Group #18013352 — subgroups

Subgroups — C₁₉×#7393 #18013352

Order 4864.

110 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 62 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×#2183	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic
4	C₈×Q₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₃₂	—	2	1	no	—
6	C₂×C₁₉×C₃₂	—	2	1	no	—
7	C₁₉×C₄⋊C₁₆	—	2	1	no	—
8	C₁₉×C₄⋊C₁₆	C₄	1	1	yes	characteristic
9	C₁₉×#346	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₄×Q₈×C₁₉	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	—	2	1	no	—
13	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
15	C₁₉×C₄⋊C₈	—	2	1	no	—
16	C₁₉×C₄⋊C₈	C₈	1	1	yes	characteristic
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₁₉×C₃₂	—	2	2	no	—
20	C₁₉×C₃₂	—	4	1	no	—
21	C₂×Q₈×C₁₉	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	C₁₆	1	1	yes	characteristic
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
29	C₁₆×C₁₉	—	2	1	no	—
30	C₁₆×C₁₉	—	4	1	no	—
31	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
33	#7393	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	Q₈×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
39	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
40	C₈×C₁₉	—	2	1	no	—
41	C₈×C₁₉	—	4	1	no	—
42	C₈×C₁₉	#103	1	1	yes	characteristic
43	C₈×C₁₉	#104	1	1	yes	characteristic
44	#2183	C₂×C₁₉	1	1	yes	characteristic
45	C₄⋊C₃₂	C₂×C₁₉	1	1	yes	characteristic
46	#1397	C₂×C₁₉	1	1	yes	characteristic
47	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	4	1	no	—
51	C₄×C₁₉	—	4	1	no	—
52	C₄×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
53	C₄×C₁₉	#350	1	1	yes	characteristic
54	C₈×Q₈	C₄×C₁₉	1	1	yes	characteristic
55	C₂×C₃₂	—	2	1	no	—
56	C₂×C₃₂	—	2	1	no	—
57	C₄⋊C₁₆	—	2	1	no	—
58	C₄⋊C₁₆	C₄×C₁₉	1	1	yes	characteristic
59	#346	—	2	1	no	—
60	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
61	C₂×C₁₉	Q₈⋊C₁₆	1	1	yes	characteristic
62	C₂×C₁₉	#1400	1	1	yes	characteristic
63	C₂×C₁₉	#1401	1	1	yes	characteristic
64	C₄×Q₈	C₈×C₁₉	1	1	yes	characteristic
65	C₂×C₁₆	—	2	1	no	—
66	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
67	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
68	C₄⋊C₈	—	2	1	no	—
69	C₄⋊C₈	C₈×C₁₉	1	1	yes	characteristic
70	C₄×C₈	—	2	1	no	—
71	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
72	C₃₂	—	2	2	no	—
73	C₃₂	—	4	1	no	—
74	C₁₉	#7393	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×Q₈	C₁₆×C₁₉	1	1	yes	characteristic
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
78	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	C₁₆×C₁₉	1	1	yes	characteristic
81	C₄²	—	2	1	no	—
82	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
83	C₁₆	—	2	1	no	—
84	C₁₆	—	4	1	no	—
85	C₁₆	SD₁₆×C₁₉	1	1	yes	characteristic
86	C₁₆	Q₁₆×C₁₉	1	1	yes	characteristic
87	Q₈	—	4	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
91	C₂×C₄	C₂×C₁₆×C₁₉	1	1	yes	characteristic
92	C₂×C₄	C₁₉×M₃₂	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	4	1	no	—
95	C₈	C₁₉×#103	1	1	yes	characteristic
96	C₈	C₁₉×#104	1	1	yes	characteristic
97	C₂²	C₁₉×C₂²⋊C₁₆	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	C₁₉×Q₈⋊C₈	1	1	yes	characteristic
103	C₄	C₁₉×#350	1	1	yes	characteristic
104	C₂	C₁₉×Q₈⋊C₁₆	1	1	yes	characteristic
105	C₂	C₁₉×#1400	1	1	yes	characteristic
106	C₂	C₁₉×#1401	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2183

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic

C₁₉×#1397

C₂

yes

maximal, characteristic

C₈×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×C₃₂

—

C₂×C₁₉×C₃₂

—

C₁₉×C₄⋊C₁₆

—

C₁₉×C₄⋊C₁₆

C₄

yes

characteristic

C₁₉×#346

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

C₈

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₈

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₃₂

—

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

C₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₁₆

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

SD₁₆

yes

characteristic

C₁₆×C₁₉

Q₁₆

yes

characteristic

#7393

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₄⋊C₃₂

C₂×C₁₉

yes

characteristic

#1397

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₈⋊C₈

yes

characteristic

C₄×C₁₉

#350

yes

characteristic

C₈×Q₈

C₄×C₁₉

yes

characteristic

C₂×C₃₂

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₄⋊C₁₆

C₄×C₁₉

yes

characteristic

#346

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

Q₈⋊C₁₆

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄×Q₈

C₈×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₈×C₁₉

yes

characteristic

C₄×C₈

—

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

C₃₂

—

C₃₂

—

C₁₉

#7393

yes

characteristic, direct product factor, Sylow

C₂×Q₈

C₁₆×C₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

M₁₆×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₁₆×C₁₉

yes

characteristic

C₄²

—

C₄²

C₂×C₈×C₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

SD₁₆×C₁₉

yes

characteristic

C₁₆

Q₁₆×C₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

C₂×C₄

C₂×C₁₆×C₁₉

yes

characteristic

C₂×C₄

C₁₉×M₃₂

yes

characteristic

C₈

—

C₈

—

C₈

C₁₉×#103

yes

characteristic

C₈

C₁₉×#104

yes

characteristic

C₂²

C₁₉×C₂²⋊C₁₆

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

C₁₉×Q₈⋊C₈

yes

characteristic

103

C₄

C₁₉×#350

yes

characteristic

104

C₂

C₁₉×Q₈⋊C₁₆

yes

characteristic

105

C₂

C₁₉×#1400

yes

characteristic

106

C₂

C₁₉×#1401

yes

characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₁₆×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle, prime radical	C₂²×C₁₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₈×C₁₉

C₂²⋊C₄

commutator

C₂×C₄

C₂×C₁₆×C₁₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₁₉

socle, prime radical

C₂²×C₁₉

C₂²⋊C₁₆

LCS

G ▷ C₂×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
33. #7393	C₁₉	direct (N × H)
74. C₁₉	#7393	direct (N × H)

H ≅ G/N

type

33. #7393

C₁₉

direct (N × H)

74. C₁₉

#7393

direct (N × H)

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

subgroup	index
C₁₉×#2183	2
C₁₉×C₄⋊C₃₂	2
C₁₉×#1397	2
#7393	19

subgroup

index

C₁₉×#2183

C₁₉×C₄⋊C₃₂

C₁₉×#1397

#7393

Subgroups — C₁₉×#7393 #18013352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7393 #18013352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7393 #18013352