Group #14559959 — subgroups

Subgroups — C₁₉×#2102 #14559959

Order 2432.

158 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 72 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×#430	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#344	C₂	1	2	yes	maximal
4	C₁₉×#339	C₂	1	2	yes	maximal
5	C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#108	—	2	2	no	—
12	C₁₉×C₄⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₁₉	—	2	1	no	—
14	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	M₁₆×C₁₉	—	2	2	no	—
16	M₁₆×C₁₉	—	2	2	no	—
17	M₁₆×C₁₉	—	2	2	no	—
18	M₁₆×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	D₄	1	2	yes	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂²⋊C₄×C₁₉	—	2	2	no	—
24	C₄²×C₁₉	—	2	1	no	—
25	C₄²×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	Q₈	1	1	yes	characteristic
27	C₄²×C₁₉	Q₈	1	1	yes	characteristic
28	C₂³×C₁₉	#41	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	4	2	no	—
32	C₂×C₄×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₁₉	#41	1	2	yes	—
36	C₂×C₄×C₁₉	#41	1	2	yes	—
37	C₈×C₁₉	—	2	2	no	—
38	C₈×C₁₉	—	4	1	no	—
39	C₈×C₁₉	—	4	2	no	—
40	#2102	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₁₉	—	4	1	no	—
42	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂²×C₁₉	#126	1	2	yes	—
44	C₄×C₁₉	—	2	2	no	—
45	C₄×C₁₉	—	4	1	no	—
46	C₄×C₁₉	—	8	2	no	—
47	C₄×C₁₉	#123	1	1	yes	characteristic
48	C₄×C₁₉	#124	1	1	yes	characteristic
49	C₄×C₁₉	#125	1	2	yes	—
50	#430	C₂×C₁₉	1	1	yes	characteristic
51	#423	C₂×C₁₉	1	1	yes	characteristic
52	#344	C₂×C₁₉	1	2	yes	—
53	#339	C₂×C₁₉	1	2	yes	—
54	H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	2	2	no	—
57	C₂×C₁₉	#400	1	1	yes	characteristic
58	C₂×M₁₆	C₂²×C₁₉	1	2	yes	—
59	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
60	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
61	#117	C₂²×C₁₉	1	2	yes	—
62	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
63	#108	—	2	2	no	—
64	C₄⋊C₈	—	2	2	no	—
65	C₁₉	#2102	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	2	2	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	D₄×C₁₉	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	1	no	—
78	C₄²	—	2	2	no	—
79	C₄²	Q₈×C₁₉	1	1	yes	characteristic
80	C₄²	Q₈×C₁₉	1	1	yes	characteristic
81	C₂³	#41×C₁₉	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
87	C₂×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
88	C₂×C₄	#41×C₁₉	1	2	yes	—
89	C₂×C₄	#41×C₁₉	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	4	1	no	—
92	C₈	—	4	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
95	C₂²	C₁₉×#126	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	—	4	1	no	—
98	C₄	—	8	2	no	—
99	C₄	C₁₉×#123	1	1	yes	characteristic
100	C₄	C₁₉×#124	1	1	yes	characteristic
101	C₄	C₁₉×#125	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	C₁₉×#400	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#430

C₂

yes

maximal, characteristic

C₁₉×#423

C₂

yes

maximal, characteristic

C₁₉×#344

C₂

yes

maximal

C₁₉×#339

C₂

yes

maximal

C₁₉×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

Q₈

yes

characteristic

C₄²×C₁₉

Q₈

yes

characteristic

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2102

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#126

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#430

C₂×C₁₉

yes

characteristic

#423

C₂×C₁₉

yes

characteristic

#344

C₂×C₁₉

yes

—

#339

C₂×C₁₉

yes

—

H(3,ℤ/4)

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#400

yes

characteristic

C₂×M₁₆

C₂²×C₁₉

yes

—

C₂×M₁₆

C₂²×C₁₉

yes

characteristic

C₂×M₁₆

C₂²×C₁₉

yes

characteristic

#117

C₂²×C₁₉

yes

—

C₂×C₄²

C₂²×C₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₁₉

#2102

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₂³×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

Q₈×C₁₉

yes

characteristic

C₄²

Q₈×C₁₉

yes

characteristic

C₂³

#41×C₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

C₂×Q₈×C₁₉

yes

characteristic

C₂×C₄

#41×C₁₉

yes

—

C₂×C₄

#41×C₁₉

yes

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₁₉×C₂²⋊Q₈

yes

characteristic

C₂²

C₁₉×#126

yes

—

C₄

—

C₄

—

C₄

—

C₄

C₁₉×#123

yes

characteristic

100

C₄

C₁₉×#124

yes

characteristic

101

C₄

C₁₉×#125

yes

—

102

C₂

—

103

C₂

—

104

C₂

C₁₉×#400

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#400
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

subgroup

G/H

center

C₄×C₁₉

#124

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

C₂×C₁₉

C₂³×C₁₉

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
40. #2102	C₁₉	direct (N × H)
65. C₁₉	#2102	direct (N × H)

H ≅ G/N

type

40. #2102

C₁₉

direct (N × H)

65. C₁₉

#2102

direct (N × H)

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

subgroup	index
C₁₉×#430	2
C₁₉×#423	2
C₁₉×#344	2
C₁₉×#339	2
C₁₉×H(3,ℤ/4)	2
#2102	19

subgroup

index

C₁₉×#430

C₁₉×#423

C₁₉×#344

C₁₉×#339

C₁₉×H(3,ℤ/4)

#2102

Subgroups — C₁₉×#2102 #14559959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2102 #14559959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2102 #14559959