Group #18013344 — subgroups

Subgroups — C₁₉×#7385 #18013344

Order 4864.

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

normal subgroups only

This group has 136 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	C₄×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1372	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×D₁₆	C₄	1	1	yes	characteristic
5	C₄×D₈×C₁₉	—	2	1	no	—
6	C₂×C₁₉×C₃₂	—	2	1	no	—
7	C₁₉×#366	C₄	1	1	yes	characteristic
8	C₁₉×#357	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#335	—	2	1	no	—
11	C₂×D₈×C₁₉	—	2	1	no	—
12	C₄×D₄×C₁₉	—	4	1	no	—
13	C₁₉×D₁₆	—	2	1	no	—
14	C₁₉×D₁₆	C₈	1	2	yes	complemented
15	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₁₉×#107	—	2	1	no	—
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉×#102	—	4	1	no	—
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₁₉×C₃₂	—	2	2	no	—
22	C₂×D₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	8	1	no	—
24	D₈×C₁₉	—	2	2	no	—
25	D₈×C₁₉	—	4	1	no	—
26	C₂×C₈×C₁₉	—	8	1	no	—
27	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₄⋊C₄×C₁₉	—	4	1	no	—
30	C₂²⋊C₄×C₁₉	—	8	1	no	—
31	C₄²×C₁₉	D₈	1	1	yes	characteristic
32	C₁₆×C₁₉	—	2	1	no	—
33	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
35	#7385	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂³×C₁₉	—	8	1	no	—
37	D₄×C₁₉	—	4	2	no	—
38	D₄×C₁₉	—	8	1	no	—
39	C₂×C₄×C₁₉	—	8	1	no	—
40	C₂×C₄×C₁₉	—	16	2	no	—
41	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
42	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
44	C₈×C₁₉	—	2	1	no	—
45	C₈×C₁₉	—	16	1	no	—
46	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
47	C₈×C₁₉	#104	1	1	yes	characteristic
48	C₄×D₁₆	C₂×C₁₉	1	1	yes	characteristic
49	#1397	C₂×C₁₉	1	1	yes	characteristic, complemented
50	#1372	C₂×C₁₉	1	1	yes	characteristic, complemented
51	C₂²×C₁₉	—	8	2	no	—
52	C₂²×C₁₉	—	16	1	no	—
53	C₂²×C₁₉	—	16	1	no	—
54	C₂²×C₁₉	#357	1	1	yes	characteristic
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	—	16	1	no	—
58	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
59	C₄×C₁₉	#359	1	1	yes	characteristic
60	C₂×D₁₆	C₄×C₁₉	1	1	yes	characteristic
61	C₄×D₈	—	2	1	no	—
62	C₂×C₃₂	—	2	1	no	—
63	#366	C₄×C₁₉	1	1	yes	characteristic
64	#357	—	2	1	no	—
65	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
66	#335	—	2	1	no	—
67	C₂×C₁₉	—	16	2	no	—
68	C₂×C₁₉	#1331	1	1	yes	characteristic
69	C₂×C₁₉	#1418	1	1	yes	characteristic
70	C₂×C₁₉	#1419	1	1	yes	characteristic
71	C₂×D₈	—	2	1	no	—
72	C₄×D₄	—	4	1	no	—
73	D₁₆	—	2	1	no	—
74	D₁₆	C₈×C₁₉	1	2	yes	complemented
75	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
76	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
77	#107	—	2	1	no	—
78	C₄⋊C₈	—	4	1	no	—
79	#102	—	4	1	no	—
80	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
81	C₃₂	—	2	2	no	—
82	C₁₉	#7385	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×D₄	—	4	1	no	—
84	C₂²×C₄	—	8	1	no	—
85	D₈	—	2	2	no	—
86	D₈	—	4	1	no	—
87	C₂×C₈	—	8	1	no	—
88	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
89	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
90	C₄⋊C₄	—	4	1	no	—
91	C₂²⋊C₄	—	8	1	no	—
92	C₄²	D₈×C₁₉	1	1	yes	characteristic
93	C₁₆	—	2	1	no	—
94	C₁₆	C₂×C₈×C₁₉	1	1	yes	characteristic
95	C₁₆	M₁₆×C₁₉	1	1	yes	characteristic
96	C₂³	—	8	1	no	—
97	D₄	—	4	2	no	—
98	D₄	—	8	1	no	—
99	C₂×C₄	—	8	1	no	—
100	C₂×C₄	—	16	2	no	—
101	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
102	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
103	C₂×C₄	C₁₉×SD₃₂	1	1	yes	characteristic
104	C₈	—	2	1	no	—
105	C₈	—	16	1	no	—
106	C₈	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
107	C₈	C₁₉×#104	1	1	yes	characteristic
108	C₂²	—	8	2	no	—
109	C₂²	—	16	1	no	—
110	C₂²	—	16	1	no	—
111	C₂²	C₁₉×#357	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	16	1	no	—
115	C₄	C₁₉×D₄⋊C₈	1	1	yes	characteristic
116	C₄	C₁₉×#359	1	1	yes	characteristic
117	C₂	—	16	2	no	—
118	C₂	C₁₉×#1331	1	1	yes	characteristic
119	C₂	C₁₉×#1418	1	1	yes	characteristic
120	C₂	C₁₉×#1419	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₁₉×D₁₆

C₂

yes

maximal, characteristic

C₁₉×#1397

C₂

yes

maximal, characteristic, complemented

C₁₉×#1372

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₄

yes

characteristic

C₄×D₈×C₁₉

—

C₂×C₁₉×C₃₂

—

C₁₉×#366

C₄

yes

characteristic

C₁₉×#357

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₂×D₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×D₁₆

—

C₁₉×D₁₆

C₈

yes

complemented

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

M₁₆

yes

characteristic

#7385

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

#104

yes

characteristic

C₄×D₁₆

C₂×C₁₉

yes

characteristic

#1397

C₂×C₁₉

yes

characteristic, complemented

#1372

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

#359

yes

characteristic

C₂×D₁₆

C₄×C₁₉

yes

characteristic

C₄×D₈

—

C₂×C₃₂

—

#366

C₄×C₁₉

yes

characteristic

#357

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

#335

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×D₈

—

C₄×D₄

—

D₁₆

—

D₁₆

C₈×C₁₉

yes

complemented

C₂×C₁₆

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

characteristic

#107

—

C₄⋊C₈

—

#102

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#7385

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

SD₁₆×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₈×C₁₉

yes

characteristic

C₁₆

—

C₁₆

C₂×C₈×C₁₉

yes

characteristic

C₁₆

M₁₆×C₁₉

yes

characteristic

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₁₉×#102

yes

characteristic

102

C₂×C₄

C₁₉×D₁₆

yes

characteristic

103

C₂×C₄

C₁₉×SD₃₂

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

C₁₉×C₂²⋊C₈

yes

characteristic

107

C₈

C₁₉×#104

yes

characteristic

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₁₉×#357

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

C₁₉×D₄⋊C₈

yes

characteristic

116

C₄

C₁₉×#359

yes

characteristic

117

C₂

—

118

C₂

C₁₉×#1331

yes

characteristic

119

C₂

C₁₉×#1418

yes

characteristic

120

C₂

C₁₉×#1419

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#357
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₄
LCS	G ▷ 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

#357

commutator

C₁₆

C₂×C₈×C₁₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₁₉

prime radical

C₂×C₁₉×D₁₆

C₄

LCS

G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
2. C₁₉×#1397	C₂	semidirect
3. C₁₉×#1372	C₂	semidirect
14. C₁₉×D₁₆	C₈	semidirect
35. #7385	C₁₉	direct (N × H)
49. #1397	C₂×C₁₉	semidirect
50. #1372	C₂×C₁₉	semidirect
74. D₁₆	C₈×C₁₉	semidirect
82. C₁₉	#7385	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1397

C₂

semidirect

3. C₁₉×#1372

C₂

semidirect

14. C₁₉×D₁₆

C₈

semidirect

35. #7385

C₁₉

direct (N × H)

49. #1397

C₂×C₁₉

semidirect

50. #1372

C₂×C₁₉

semidirect

74. D₁₆

C₈×C₁₉

semidirect

82. C₁₉

#7385

direct (N × H)

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

subgroup	index
C₄×C₁₉×D₁₆	2
C₁₉×#1397	2
C₁₉×#1372	2
#7385	19

subgroup

index

C₄×C₁₉×D₁₆

C₁₉×#1397

C₁₉×#1372

#7385

Subgroups — C₁₉×#7385 #18013344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7385 #18013344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7385 #18013344