	—
53	C₄×C₁₉	—	8	2	no	—
54	C₄×C₁₉	#121	1	1	yes	characteristic
55	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
56	#510	C₂×C₁₉	1	2	yes	—
57	#494	C₂×C₁₉	1	1	yes	characteristic, complemented
58	#443	C₂×C₁₉	1	1	yes	characteristic
59	#364	C₂×C₁₉	1	1	yes	characteristic, complemented
60	#362	C₂×C₁₉	1	2	yes	complemented
61	C₂×C₁₉	—	2	1	no	—
62	C₂×C₁₉	—	8	1	no	—
63	C₂×C₁₉	#459	1	1	yes	characteristic
64	#135	C₂²×C₁₉	1	1	yes	characteristic
65	C₂×Q₁₆	—	2	1	no	—
66	C₂×Q₁₆	C₂²×C₁₉	1	2	yes	—
67	#131	—	2	1	no	—
68	C₄⋊Q₈	—	2	1	no	—
69	Q₃₂	—	2	2	no	—
70	SD₃₂	—	2	2	no	—
71	M₃₂	C₂²×C₁₉	1	2	yes	—
72	#108	C₂²×C₁₉	1	1	yes	characteristic
73	#104	—	2	1	no	—
74	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
75	C₁₉	#2214	1	1	yes	characteristic, direct product factor, Sylow
76	#41	—	2	1	no	—
77	C₂×Q₈	—	2	2	no	—
78	Q₁₆	—	2	2	no	—
79	Q₁₆	—	2	2	no	—
80	Q₁₆	—	4	1	no	—
81	Q₁₆	—	4	1	no	—
82	Q₁₆	D₄×C₁₉	1	1	yes	characteristic
83	SD₁₆	—	2	1	no	—
84	D₈	D₄×C₁₉	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	4	1	no	—
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
89	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
90	C₄⋊C₄	—	4	2	no	—
91	C₄²	D₄×C₁₉	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	Q₈	—	2	1	no	—
94	Q₈	—	4	2	no	—
95	Q₈	—	4	2	no	—
96	D₄	—	2	1	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
102	C₈	—	4	1	no	—
103	C₈	D₈×C₁₉	1	1	yes	characteristic
104	C₈	D₈×C₁₉	1	1	yes	characteristic
105	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
106	C₈	#41×C₁₉	1	1	yes	characteristic
107	C₂²	—	4	1	no	—
108	C₂²	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	4	1	no	—
111	C₄	—	8	2	no	—
112	C₄	C₁₉×#121	1	1	yes	characteristic
113	C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	8	1	no	—
116	C₂	C₁₉×#459	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#510

C₂

yes

maximal

C₁₉×#494

C₂

yes

maximal, characteristic, complemented

C₁₉×#443

C₂

yes

maximal, characteristic

C₁₉×#364

C₂

yes

maximal, characteristic, complemented

C₁₉×#362

C₂

yes

maximal, complemented

C₁₉×#135

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×#131

—

C₁₉×C₄⋊Q₈

—

C₁₉×Q₃₂

—

C₁₉×SD₃₂

—

C₁₉×M₃₂

C₂²

yes

—

C₁₉×#108

C₂²

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#41×C₁₉

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

D₄

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

#510

C₂×C₁₉

yes

—

#494

C₂×C₁₉

yes

characteristic, complemented

#443

C₂×C₁₉

yes

characteristic

#364

C₂×C₁₉

yes

characteristic, complemented

#362

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

#135

C₂²×C₁₉

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

C₂²×C₁₉

yes

—

#131

—

C₄⋊Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

C₂²×C₁₉

yes

—

#108

C₂²×C₁₉

yes

characteristic

#104

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2214

yes

characteristic, direct product factor, Sylow

#41

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

D₄×C₁₉

yes

characteristic

SD₁₆

—

D₈

D₄×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

102

C₈

—

103

C₈

D₈×C₁₉

yes

characteristic

104

C₈

D₈×C₁₉

yes

characteristic

105

C₈

C₂×D₄×C₁₉

yes

characteristic

106

C₈

#41×C₁₉

yes

characteristic

107

C₂²

—

108

C₂²

C₁₉×AGL(1,ℤ/8)

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

C₁₉×#121

yes

characteristic

113

C₄

C₂×D₈×C₁₉

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

C₁₉×#459

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#459

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₁₉×#135

C₂²

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#494	C₂	semidirect
4. C₁₉×#364	C₂	semidirect
5. C₁₉×#362	C₂	semidirect
48. #2214	C₁₉	direct (N × H)
57. #494	C₂×C₁₉	semidirect
59. #364	C₂×C₁₉	semidirect
60. #362	C₂×C₁₉	semidirect
75. C₁₉	#2214	direct (N × H)

H ≅ G/N

type

2. C₁₉×#494

C₂

semidirect

4. C₁₉×#364

C₂

semidirect

5. C₁₉×#362

C₂

semidirect

48. #2214

C₁₉

direct (N × H)

57. #494

C₂×C₁₉

semidirect

59. #364

C₂×C₁₉

semidirect

60. #362

C₂×C₁₉

semidirect

75. C₁₉

#2214

direct (N × H)

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

subgroup	index
C₁₉×#510	2
C₁₉×#494	2
C₁₉×#443	2
C₁₉×#364	2
C₁₉×#362	2
#2214	19

subgroup

index

C₁₉×#510

C₁₉×#494

C₁₉×#443

C₁₉×#364

C₁₉×#362

#2214

Subgroups — C₁₉×#2214 #14560071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2214 #14560071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2214 #14560071