Group #14560501 — subgroups

Subgroups — C₁₉×#2644 #14560501

Order 2432.

420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 184 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×#397	C₂	1	6	yes	maximal, complemented
2	C₁₉×#396	C₂	1	2	yes	maximal, complemented
3	C₁₉×#390	C₂	1	3	yes	maximal
4	C₁₉×#389	C₂	1	3	yes	maximal, complemented
5	C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
9	C₂×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
10	C₂×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
12	C₁₉×#95	C₂²	1	1	yes	characteristic
13	C₁₉×#95	C₂²	1	3	yes	—
14	C₁₉×#95	C₂²	1	6	yes	—
15	C₂⁴×C₁₉	C₂³	1	2	yes	—
16	C₂×D₄×C₁₉	—	2	6	no	—
17	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	2	6	no	—
22	C₄⋊C₄×C₁₉	—	4	6	no	—
23	C₂²⋊C₄×C₁₉	—	4	6	no	—
24	C₂²⋊C₄×C₁₉	—	4	6	no	—
25	C₄²×C₁₉	—	2	6	no	—
26	C₂³×C₁₉	—	2	6	no	—
27	C₂³×C₁₉	—	2	6	no	—
28	C₂³×C₁₉	—	2	2	no	—
29	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
30	D₄×C₁₉	—	4	4	no	—
31	C₂×C₄×C₁₉	—	2	3	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	—	2	6	no	—
34	C₂×C₄×C₁₉	—	2	3	no	—
35	C₂×C₄×C₁₉	—	2	3	no	—
36	C₂×C₄×C₁₉	—	2	6	no	—
37	C₂×C₄×C₁₉	—	2	6	no	—
38	C₂×C₄×C₁₉	—	2	3	no	—
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×C₄×C₁₉	#41	1	6	yes	—
41	#2644	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₁₉	—	4	2	no	—
43	C₂²×C₁₉	—	4	6	no	—
44	C₂²×C₁₉	—	4	6	no	—
45	C₂²×C₁₉	C₂×#41	1	3	yes	—
46	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
47	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
48	C₄×C₁₉	—	4	3	no	—
49	C₄×C₁₉	—	4	6	no	—
50	C₄×C₁₉	—	4	3	no	—
51	C₄×C₁₉	#126	1	4	yes	—
52	#397	C₂×C₁₉	1	6	yes	complemented
53	#396	C₂×C₁₉	1	2	yes	complemented
54	#390	C₂×C₁₉	1	3	yes	—
55	#389	C₂×C₁₉	1	3	yes	complemented
56	#376	C₂×C₁₉	1	1	yes	characteristic, complemented
57	C₂×C₁₉	—	8	2	no	—
58	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
59	C₂×C₁₉	#540	1	3	yes	—
60	C₂×C₁₉	#542	1	3	yes	—
61	C₂²×D₄	C₂²×C₁₉	1	1	yes	characteristic
62	C₂×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
63	C₂×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
64	C₂×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
65	C₂×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
66	C₂×C₄²	C₂²×C₁₉	1	3	yes	—
67	#95	C₂²×C₁₉	1	1	yes	characteristic
68	#95	C₂²×C₁₉	1	3	yes	—
69	#95	C₂²×C₁₉	1	6	yes	—
70	C₁₉	#2644	1	1	yes	characteristic, direct product factor, Sylow
71	C₂⁴	C₂³×C₁₉	1	2	yes	—
72	C₂×D₄	—	2	6	no	—
73	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
74	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
75	C₂²×C₄	C₂³×C₁₉	1	6	yes	—
76	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
77	C₄⋊C₄	—	2	6	no	—
78	C₄⋊C₄	—	4	6	no	—
79	C₂²⋊C₄	—	4	6	no	—
80	C₂²⋊C₄	—	4	6	no	—
81	C₄²	—	2	6	no	—
82	C₂³	—	2	6	no	—
83	C₂³	—	2	6	no	—
84	C₂³	—	2	2	no	—
85	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
86	D₄	—	4	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	6	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	6	no	—
93	C₂×C₄	—	2	6	no	—
94	C₂×C₄	—	2	3	no	—
95	C₂×C₄	—	2	3	no	—
96	C₂×C₄	#41×C₁₉	1	6	yes	—
97	C₂²	—	4	2	no	—
98	C₂²	—	4	6	no	—
99	C₂²	—	4	6	no	—
100	C₂²	C₂×#41×C₁₉	1	3	yes	—
101	C₂²	C₁₉×H(5,𝔽₂)	1	3	yes	—
102	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	6	no	—
105	C₄	—	4	3	no	—
106	C₄	C₁₉×#126	1	4	yes	—
107	C₂	—	8	2	no	—
108	C₂	C₂×C₁₉×#126	1	1	yes	characteristic
109	C₂	C₁₉×#540	1	3	yes	—
110	C₂	C₁₉×#542	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#397

C₂

yes

maximal, complemented

C₁₉×#396

C₂

yes

maximal, complemented

C₁₉×#390

C₂

yes

maximal

C₁₉×#389

C₂

yes

maximal, complemented

C₁₉×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉×#95

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#41

yes

—

#2644

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#126

yes

—

#397

C₂×C₁₉

yes

complemented

#396

C₂×C₁₉

yes

complemented

#390

C₂×C₁₉

yes

—

#389

C₂×C₁₉

yes

complemented

#376

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₂×#126

yes

characteristic

C₂×C₁₉

#540

yes

—

C₂×C₁₉

#542

yes

—

C₂²×D₄

C₂²×C₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂×C₂²⋊C₄

C₂²×C₁₉

yes

—

C₂×C₂²⋊C₄

C₂²×C₁₉

yes

—

C₂×C₄²

C₂²×C₁₉

yes

—

#95

C₂²×C₁₉

yes

characteristic

#95

C₂²×C₁₉

yes

—

#95

C₂²×C₁₉

yes

—

C₁₉

#2644

yes

characteristic, direct product factor, Sylow

C₂⁴

C₂³×C₁₉

yes

—

C₂×D₄

—

C₂²×C₄

C₂³×C₁₉

yes

—

C₂²×C₄

C₂³×C₁₉

yes

—

C₂²×C₄

C₂³×C₁₉

yes

—

C₂²×C₄

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂⁴×C₁₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#41×C₁₉

yes

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#41×C₁₉

yes

—

101

C₂²

C₁₉×H(5,𝔽₂)

yes

—

102

C₂²

C₁₉×2₋¹⁺⁴

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

C₁₉×#126

yes

—

107

C₂

—

108

C₂

C₂×C₁₉×#126

yes

characteristic

109

C₂

C₁₉×#540

yes

—

110

C₂

C₁₉×#542

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂⁴

commutator, Frattini, cosocle

C₂³

C₂⁴×C₁₉

prime radical

C₂²×D₄×C₁₉

C₂²

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#397	C₂	semidirect
2. C₁₉×#396	C₂	semidirect
4. C₁₉×#389	C₂	semidirect
5. C₁₉×#376	C₂	semidirect
41. #2644	C₁₉	direct (N × H)
52. #397	C₂×C₁₉	semidirect
53. #396	C₂×C₁₉	semidirect
55. #389	C₂×C₁₉	semidirect
56. #376	C₂×C₁₉	semidirect
70. C₁₉	#2644	direct (N × H)

H ≅ G/N

type

1. C₁₉×#397

C₂

semidirect

2. C₁₉×#396

C₂

semidirect

4. C₁₉×#389

C₂

semidirect

5. C₁₉×#376

C₂

semidirect

41. #2644

C₁₉

direct (N × H)

52. #397

C₂×C₁₉

semidirect

53. #396

C₂×C₁₉

semidirect

55. #389

C₂×C₁₉

semidirect

56. #376

C₂×C₁₉

semidirect

70. C₁₉

#2644

direct (N × H)

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

subgroup	index
C₁₉×#397	2
C₁₉×#396	2
C₁₉×#390	2
C₁₉×#389	2
C₁₉×#376	2
#2644	19

subgroup

index

C₁₉×#397

C₁₉×#396

C₁₉×#390

C₁₉×#389

C₁₉×#376

#2644

Subgroups — C₁₉×#2644 #14560501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2644 #14560501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2644 #14560501