Group #14560095 — subgroups

Subgroups — C₁₉×#2238 #14560095

Order 2432.

134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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×#469	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#365	C₂	1	2	yes	maximal, complemented
4	C₁₉×#361	C₂	1	2	yes	maximal, complemented
5	C₁₉×#349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	—	2	1	no	—
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#121	—	2	1	no	—
10	C₁₉×M₃₂	C₂²	1	2	yes	—
11	C₁₉×#108	—	2	1	no	—
12	C₁₉×#108	C₂²	1	2	yes	—
13	C₁₉×#106	C₂²	1	1	yes	characteristic
14	C₁₉×#102	—	2	1	no	—
15	C₂×D₄×C₁₉	—	2	1	no	—
16	C₂×D₄×C₁₉	—	4	1	no	—
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	D₈×C₁₉	—	2	2	no	—
19	M₁₆×C₁₉	—	2	2	no	—
20	M₁₆×C₁₉	—	2	2	no	—
21	M₁₆×C₁₉	—	4	1	no	—
22	C₂×C₈×C₁₉	—	4	1	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂²⋊C₄×C₁₉	—	4	1	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	—	4	1	no	—
29	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
30	D₄×C₁₉	—	4	1	no	—
31	D₄×C₁₉	—	4	1	no	—
32	D₄×C₁₉	—	8	2	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	—	4	2	no	—
40	C₈×C₁₉	#41	1	2	yes	—
41	#2238	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	4	1	no	—
44	C₂²×C₁₉	—	8	1	no	—
45	C₂²×C₁₉	—	8	1	no	—
46	C₂²×C₁₉	—	8	1	no	—
47	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	8	1	no	—
50	C₄×C₁₉	#123	1	1	yes	characteristic
51	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
52	#469	C₂×C₁₉	1	1	yes	characteristic
53	#430	C₂×C₁₉	1	1	yes	characteristic, complemented
54	#365	C₂×C₁₉	1	2	yes	complemented
55	#361	C₂×C₁₉	1	2	yes	complemented
56	#349	C₂×C₁₉	1	1	yes	characteristic, complemented
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	—	4	1	no	—
59	C₂×C₁₉	—	16	1	no	—
60	C₂×C₁₉	#481	1	1	yes	characteristic
61	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
62	C₂×M₁₆	—	2	1	no	—
63	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
64	#121	—	2	1	no	—
65	M₃₂	C₂²×C₁₉	1	2	yes	—
66	#108	—	2	1	no	—
67	#108	C₂²×C₁₉	1	2	yes	—
68	#106	C₂²×C₁₉	1	1	yes	characteristic
69	#102	—	2	1	no	—
70	C₁₉	#2238	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×D₄	—	2	1	no	—
72	C₂×D₄	—	4	1	no	—
73	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
74	D₈	—	2	2	no	—
75	M₁₆	—	2	2	no	—
76	M₁₆	—	2	2	no	—
77	M₁₆	—	4	1	no	—
78	C₂×C₈	—	4	1	no	—
79	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₁₆	—	2	2	no	—
84	C₂³	—	4	1	no	—
85	C₂³	SD₁₆×C₁₉	1	1	yes	characteristic
86	D₄	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	8	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	2	no	—
96	C₈	#41×C₁₉	1	2	yes	—
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	8	1	no	—
100	C₂²	—	8	1	no	—
101	C₂²	—	8	1	no	—
102	C₂²	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	8	1	no	—
105	C₄	C₁₉×#123	1	1	yes	characteristic
106	C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	4	1	no	—
109	C₂	—	16	1	no	—
110	C₂	C₁₉×#481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#469

C₂

yes

maximal, characteristic

C₁₉×#430

C₂

yes

maximal, characteristic, complemented

C₁₉×#365

C₂

yes

maximal, complemented

C₁₉×#361

C₂

yes

maximal, complemented

C₁₉×#349

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#121

—

C₁₉×M₃₂

C₂²

yes

—

C₁₉×#108

—

C₁₉×#108

C₂²

yes

—

C₁₉×#106

C₂²

yes

characteristic

C₁₉×#102

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

D₈×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₁₆×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

SD₁₆

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#41

yes

—

#2238

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

#430

C₂×C₁₉

yes

characteristic, complemented

#365

C₂×C₁₉

yes

complemented

#361

C₂×C₁₉

yes

complemented

#349

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#481

yes

characteristic

C₂×D₈

C₂²×C₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂²×C₁₉

yes

characteristic

#121

—

M₃₂

C₂²×C₁₉

yes

—

#108

—

#108

C₂²×C₁₉

yes

—

#106

C₂²×C₁₉

yes

characteristic

#102

—

C₁₉

#2238

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

D₄×C₁₉

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

SD₁₆×C₁₉

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

SD₁₆×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

—

C₈

#41×C₁₉

yes

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×SD₁₆×C₁₉

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

C₁₉×#123

yes

characteristic

106

C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

C₁₉×#481

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#481
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#469	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#481

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₁₉×#469

C₂

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#430	C₂	semidirect
3. C₁₉×#365	C₂	semidirect
4. C₁₉×#361	C₂	semidirect
5. C₁₉×#349	C₂	semidirect
41. #2238	C₁₉	direct (N × H)
53. #430	C₂×C₁₉	semidirect
54. #365	C₂×C₁₉	semidirect
55. #361	C₂×C₁₉	semidirect
56. #349	C₂×C₁₉	semidirect
70. C₁₉	#2238	direct (N × H)

H ≅ G/N

type

2. C₁₉×#430

C₂

semidirect

3. C₁₉×#365

C₂

semidirect

4. C₁₉×#361

C₂

semidirect

5. C₁₉×#349

C₂

semidirect

41. #2238

C₁₉

direct (N × H)

53. #430

C₂×C₁₉

semidirect

54. #365

C₂×C₁₉

semidirect

55. #361

C₂×C₁₉

semidirect

56. #349

C₂×C₁₉

semidirect

70. C₁₉

#2238

direct (N × H)

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

subgroup	index
C₁₉×#469	2
C₁₉×#430	2
C₁₉×#365	2
C₁₉×#361	2
C₁₉×#349	2
#2238	19

subgroup

index

C₁₉×#469

C₁₉×#430

C₁₉×#365

C₁₉×#361

C₁₉×#349

#2238

Subgroups — C₁₉×#2238 #14560095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2238 #14560095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2238 #14560095