Group #14560083 — subgroups

Subgroups — C₁₉×#2226 #14560083

Order 2432.

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

normal subgroups only

This group has 142 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	C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#367	C₂	1	2	yes	maximal, complemented
4	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#357	C₂	1	2	yes	maximal
6	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊Q₈	—	2	1	no	—
8	C₄×D₄×C₁₉	—	2	1	no	—
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#107	—	2	1	no	—
11	C₁₉×#107	C₂²	1	2	yes	—
12	C₁₉×#107	C₂²	1	1	yes	characteristic
13	C₁₉×#102	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₉	—	4	1	no	—
16	C₂×D₄×C₁₉	—	2	1	no	—
17	C₂²×C₄×C₁₉	—	4	1	no	—
18	D₈×C₁₉	—	2	1	no	—
19	D₈×C₁₉	Q₈	1	2	yes	complemented
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	4	1	no	—
25	C₂²⋊C₄×C₁₉	—	4	1	no	—
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	—	4	1	no	—
29	Q₈×C₁₉	—	8	2	no	—
30	D₄×C₁₉	—	2	2	no	—
31	D₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	—	4	1	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	8	2	no	—
35	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₁₉	#41	1	1	yes	characteristic
41	#2226	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₁₉	—	4	2	no	—
43	C₂²×C₁₉	—	8	1	no	—
44	C₂²×C₁₉	—	8	1	no	—
45	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	8	1	no	—
48	C₄×C₁₉	—	8	2	no	—
49	C₄×C₁₉	SD₃₂	1	2	yes	—
50	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₄×C₁₉	#137	1	1	yes	characteristic
52	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
53	C₄×D₈	C₂×C₁₉	1	1	yes	characteristic
54	#367	C₂×C₁₉	1	2	yes	complemented
55	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
56	#357	C₂×C₁₉	1	2	yes	—
57	C₂×C₁₉	—	8	2	no	—
58	C₂×C₁₉	#474	1	1	yes	characteristic
59	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
60	C₂×C₁₉	#509	1	1	yes	characteristic
61	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
62	C₄⋊Q₈	—	2	1	no	—
63	C₄×D₄	—	2	1	no	—
64	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
65	#107	—	2	1	no	—
66	#107	C₂²×C₁₉	1	2	yes	—
67	#107	C₂²×C₁₉	1	1	yes	characteristic
68	#102	—	2	1	no	—
69	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
70	C₁₉	#2226	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×Q₈	—	4	1	no	—
72	C₂×D₄	—	2	1	no	—
73	C₂²×C₄	—	4	1	no	—
74	D₈	—	2	1	no	—
75	D₈	Q₈×C₁₉	1	2	yes	complemented
76	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
77	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	4	1	no	—
81	C₂²⋊C₄	—	4	1	no	—
82	C₄²	D₄×C₁₉	1	1	yes	characteristic
83	C₁₆	—	2	2	no	—
84	C₂³	—	4	1	no	—
85	Q₈	—	8	2	no	—
86	D₄	—	2	2	no	—
87	D₄	—	4	1	no	—
88	C₂×C₄	—	4	1	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	8	2	no	—
91	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
92	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
96	C₈	#41×C₁₉	1	1	yes	characteristic
97	C₂²	—	4	2	no	—
98	C₂²	—	8	1	no	—
99	C₂²	—	8	1	no	—
100	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	8	1	no	—
103	C₄	—	8	2	no	—
104	C₄	C₁₉×SD₃₂	1	2	yes	—
105	C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
106	C₄	C₁₉×#137	1	1	yes	characteristic
107	C₂	—	8	2	no	—
108	C₂	C₁₉×#474	1	1	yes	characteristic
109	C₂	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
110	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic, complemented

C₄×D₈×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#367

C₂

yes

maximal, complemented

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₄×D₄×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

—

C₁₉×#107

C₂²

yes

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×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

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

SD₃₂

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic, complemented

C₄×D₈

C₂×C₁₉

yes

characteristic

#367

C₂×C₁₉

yes

complemented

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

#357

C₂×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#474

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×D₈

C₂²×C₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×D₄

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

—

#107

C₂²×C₁₉

yes

—

#107

C₂²×C₁₉

yes

characteristic

#102

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2226

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

Q₈×C₁₉

yes

complemented

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

C₂×Q₈×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×D₈×C₁₉

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

C₁₉×SD₃₂

yes

—

105

C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

106

C₄

C₁₉×#137

yes

characteristic

107

C₂

—

108

C₂

C₁₉×#474

yes

characteristic

109

C₂

C₂×C₁₉×SD₃₂

yes

characteristic

110

C₂

C₁₉×#509

yes

characteristic

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

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₂×D₈×C₁₉

C₂²

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
1. C₁₉×#500	C₂	semidirect
3. C₁₉×#367	C₂	semidirect
4. C₁₉×C₄⋊C₁₆	C₂	semidirect
19. D₈×C₁₉	Q₈	semidirect
41. #2226	C₁₉	direct (N × H)
52. #500	C₂×C₁₉	semidirect
54. #367	C₂×C₁₉	semidirect
55. C₄⋊C₁₆	C₂×C₁₉	semidirect
70. C₁₉	#2226	direct (N × H)
75. D₈	Q₈×C₁₉	semidirect

H ≅ G/N

type

1. C₁₉×#500

C₂

semidirect

3. C₁₉×#367

C₂

semidirect

4. C₁₉×C₄⋊C₁₆

C₂

semidirect

19. D₈×C₁₉

Q₈

semidirect

41. #2226

C₁₉

direct (N × H)

52. #500

C₂×C₁₉

semidirect

54. #367

C₂×C₁₉

semidirect

55. C₄⋊C₁₆

C₂×C₁₉

semidirect

70. C₁₉

#2226

direct (N × H)

75. D₈

Q₈×C₁₉

semidirect

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

subgroup	index
C₁₉×#500	2
C₄×D₈×C₁₉	2
C₁₉×#367	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#357	2
#2226	19

subgroup

index

C₁₉×#500

C₄×D₈×C₁₉

C₁₉×#367

C₁₉×C₄⋊C₁₆

C₁₉×#357

#2226

Subgroups — C₁₉×#2226 #14560083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2226 #14560083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2226 #14560083