Group #18013341 — subgroups

Subgroups — C₁₉×#7382 #18013341

Order 4864.

118 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 58 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×#2170	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1422	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#504	—	2	1	no	—
5	C₁₉×#443	C₄	1	1	yes	characteristic
6	C₁₉×M₆₄	—	2	1	no	—
7	C₂×C₁₉×C₃₂	—	2	1	no	—
8	C₁₉×#364	C₄	1	1	yes	characteristic
9	C₁₉×#350	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#135	C₈	1	1	yes	characteristic
12	C₁₉×#131	—	2	1	no	—
13	C₁₉×M₃₂	—	2	1	no	—
14	C₁₉×M₃₂	—	4	1	no	—
15	C₂×C₁₆×C₁₉	—	4	1	no	—
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉×#108	C₈	1	1	yes	characteristic
19	C₁₉×#104	—	2	1	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₁₉×C₃₂	—	2	2	no	—
22	C₁₉×C₃₂	—	4	1	no	—
23	#41×C₁₉	—	2	1	no	—
24	Q₁₆×C₁₉	C₁₆	1	1	yes	characteristic
25	SD₁₆×C₁₉	—	2	1	no	—
26	D₈×C₁₉	C₁₆	1	1	yes	characteristic
27	M₁₆×C₁₉	—	2	1	no	—
28	M₁₆×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₆×C₁₉	—	4	1	no	—
35	C₁₆×C₁₉	D₈	1	1	yes	characteristic
36	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
37	#7382	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	Q₈×C₁₉	—	2	1	no	—
39	D₄×C₁₉	—	2	1	no	—
40	D₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
44	C₈×C₁₉	—	4	1	no	—
45	C₈×C₁₉	#102	1	1	yes	characteristic
46	C₈×C₁₉	#104	1	1	yes	characteristic
47	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
48	C₈×C₁₉	M₃₂	1	1	yes	characteristic
49	#2170	C₂×C₁₉	1	1	yes	characteristic
50	#1422	C₂×C₁₉	1	1	yes	characteristic, complemented
51	#1397	C₂×C₁₉	1	1	yes	characteristic, complemented
52	C₂²×C₁₉	—	4	1	no	—
53	C₂²×C₁₉	#350	1	1	yes	characteristic
54	C₄×C₁₉	—	4	1	no	—
55	C₄×C₁₉	—	4	1	no	—
56	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
57	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
58	#504	—	2	1	no	—
59	#443	C₄×C₁₉	1	1	yes	characteristic
60	M₆₄	—	2	1	no	—
61	C₂×C₃₂	—	2	1	no	—
62	#364	C₄×C₁₉	1	1	yes	characteristic
63	#350	—	2	1	no	—
64	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	—	8	1	no	—
67	C₂×C₁₉	D₄⋊C₁₆	1	1	yes	characteristic
68	#135	C₈×C₁₉	1	1	yes	characteristic
69	#131	—	2	1	no	—
70	M₃₂	—	2	1	no	—
71	M₃₂	—	4	1	no	—
72	C₂×C₁₆	—	4	1	no	—
73	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
74	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
75	#108	C₈×C₁₉	1	1	yes	characteristic
76	#104	—	2	1	no	—
77	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
78	C₃₂	—	2	2	no	—
79	C₃₂	—	4	1	no	—
80	C₁₉	#7382	1	1	yes	characteristic, direct product factor, Sylow
81	#41	—	2	1	no	—
82	Q₁₆	C₁₆×C₁₉	1	1	yes	characteristic
83	SD₁₆	—	2	1	no	—
84	D₈	C₁₆×C₁₉	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	4	1	no	—
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
89	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
90	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	4	1	no	—
93	C₁₆	D₈×C₁₉	1	1	yes	characteristic
94	C₁₆	SD₁₆×C₁₉	1	1	yes	characteristic
95	Q₈	—	2	1	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	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
101	C₈	—	4	1	no	—
102	C₈	C₁₉×#102	1	1	yes	characteristic
103	C₈	C₁₉×#104	1	1	yes	characteristic
104	C₈	C₂×C₁₆×C₁₉	1	1	yes	characteristic
105	C₈	C₁₉×M₃₂	1	1	yes	characteristic
106	C₂²	—	4	1	no	—
107	C₂²	C₁₉×#350	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	4	1	no	—
110	C₄	C₁₉×D₄⋊C₈	1	1	yes	characteristic
111	C₄	C₁₉×C₂²⋊C₁₆	1	1	yes	characteristic
112	C₂	—	2	1	no	—
113	C₂	—	8	1	no	—
114	C₂	C₁₉×D₄⋊C₁₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2170

C₂

yes

maximal, characteristic

C₁₉×#1422

C₂

yes

maximal, characteristic, complemented

C₁₉×#1397

C₂

yes

maximal, characteristic, complemented

C₁₉×#504

—

C₁₉×#443

C₄

yes

characteristic

C₁₉×M₆₄

—

C₂×C₁₉×C₃₂

—

C₁₉×#364

C₄

yes

characteristic

C₁₉×#350

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#135

C₈

yes

characteristic

C₁₉×#131

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#108

C₈

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₃₂

—

C₁₉×C₃₂

—

#41×C₁₉

—

Q₁₆×C₁₉

C₁₆

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

C₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

#7382

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

C₂×C₁₆

yes

characteristic

C₈×C₁₉

M₃₂

yes

characteristic

#2170

C₂×C₁₉

yes

characteristic

#1422

C₂×C₁₉

yes

characteristic, complemented

#1397

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

#350

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

C₂²⋊C₁₆

yes

characteristic

#504

—

#443

C₄×C₁₉

yes

characteristic

M₆₄

—

C₂×C₃₂

—

#364

C₄×C₁₉

yes

characteristic

#350

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

D₄⋊C₁₆

yes

characteristic

#135

C₈×C₁₉

yes

characteristic

#131

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

characteristic

#108

C₈×C₁₉

yes

characteristic

#104

—

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

C₃₂

—

C₃₂

—

C₁₉

#7382

yes

characteristic, direct product factor, Sylow

#41

—

Q₁₆

C₁₆×C₁₉

yes

characteristic

SD₁₆

—

D₈

C₁₆×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₂×C₈×C₁₉

yes

characteristic

C₄²

M₁₆×C₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

D₈×C₁₉

yes

characteristic

C₁₆

SD₁₆×C₁₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

101

C₈

—

102

C₈

C₁₉×#102

yes

characteristic

103

C₈

C₁₉×#104

yes

characteristic

104

C₈

C₂×C₁₆×C₁₉

yes

characteristic

105

C₈

C₁₉×M₃₂

yes

characteristic

106

C₂²

—

107

C₂²

C₁₉×#350

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

C₁₉×D₄⋊C₈

yes

characteristic

111

C₄

C₁₉×C₂²⋊C₁₆

yes

characteristic

112

C₂

—

113

C₂

—

114

C₂

C₁₉×D₄⋊C₁₆

yes

characteristic

	subgroup	G/H
center	C₈×C₁₉	#102
commutator	C₈	C₂×C₁₆×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	D₄⋊C₁₆
prime radical	C₁₉×#135	C₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center

C₈×C₁₉

#102

commutator

C₈

C₂×C₁₆×C₁₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₁₉

socle

C₂×C₁₉

D₄⋊C₁₆

prime radical

C₁₉×#135

C₈

LCS

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1422	C₂	semidirect
3. C₁₉×#1397	C₂	semidirect
37. #7382	C₁₉	direct (N × H)
50. #1422	C₂×C₁₉	semidirect
51. #1397	C₂×C₁₉	semidirect
80. C₁₉	#7382	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1422

C₂

semidirect

3. C₁₉×#1397

C₂

semidirect

37. #7382

C₁₉

direct (N × H)

50. #1422

C₂×C₁₉

semidirect

51. #1397

C₂×C₁₉

semidirect

80. C₁₉

#7382

direct (N × H)

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

subgroup	index
C₁₉×#2170	2
C₁₉×#1422	2
C₁₉×#1397	2
#7382	19

subgroup

index

C₁₉×#2170

C₁₉×#1422

C₁₉×#1397

#7382

Subgroups — C₁₉×#7382 #18013341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7382 #18013341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7382 #18013341