Group #18014785 — subgroups

Subgroups — C₁₉×#8826 #18014785

Order 4864.

338 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 198 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×#1848	C₂	1	2	yes	maximal
2	C₁₉×#1567	C₂	1	4	yes	maximal
3	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#108	—	2	4	no	—
5	C₁₉×#423	C₂²	1	4	yes	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
8	C₁₉×#335	—	2	8	no	—
9	C₁₉×#322	C₄	1	4	yes	—
10	C₂×M₁₆×C₁₉	—	2	4	no	—
11	C₂²×C₈×C₁₉	D₄	1	2	yes	—
12	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₁₉×#108	—	4	8	no	—
15	C₁₉×C₄⋊C₈	—	2	8	no	—
16	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₉	D₄	1	4	yes	—
19	C₄×C₈×C₁₉	Q₈	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
22	M₁₆×C₁₉	—	4	8	no	—
23	C₂×C₈×C₁₉	—	4	4	no	—
24	C₂×C₈×C₁₉	—	4	4	no	—
25	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
26	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
27	C₂×C₈×C₁₉	D₈	1	4	yes	—
28	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
29	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₄²×C₁₉	C₂×D₄	1	2	yes	—
31	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
32	#8826	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
39	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
40	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
41	C₈×C₁₉	—	2	8	no	—
42	C₈×C₁₉	—	8	4	no	—
43	C₈×C₁₉	#107	1	8	yes	—
44	#1848	C₂×C₁₉	1	2	yes	—
45	#1567	C₂×C₁₉	1	4	yes	—
46	C₂×#322	C₂×C₁₉	1	1	yes	characteristic
47	C₂²×C₁₉	—	2	2	no	—
48	C₂²×C₁₉	#384	1	1	yes	characteristic
49	C₂²×C₁₉	#500	1	2	yes	—
50	C₄×C₁₉	—	2	2	no	—
51	C₄×C₁₉	C₂×#107	1	2	yes	—
52	C₄×C₁₉	#430	1	4	yes	—
53	C₄×C₁₉	#493	1	1	yes	characteristic
54	C₄×C₁₉	#494	1	1	yes	characteristic
55	C₂×#108	—	2	4	no	—
56	#423	C₂²×C₁₉	1	4	yes	—
57	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
58	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
59	#335	—	2	8	no	—
60	#322	C₄×C₁₉	1	4	yes	—
61	C₂×C₁₉	—	2	2	no	—
62	C₂×C₁₉	#1845	1	1	yes	characteristic
63	C₂×C₁₉	#1849	1	2	yes	—
64	C₂×M₁₆	—	2	4	no	—
65	C₂²×C₈	D₄×C₁₉	1	2	yes	—
66	C₂²×C₈	Q₈×C₁₉	1	4	yes	—
67	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
68	#108	—	4	8	no	—
69	C₄⋊C₈	—	2	8	no	—
70	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	—
71	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
72	C₄×C₈	D₄×C₁₉	1	4	yes	—
73	C₄×C₈	Q₈×C₁₉	1	2	yes	—
74	C₁₉	#8826	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
76	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
77	M₁₆	—	4	8	no	—
78	C₂×C₈	—	4	4	no	—
79	C₂×C₈	—	4	4	no	—
80	C₂×C₈	C₄⋊C₄×C₁₉	1	8	yes	—
81	C₂×C₈	C₄⋊C₄×C₁₉	1	4	yes	—
82	C₂×C₈	D₈×C₁₉	1	4	yes	—
83	C₂×C₈	Q₁₆×C₁₉	1	4	yes	—
84	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
85	C₄²	C₂×D₄×C₁₉	1	2	yes	—
86	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
87	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
91	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
92	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
93	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
94	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	—	8	4	no	—
97	C₈	C₁₉×#107	1	8	yes	—
98	C₂²	—	2	2	no	—
99	C₂²	C₁₉×#384	1	1	yes	characteristic
100	C₂²	C₁₉×#500	1	2	yes	—
101	C₄	—	2	2	no	—
102	C₄	C₂×C₁₉×#107	1	2	yes	—
103	C₄	C₁₉×#430	1	4	yes	—
104	C₄	C₁₉×#493	1	1	yes	characteristic
105	C₄	C₁₉×#494	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	C₁₉×#1845	1	1	yes	characteristic
108	C₂	C₁₉×#1849	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1848

C₂

yes

maximal

C₁₉×#1567

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₁₉×#335

—

C₁₉×#322

C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#8826

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#107

yes

—

#1848

C₂×C₁₉

yes

—

#1567

C₂×C₁₉

yes

—

C₂×#322

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#500

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#430

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂²×C₁₉

yes

—

C₂×C₄×C₈

C₂²×C₁₉

yes

—

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

#335

—

#322

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#1845

yes

characteristic

C₂×C₁₉

#1849

yes

—

C₂×M₁₆

—

C₂²×C₈

D₄×C₁₉

yes

—

C₂²×C₈

Q₈×C₁₉

yes

—

C₂×C₄²

C₂³×C₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

D₄×C₁₉

yes

—

C₄×C₈

Q₈×C₁₉

yes

—

C₁₉

#8826

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂²×C₄

C₂×Q₈×C₁₉

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

C₂×C₈

D₈×C₁₉

yes

—

C₂×C₈

Q₁₆×C₁₉

yes

—

C₄²

C₂²×C₄×C₁₉

yes

characteristic

C₄²

C₂×D₄×C₁₉

yes

—

C₄²

C₂×Q₈×C₁₉

yes

characteristic

C₂³

C₁₉×C₄⋊Q₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₄

C₂×C₄⋊C₄×C₁₉

yes

—

C₂×C₄

C₁₉×#127

yes

characteristic

C₂×C₄

C₁₉×C₄⋊Q₈

yes

—

C₂×C₄

C₂×D₈×C₁₉

yes

—

C₂×C₄

C₂×Q₁₆×C₁₉

yes

—

C₈

—

C₈

—

C₈

C₁₉×#107

yes

—

C₂²

—

C₂²

C₁₉×#384

yes

characteristic

100

C₂²

C₁₉×#500

yes

—

101

C₄

—

102

C₄

C₂×C₁₉×#107

yes

—

103

C₄

C₁₉×#430

yes

—

104

C₄

C₁₉×#493

yes

characteristic

105

C₄

C₁₉×#494

yes

characteristic

106

C₂

—

107

C₂

C₁₉×#1845

yes

characteristic

108

C₂

C₁₉×#1849

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#127

commutator

C₄²

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
32. #8826	C₁₉	direct (N × H)
74. C₁₉	#8826	direct (N × H)

H ≅ G/N

type

32. #8826

C₁₉

direct (N × H)

74. C₁₉

#8826

direct (N × H)

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

subgroup	index
C₁₉×#1848	2
C₁₉×#1567	2
C₂×C₁₉×#322	2
#8826	19

subgroup

index

C₁₉×#1848

C₁₉×#1567

C₂×C₁₉×#322

#8826

Subgroups — C₁₉×#8826 #18014785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8826 #18014785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8826 #18014785