Group #14560087 — subgroups

Subgroups — C₁₉×#2230 #14560087

Order 2432.

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

normal subgroups only

This group has 126 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×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#443	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#365	C₂	1	2	yes	maximal, complemented
4	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#360	C₂	1	2	yes	maximal
6	C₁₉×#135	C₂²	1	1	yes	characteristic
7	C₁₉×#131	—	2	1	no	—
8	C₁₉×C₄⋊Q₈	—	2	1	no	—
9	C₁₉×M₃₂	C₂²	1	2	yes	—
10	C₁₉×#108	C₂²	1	1	yes	characteristic
11	C₁₉×#106	—	2	1	no	—
12	C₁₉×#106	C₂²	1	2	yes	—
13	C₁₉×#104	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#41×C₁₉	—	2	1	no	—
16	C₂×Q₈×C₁₉	—	4	1	no	—
17	Q₁₆×C₁₉	Q₈	1	1	yes	characteristic, complemented
18	SD₁₆×C₁₉	—	2	1	no	—
19	D₈×C₁₉	Q₈	1	1	yes	characteristic, complemented
20	M₁₆×C₁₉	—	2	1	no	—
21	M₁₆×C₁₉	—	4	1	no	—
22	C₂×C₈×C₁₉	—	4	1	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	4	1	no	—
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₁₆×C₁₉	—	2	2	no	—
29	Q₈×C₁₉	—	2	1	no	—
30	Q₈×C₁₉	—	8	2	no	—
31	D₄×C₁₉	—	2	1	no	—
32	D₄×C₁₉	—	4	1	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₈×C₁₉	—	4	1	no	—
38	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
39	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
40	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₁₉	#41	1	1	yes	characteristic
42	#2230	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₁₉	—	4	1	no	—
44	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₄×C₁₉	—	2	2	no	—
46	C₄×C₁₉	—	4	1	no	—
47	C₄×C₁₉	—	8	2	no	—
48	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
49	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
50	#498	C₂×C₁₉	1	1	yes	characteristic, complemented
51	#443	C₂×C₁₉	1	1	yes	characteristic
52	#365	C₂×C₁₉	1	2	yes	complemented
53	#364	C₂×C₁₉	1	1	yes	characteristic, complemented
54	#360	C₂×C₁₉	1	2	yes	—
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	8	1	no	—
57	C₂×C₁₉	#476	1	1	yes	characteristic
58	#135	C₂²×C₁₉	1	1	yes	characteristic
59	#131	—	2	1	no	—
60	C₄⋊Q₈	—	2	1	no	—
61	M₃₂	C₂²×C₁₉	1	2	yes	—
62	#108	C₂²×C₁₉	1	1	yes	characteristic
63	#106	—	2	1	no	—
64	#106	C₂²×C₁₉	1	2	yes	—
65	#104	—	2	1	no	—
66	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
67	C₁₉	#2230	1	1	yes	characteristic, direct product factor, Sylow
68	#41	—	2	1	no	—
69	C₂×Q₈	—	4	1	no	—
70	Q₁₆	Q₈×C₁₉	1	1	yes	characteristic, complemented
71	SD₁₆	—	2	1	no	—
72	D₈	Q₈×C₁₉	1	1	yes	characteristic, complemented
73	M₁₆	—	2	1	no	—
74	M₁₆	—	4	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
77	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	2	no	—
79	C₄⋊C₄	—	4	1	no	—
80	C₄²	D₄×C₁₉	1	1	yes	characteristic
81	C₁₆	—	2	2	no	—
82	Q₈	—	2	1	no	—
83	Q₈	—	8	2	no	—
84	D₄	—	2	1	no	—
85	D₄	—	4	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	SD₁₆×C₁₉	1	1	yes	characteristic
92	C₈	SD₁₆×C₁₉	1	1	yes	characteristic
93	C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
94	C₈	#41×C₁₉	1	1	yes	characteristic
95	C₂²	—	4	1	no	—
96	C₂²	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	4	1	no	—
99	C₄	—	8	2	no	—
100	C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
101	C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	8	1	no	—
104	C₂	C₁₉×#476	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#498

C₂

yes

maximal, characteristic, complemented

C₁₉×#443

C₂

yes

maximal, characteristic

C₁₉×#365

C₂

yes

maximal, complemented

C₁₉×#364

C₂

yes

maximal, characteristic, complemented

C₁₉×#360

C₂

yes

maximal

C₁₉×#135

C₂²

yes

characteristic

C₁₉×#131

—

C₁₉×C₄⋊Q₈

—

C₁₉×M₃₂

C₂²

yes

—

C₁₉×#108

C₂²

yes

characteristic

C₁₉×#106

—

C₁₉×#106

C₂²

yes

—

C₁₉×#104

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#41×C₁₉

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

characteristic, complemented

SD₁₆×C₁₉

—

D₈×C₁₉

Q₈

yes

characteristic, complemented

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×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

SD₁₆

yes

characteristic

C₈×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

C₂×Q₈

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

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

#498

C₂×C₁₉

yes

characteristic, complemented

#443

C₂×C₁₉

yes

characteristic

#365

C₂×C₁₉

yes

complemented

#364

C₂×C₁₉

yes

characteristic, complemented

#360

C₂×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#476

yes

characteristic

#135

C₂²×C₁₉

yes

characteristic

#131

—

C₄⋊Q₈

—

M₃₂

C₂²×C₁₉

yes

—

#108

C₂²×C₁₉

yes

characteristic

#106

—

#106

C₂²×C₁₉

yes

—

#104

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2230

yes

characteristic, direct product factor, Sylow

#41

—

C₂×Q₈

—

Q₁₆

Q₈×C₁₉

yes

characteristic, complemented

SD₁₆

—

D₈

Q₈×C₁₉

yes

characteristic, complemented

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

SD₁₆×C₁₉

yes

characteristic

C₈

SD₁₆×C₁₉

yes

characteristic

C₈

C₂×Q₈×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

C₁₉×AGL(1,ℤ/8)

yes

characteristic

C₄

—

C₄

—

C₄

—

100

C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

101

C₄

C₂×SD₁₆×C₁₉

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

C₁₉×#476

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#476
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

#476

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
1. C₁₉×#498	C₂	semidirect
3. C₁₉×#365	C₂	semidirect
4. C₁₉×#364	C₂	semidirect
17. Q₁₆×C₁₉	Q₈	semidirect
19. D₈×C₁₉	Q₈	semidirect
42. #2230	C₁₉	direct (N × H)
50. #498	C₂×C₁₉	semidirect
52. #365	C₂×C₁₉	semidirect
53. #364	C₂×C₁₉	semidirect
67. C₁₉	#2230	direct (N × H)
70. Q₁₆	Q₈×C₁₉	semidirect
72. D₈	Q₈×C₁₉	semidirect

H ≅ G/N

type

1. C₁₉×#498

C₂

semidirect

3. C₁₉×#365

C₂

semidirect

4. C₁₉×#364

C₂

semidirect

17. Q₁₆×C₁₉

Q₈

semidirect

19. D₈×C₁₉

Q₈

semidirect

42. #2230

C₁₉

direct (N × H)

50. #498

C₂×C₁₉

semidirect

52. #365

C₂×C₁₉

semidirect

53. #364

C₂×C₁₉

semidirect

67. C₁₉

#2230

direct (N × H)

70. Q₁₆

Q₈×C₁₉

semidirect

72. D₈

Q₈×C₁₉

semidirect

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

subgroup	index
C₁₉×#498	2
C₁₉×#443	2
C₁₉×#365	2
C₁₉×#364	2
C₁₉×#360	2
#2230	19

subgroup

index

C₁₉×#498

C₁₉×#443

C₁₉×#365

C₁₉×#364

C₁₉×#360

#2230

Subgroups — C₁₉×#2230 #14560087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2230 #14560087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2230 #14560087