Group #14569595 — subgroups

Subgroups — #14569595

Order 2432.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11926473	C₂	1	6	yes	maximal, complemented
2	#11926468	C₂	1	2	yes	maximal, complemented
3	#11926446	C₂	1	3	yes	maximal
4	#11926442	C₂	1	3	yes	maximal, complemented
5	C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
8	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
9	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
11	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
12	C₁₉×#95	C₂²	1	1	yes	characteristic
13	C₁₉×#95	C₂²	1	3	yes	—
14	C₁₉⋊#95	C₂²	1	6	yes	—
15	C₂³×D₁₉	C₂³	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	C₂³	1	6	yes	—
20	C₂×D₇₆	—	2	6	no	—
21	C₄²×C₁₉	—	2	6	no	—
22	(C₂×D₁₉)⋊C₄	—	4	6	no	—
23	(C₂×D₁₉)⋊C₄	—	4	6	no	—
24	C₄⋊Dic₁₉	—	2	6	no	—
25	Dic₁₉⋊C₄	—	4	6	no	—
26	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
27	C₂²×D₁₉	—	2	6	no	—
28	C₂²×D₁₉	—	2	6	no	—
29	C₂²×D₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	—	2	3	no	—
31	C₂×C₄×C₁₉	—	2	3	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	—	2	3	no	—
34	C₂×C₄×C₁₉	—	2	3	no	—
35	C₂×C₄×C₁₉	—	2	3	no	—
36	C₂×C₄×C₁₉	#41	1	6	yes	—
37	C₂×Dic₁₉	—	2	6	no	—
38	C₂×Dic₁₉	—	2	6	no	—
39	C₂×Dic₁₉	—	2	6	no	—
40	D₇₆	—	4	4	no	—
41	#2644	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	C₂×#41	1	3	yes	—
43	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
44	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
45	C₂×D₁₉	—	4	2	no	—
46	C₂×D₁₉	—	4	6	no	—
47	C₂×D₁₉	—	4	6	no	—
48	C₄×C₁₉	—	4	3	no	—
49	C₄×C₁₉	—	4	3	no	—
50	C₄×C₁₉	#126	1	4	yes	—
51	Dic₁₉	—	4	6	no	—
52	#397	—	19	6	no	—
53	#396	—	19	2	no	—
54	#390	—	19	3	no	—
55	#389	—	19	3	no	—
56	#376	D₁₉	1	1	yes	characteristic, complemented
57	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
58	C₂×C₁₉	#540	1	3	yes	—
59	C₂×C₁₉	#542	1	3	yes	—
60	D₁₉	—	8	2	no	—
61	C₂²×D₄	—	19	1	no	—
62	C₂×C₄⋊C₄	—	19	3	no	—
63	C₂×C₄⋊C₄	—	19	6	no	—
64	C₂×C₂²⋊C₄	—	19	6	no	—
65	C₂×C₂²⋊C₄	—	19	6	no	—
66	C₂×C₄²	C₂×D₁₉	1	3	yes	—
67	#95	—	19	6	no	—
68	#95	C₂×D₁₉	1	1	yes	characteristic
69	#95	C₂×D₁₉	1	3	yes	—
70	C₁₉	#2644	1	1	yes	characteristic, complemented, Sylow
71	C₂⁴	—	19	2	no	—
72	C₂×D₄	—	38	6	no	—
73	C₂²×C₄	—	19	6	no	—
74	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
75	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
76	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
77	C₄⋊C₄	—	38	6	no	—
78	C₄⋊C₄	—	76	6	no	—
79	C₂²⋊C₄	—	76	6	no	—
80	C₂²⋊C₄	—	76	6	no	—
81	C₄²	—	2	6	no	—
82	C₂³	—	38	6	no	—
83	C₂³	—	38	6	no	—
84	C₂³	—	38	2	no	—
85	C₂³	C₂³×D₁₉	1	1	yes	characteristic
86	D₄	—	76	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	38	6	no	—
94	C₂×C₄	—	38	6	no	—
95	C₂×C₄	—	38	6	no	—
96	C₂×C₄	#64541	1	6	yes	—
97	C₂²	—	76	2	no	—
98	C₂²	—	76	6	no	—
99	C₂²	—	76	6	no	—
100	C₂²	C₂×#64541	1	3	yes	—
101	C₂²	#10597435	1	3	yes	—
102	C₂²	#10597436	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	76	6	no	—
106	C₄	#10597322	1	4	yes	—
107	C₂	—	152	2	no	—
108	C₂	C₂×#10597322	1	1	yes	characteristic
109	C₂	#11927149	1	3	yes	—
110	C₂	#11927165	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926473

C₂

yes

maximal, complemented

#11926468

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal

#11926442

C₂

yes

maximal, complemented

C₁₉×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₄²×C₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2644

—

maximal, Sylow

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#126

yes

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

C₂×#126

yes

characteristic

C₂×C₁₉

#540

yes

—

C₂×C₁₉

#542

yes

—

D₁₉

—

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

#95

—

#95

C₂×D₁₉

yes

characteristic

#95

C₂×D₁₉

yes

—

C₁₉

#2644

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64541

yes

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#64541

yes

—

101

C₂²

#10597435

yes

—

102

C₂²

#10597436

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

#10597322

yes

—

107

C₂

—

152

—

108

C₂

C₂×#10597322

yes

characteristic

109

C₂

#11927149

yes

—

110

C₂

#11927165

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#376	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	#376	D₁₉
hypocenter	C₁₉	#2644
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#376

C₂

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. #11926473	C₂	semidirect
2. #11926468	C₂	semidirect
4. #11926442	C₂	semidirect
5. C₁₉×#376	C₂	semidirect
56. #376	D₁₉	semidirect
70. C₁₉	#2644	semidirect

H ≅ G/N

type

1. #11926473

C₂

semidirect

2. #11926468

C₂

semidirect

4. #11926442

C₂

semidirect

5. C₁₉×#376

C₂

semidirect

56. #376

D₁₉

semidirect

70. C₁₉

#2644

semidirect

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

subgroup	index
#11926473	2
#11926468	2
#11926446	2
#11926442	2
C₁₉×#376	2
#2644	19

subgroup

index

C₁₉×#376

Subgroups — #14569595

Conjugacy classes of subgroups

Complements

Maximal subgroups