Group #18013349 — subgroups

Subgroups — C₁₉×#7390 #18013349

Order 4864.

128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 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×#2177	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×D₁₆	C₄	1	1	yes	characteristic
5	C₄×D₈×C₁₉	—	2	1	no	—
6	C₁₉×M₆₄	—	2	1	no	—
7	C₁₉×#367	C₄	1	1	yes	characteristic
8	C₁₉×#364	—	2	1	no	—
9	C₁₉×#357	—	2	1	no	—
10	C₁₉×#346	C₂²	1	1	yes	characteristic
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	—
15	C₁₉×M₃₂	—	4	1	no	—
16	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉×#107	—	2	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	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	4	1	no	—
29	C₂²⋊C₄×C₁₉	—	8	1	no	—
30	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
31	C₁₆×C₁₉	—	2	1	no	—
32	C₁₆×C₁₉	—	8	1	no	—
33	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
35	#7390	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	—	2	1	no	—
40	C₂×C₄×C₁₉	—	8	1	no	—
41	C₂×C₄×C₁₉	—	16	2	no	—
42	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₈×C₁₉	#104	1	1	yes	characteristic
46	#2177	C₂×C₁₉	1	1	yes	characteristic
47	#1398	C₂×C₁₉	1	1	yes	characteristic, complemented
48	#1369	C₂×C₁₉	1	1	yes	characteristic, complemented
49	C₂²×C₁₉	—	8	2	no	—
50	C₂²×C₁₉	—	16	1	no	—
51	C₂²×C₁₉	—	16	1	no	—
52	C₂²×C₁₉	#361	1	1	yes	characteristic
53	C₄×C₁₉	—	4	1	no	—
54	C₄×C₁₉	—	16	1	no	—
55	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
56	C₄×C₁₉	#360	1	1	yes	characteristic
57	C₂×D₁₆	C₄×C₁₉	1	1	yes	characteristic
58	C₄×D₈	—	2	1	no	—
59	M₆₄	—	2	1	no	—
60	#367	C₄×C₁₉	1	1	yes	characteristic
61	#364	—	2	1	no	—
62	#357	—	2	1	no	—
63	#346	C₂²×C₁₉	1	1	yes	characteristic
64	C₂×C₁₉	—	2	1	no	—
65	C₂×C₁₉	—	16	2	no	—
66	C₂×C₁₉	#1333	1	1	yes	characteristic
67	C₂×D₈	—	2	1	no	—
68	C₄×D₄	—	4	1	no	—
69	D₁₆	—	2	1	no	—
70	D₁₆	C₈×C₁₉	1	2	yes	—
71	M₃₂	—	4	1	no	—
72	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
73	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
74	#107	—	2	1	no	—
75	#102	—	4	1	no	—
76	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
77	C₃₂	—	2	2	no	—
78	C₁₉	#7390	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×D₄	—	4	1	no	—
80	C₂²×C₄	—	8	1	no	—
81	D₈	—	2	2	no	—
82	D₈	—	4	1	no	—
83	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
84	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
85	C₄⋊C₄	—	4	1	no	—
86	C₂²⋊C₄	—	8	1	no	—
87	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
88	C₁₆	—	2	1	no	—
89	C₁₆	—	8	1	no	—
90	C₁₆	C₂×C₈×C₁₉	1	1	yes	characteristic
91	C₁₆	M₁₆×C₁₉	1	1	yes	characteristic
92	C₂³	—	8	1	no	—
93	D₄	—	4	2	no	—
94	D₄	—	8	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	8	1	no	—
97	C₂×C₄	—	16	2	no	—
98	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
101	C₈	C₁₉×#104	1	1	yes	characteristic
102	C₂²	—	8	2	no	—
103	C₂²	—	16	1	no	—
104	C₂²	—	16	1	no	—
105	C₂²	C₁₉×#361	1	1	yes	characteristic
106	C₄	—	4	1	no	—
107	C₄	—	16	1	no	—
108	C₄	C₁₉×D₄⋊C₈	1	1	yes	characteristic
109	C₄	C₁₉×#360	1	1	yes	characteristic
110	C₂	—	2	1	no	—
111	C₂	—	16	2	no	—
112	C₂	C₁₉×#1333	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2177

C₂

yes

maximal, characteristic

C₁₉×#1398

C₂

yes

maximal, characteristic, complemented

C₁₉×#1369

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₄

yes

characteristic

C₄×D₈×C₁₉

—

C₁₉×M₆₄

—

C₁₉×#367

C₄

yes

characteristic

C₁₉×#364

—

C₁₉×#357

—

C₁₉×#346

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×D₁₆

—

C₁₉×D₁₆

C₈

yes

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#102

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

M₁₆

yes

characteristic

#7390

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

#1398

C₂×C₁₉

yes

characteristic, complemented

#1369

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#361

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

#360

yes

characteristic

C₂×D₁₆

C₄×C₁₉

yes

characteristic

C₄×D₈

—

M₆₄

—

#367

C₄×C₁₉

yes

—

—

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1333

yes

characteristic

C₂×D₈

—

C₄×D₄

—

D₁₆

—

D₁₆

C₈×C₁₉

yes

—

M₃₂

—

C₂×C₁₆

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

characteristic

#107

—

#102

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#7390

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

D₈×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

SD₁₆×C₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

C₂×C₈×C₁₉

yes

characteristic

C₁₆

M₁₆×C₁₉

yes

characteristic

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₉×#102

yes

characteristic

C₈

—

100

C₈

C₁₉×C₂²⋊C₈

yes

characteristic

101

C₈

C₁₉×#104

yes

characteristic

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₁₉×#361

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

C₁₉×D₄⋊C₈

yes

characteristic

109

C₄

C₁₉×#360

yes

characteristic

110

C₂

—

111

C₂

—

112

C₂

C₁₉×#1333

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1333
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	#346	C₂²×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₁₉×#346 ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#1333

commutator

C₁₆

C₂×C₈×C₁₉

Frattini, cosocle

#346

C₂²×C₁₉

prime radical

C₂×C₁₉×D₁₆

C₄

LCS

G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₁₉×#346 ◁ G

N	H ≅ G/N	type
2. C₁₉×#1398	C₂	semidirect
3. C₁₉×#1369	C₂	semidirect
35. #7390	C₁₉	direct (N × H)
47. #1398	C₂×C₁₉	semidirect
48. #1369	C₂×C₁₉	semidirect
78. C₁₉	#7390	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1398

C₂

semidirect

3. C₁₉×#1369

C₂

semidirect

35. #7390

C₁₉

direct (N × H)

47. #1398

C₂×C₁₉

semidirect

48. #1369

C₂×C₁₉

semidirect

78. C₁₉

#7390

direct (N × H)

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

subgroup	index
C₁₉×#2177	2
C₁₉×#1398	2
C₁₉×#1369	2
#7390	19

subgroup

index

C₁₉×#2177

C₁₉×#1398

C₁₉×#1369

#7390

Subgroups — C₁₉×#7390 #18013349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7390 #18013349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7390 #18013349