Group #18019682 — subgroups

Subgroups — C₁₉×#13723 #18019682

Order 4864.

194 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 78 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×#2253	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2246	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1415	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×D₁₆	—	2	1	no	—
6	C₂×C₁₉×D₁₆	C₂²	1	2	yes	—
7	C₁₉×#499	—	2	1	no	—
8	C₁₉×#493	—	2	1	no	—
9	C₂×C₁₉×C₃₂	C₂²	1	2	yes	—
10	C₁₉×#367	—	2	1	no	—
11	C₁₉×#366	C₂²	1	2	yes	—
12	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×D₈×C₁₉	—	2	2	no	—
14	C₂×D₈×C₁₉	—	4	1	no	—
15	C₁₉×#127	—	4	1	no	—
16	C₁₉×#125	—	4	1	no	—
17	C₁₉×D₁₆	—	2	4	no	—
18	C₁₉×D₁₆	—	4	2	no	—
19	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉×#107	—	2	2	no	—
22	C₁₉×#106	—	4	1	no	—
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₁₉×C₃₂	—	2	2	no	—
25	C₂×D₄×C₁₉	—	4	2	no	—
26	C₂×D₄×C₁₉	—	8	2	no	—
27	D₈×C₁₉	—	4	2	no	—
28	D₈×C₁₉	—	4	2	no	—
29	D₈×C₁₉	—	8	2	no	—
30	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	—	4	2	no	—
33	C₄⋊C₄×C₁₉	—	8	2	no	—
34	C₄²×C₁₉	D₈	1	1	yes	characteristic
35	C₁₆×C₁₉	SD₁₆	1	2	yes	—
36	C₁₆×C₁₉	#41	1	2	yes	—
37	#13723	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂³×C₁₉	—	8	2	no	—
39	D₄×C₁₉	—	8	2	no	—
40	D₄×C₁₉	—	8	2	no	—
41	D₄×C₁₉	—	16	4	no	—
42	C₂×C₄×C₁₉	—	8	2	no	—
43	C₂×C₄×C₁₉	D₁₆	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
45	C₈×C₁₉	SD₃₂	1	2	yes	—
46	C₈×C₁₉	#124	1	1	yes	characteristic
47	C₈×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
48	#2253	C₂×C₁₉	1	1	yes	characteristic, complemented
49	#2246	C₂×C₁₉	1	1	yes	characteristic
50	#1415	C₂×C₁₉	1	4	yes	complemented
51	#1397	C₂×C₁₉	1	1	yes	characteristic, complemented
52	C₂²×C₁₉	—	16	2	no	—
53	C₂²×C₁₉	—	16	4	no	—
54	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
55	C₄×C₁₉	—	2	2	no	—
56	C₄×C₁₉	—	16	2	no	—
57	C₄×C₁₉	#486	1	1	yes	characteristic
58	C₄×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
59	C₂×D₁₆	—	2	1	no	—
60	C₂×D₁₆	C₂²×C₁₉	1	2	yes	—
61	#499	—	2	1	no	—
62	#493	—	2	1	no	—
63	C₂×C₃₂	C₂²×C₁₉	1	2	yes	—
64	#367	—	2	1	no	—
65	#366	C₂²×C₁₉	1	2	yes	—
66	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
67	C₂×C₁₉	—	32	2	no	—
68	C₂×C₁₉	#2240	1	1	yes	characteristic
69	C₂×C₁₉	#2263	1	2	yes	—
70	C₂×D₈	—	2	2	no	—
71	C₂×D₈	—	4	1	no	—
72	#127	—	4	1	no	—
73	#125	—	4	1	no	—
74	D₁₆	—	2	4	no	—
75	D₁₆	—	4	2	no	—
76	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
77	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
78	#107	—	2	2	no	—
79	#106	—	4	1	no	—
80	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
81	C₃₂	—	2	2	no	—
82	C₁₉	#13723	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×D₄	—	4	2	no	—
84	C₂×D₄	—	8	2	no	—
85	D₈	—	4	2	no	—
86	D₈	—	4	2	no	—
87	D₈	—	8	2	no	—
88	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
89	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
90	C₄⋊C₄	—	4	2	no	—
91	C₄⋊C₄	—	8	2	no	—
92	C₄²	D₈×C₁₉	1	1	yes	characteristic
93	C₁₆	SD₁₆×C₁₉	1	2	yes	—
94	C₁₆	#41×C₁₉	1	2	yes	—
95	C₂³	—	8	2	no	—
96	D₄	—	8	2	no	—
97	D₄	—	8	2	no	—
98	D₄	—	16	4	no	—
99	C₂×C₄	—	8	2	no	—
100	C₂×C₄	C₁₉×D₁₆	1	2	yes	—
101	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
102	C₈	C₁₉×SD₃₂	1	2	yes	—
103	C₈	C₁₉×#124	1	1	yes	characteristic
104	C₈	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
105	C₂²	—	16	2	no	—
106	C₂²	—	16	4	no	—
107	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	16	2	no	—
110	C₄	C₁₉×#486	1	1	yes	characteristic
111	C₄	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
112	C₂	—	32	2	no	—
113	C₂	C₁₉×#2240	1	1	yes	characteristic
114	C₂	C₁₉×#2263	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2253

C₂

yes

maximal, characteristic, complemented

C₁₉×#2246

C₂

yes

maximal, characteristic

C₁₉×#1415

C₂

yes

maximal, complemented

C₁₉×#1397

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

—

C₂×C₁₉×D₁₆

C₂²

yes

—

C₁₉×#499

—

C₁₉×#493

—

C₂×C₁₉×C₃₂

C₂²

yes

—

C₁₉×#367

—

C₁₉×#366

C₂²

yes

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×#127

—

C₁₉×#125

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

—

C₁₆×C₁₉

#41

yes

—

#13723

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

SD₃₂

yes

—

C₈×C₁₉

#124

yes

characteristic

C₈×C₁₉

C₂×SD₁₆

yes

characteristic

#2253

C₂×C₁₉

yes

characteristic, complemented

#2246

C₂×C₁₉

yes

characteristic

#1415

C₂×C₁₉

yes

complemented

#1397

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#486

yes

characteristic

C₄×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×D₁₆

—

C₂×D₁₆

C₂²×C₁₉

yes

—

#499

—

#493

—

C₂×C₃₂

C₂²×C₁₉

yes

—

#367

—

#366

C₂²×C₁₉

yes

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#2240

yes

characteristic

C₂×C₁₉

#2263

yes

—

C₂×D₈

—

C₂×D₈

—

#127

—

#125

—

D₁₆

—

D₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

#107

—

#106

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#13723

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

D₈×C₁₉

yes

characteristic

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₈×C₁₉

yes

characteristic

C₁₆

SD₁₆×C₁₉

yes

—

C₁₆

#41×C₁₉

yes

—

C₂³

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

C₁₉×D₁₆

yes

—

101

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

102

C₈

C₁₉×SD₃₂

yes

—

103

C₈

C₁₉×#124

yes

characteristic

104

C₈

C₂×SD₁₆×C₁₉

yes

characteristic

105

C₂²

—

106

C₂²

—

107

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

C₁₉×#486

yes

characteristic

111

C₄

C₂×C₁₉×SD₃₂

yes

characteristic

112

C₂

—

113

C₂

C₁₉×#2240

yes

characteristic

114

C₂

C₁₉×#2263

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

prime radical

C₁₉×#2246

C₂

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2253	C₂	semidirect
3. C₁₉×#1415	C₂	semidirect
4. C₁₉×#1397	C₂	semidirect
37. #13723	C₁₉	direct (N × H)
48. #2253	C₂×C₁₉	semidirect
50. #1415	C₂×C₁₉	semidirect
51. #1397	C₂×C₁₉	semidirect
82. C₁₉	#13723	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2253

C₂

semidirect

3. C₁₉×#1415

C₂

semidirect

4. C₁₉×#1397

C₂

semidirect

37. #13723

C₁₉

direct (N × H)

48. #2253

C₂×C₁₉

semidirect

50. #1415

C₂×C₁₉

semidirect

51. #1397

C₂×C₁₉

semidirect

82. C₁₉

#13723

direct (N × H)

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

subgroup	index
C₁₉×#2253	2
C₁₉×#2246	2
C₁₉×#1415	2
C₁₉×#1397	2
#13723	19

subgroup

index

C₁₉×#2253

C₁₉×#2246

C₁₉×#1415

C₁₉×#1397

#13723

Subgroups — C₁₉×#13723 #18019682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13723 #18019682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13723 #18019682