Group #14571899 — subgroups

Subgroups — #14571899

Order 2432.

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

normal subgroups only

This group has 548 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	#11926480	C₂	1	4	yes	maximal, complemented
2	#11926467	C₂	1	8	yes	maximal, complemented
3	#11926400	C₂	1	2	yes	maximal
4	C₁₉×#379	C₂	1	1	yes	maximal, characteristic
5	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
7	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
9	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
10	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	complemented
12	C₂×Dic₁₉⋊C₄	C₂²	1	8	yes	complemented
13	C₁₉⋊#95	C₂²	1	4	yes	complemented
14	C₂⁴×C₁₉	—	4	4	no	—
15	C₂⁴×C₁₉	—	4	2	no	—
16	C₂⁴×C₁₉	Q₈	1	4	yes	—
17	C₂⁴×C₁₉	C₂³	1	2	yes	—
18	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
20	C₂²×Dic₁₉	C₂³	1	8	yes	—
21	C₂²⋊C₄×C₁₉	—	4	4	no	—
22	C₂²⋊C₄×C₁₉	—	4	2	no	—
23	C₂²⋊Dic₁₉	—	4	4	no	—
24	C₂²⋊Dic₁₉	—	4	4	no	—
25	C₂²⋊Dic₁₉	—	4	4	no	—
26	C₄⋊Dic₁₉	—	4	4	no	—
27	Dic₁₉⋊C₄	—	4	8	no	—
28	C₂³×C₁₉	—	2	4	no	—
29	C₂³×C₁₉	—	2	4	no	—
30	C₂³×C₁₉	—	2	4	no	—
31	C₂³×C₁₉	—	2	4	no	—
32	C₂³×C₁₉	—	2	2	no	—
33	C₂³×C₁₉	—	4	8	no	—
34	C₂³×C₁₉	—	4	4	no	—
35	C₂³×C₁₉	—	4	16	no	—
36	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
37	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
38	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	8	no	—
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×Dic₁₉	—	2	8	no	—
42	C₂×Dic₁₉	—	2	8	no	—
43	C₂×Dic₁₉	—	2	8	no	—
44	#2842	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	—	2	4	no	—
46	C₂²×C₁₉	—	2	4	no	—
47	C₂²×C₁₉	—	2	4	no	—
48	C₂²×C₁₉	—	2	4	no	—
49	C₂²×C₁₉	—	2	2	no	—
50	C₂²×C₁₉	—	4	16	no	—
51	C₂²×C₁₉	—	4	8	no	—
52	C₂²×C₁₉	—	4	4	no	—
53	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
54	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
55	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
56	C₄×C₁₉	—	4	4	no	—
57	Dic₁₉	—	4	8	no	—
58	#399	—	19	4	no	—
59	#396	—	19	8	no	—
60	#379	—	19	2	no	—
61	#379	D₁₉	1	1	yes	characteristic
62	C₂×C₁₉	—	4	4	no	—
63	C₂×C₁₉	—	4	2	no	—
64	C₂×C₁₉	#543	1	2	yes	—
65	C₂×C₁₉	#543	1	1	yes	characteristic
66	C₂×C₁₉	#560	1	4	yes	—
67	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
68	C₂×C₄⋊C₄	—	19	8	no	—
69	C₂×C₄⋊C₄	—	19	4	no	—
70	C₂×C₂²⋊C₄	—	19	4	no	—
71	C₂×C₂²⋊C₄	—	19	4	no	—
72	C₂×C₂²⋊C₄	—	19	4	no	—
73	C₂×C₂²⋊C₄	C₂×D₁₉	1	4	yes	—
74	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
75	#95	—	19	4	no	—
76	C₁₉	#2842	1	1	yes	characteristic, complemented, Sylow
77	C₂⁴	—	4	4	no	—
78	C₂⁴	—	4	2	no	—
79	C₂⁴	Dic₃₈	1	4	yes	—
80	C₂⁴	C₂²×D₁₉	1	2	yes	—
81	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
82	C₂²×C₄	—	19	8	no	—
83	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
84	C₄⋊C₄	—	76	8	no	—
85	C₄⋊C₄	—	76	4	no	—
86	C₂²⋊C₄	—	4	4	no	—
87	C₂²⋊C₄	—	4	2	no	—
88	C₂²⋊C₄	—	76	4	no	—
89	C₂²⋊C₄	—	76	4	no	—
90	C₂²⋊C₄	—	76	4	no	—
91	C₂³	—	2	4	no	—
92	C₂³	—	2	2	no	—
93	C₂³	—	2	4	no	—
94	C₂³	—	2	4	no	—
95	C₂³	—	2	4	no	—
96	C₂³	—	4	8	no	—
97	C₂³	—	4	4	no	—
98	C₂³	—	4	16	no	—
99	C₂³	C₂×Dic₃₈	1	4	yes	—
100	C₂³	C₂×Dic₃₈	1	2	yes	—
101	C₂³	C₂³×D₁₉	1	1	yes	characteristic
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	38	8	no	—
105	C₂×C₄	—	38	8	no	—
106	C₂×C₄	—	38	8	no	—
107	C₂²	—	2	4	no	—
108	C₂²	—	2	2	no	—
109	C₂²	—	2	4	no	—
110	C₂²	—	2	4	no	—
111	C₂²	—	2	4	no	—
112	C₂²	—	4	16	no	—
113	C₂²	—	4	8	no	—
114	C₂²	—	4	4	no	—
115	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
116	C₂²	#10597430	1	4	yes	—
117	C₂²	#10597430	1	2	yes	—
118	C₄	—	4	4	no	—
119	C₄	—	76	8	no	—
120	C₂	—	4	4	no	—
121	C₂	—	4	2	no	—
122	C₂	#11927170	1	2	yes	—
123	C₂	#11927170	1	1	yes	characteristic
124	C₂	#11927283	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926480

C₂

yes

maximal, complemented

#11926467

C₂

yes

maximal, complemented

#11926400

C₂

yes

maximal

C₁₉×#379

C₂

yes

maximal, characteristic

C₂⁵×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

C₂×Dic₁₉⋊C₄

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

Q₈

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2842

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#543

yes

—

C₂×C₁₉

#543

yes

characteristic

C₂×C₁₉

#560

yes

—

C₂⁵

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

C₁₉

#2842

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

Dic₃₈

yes

—

C₂⁴

C₂²×D₁₉

yes

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×Dic₃₈

yes

—

100

C₂³

C₂×Dic₃₈

yes

—

101

C₂³

C₂³×D₁₉

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂²×Dic₃₈

yes

characteristic

116

C₂²

#10597430

yes

—

117

C₂²

#10597430

yes

—

118

C₄

—

119

C₄

—

120

C₂

—

121

C₂

—

122

C₂

#11927170

yes

—

123

C₂

#11927170

yes

characteristic

124

C₂

#11927283

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#379	C₂
prime radical	C₂⁵×C₁₉	C₂²
hypercenter	#379	D₁₉
hypocenter	C₁₉	#2842
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #379

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#379

C₂

prime radical

C₂⁵×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #379

N	H ≅ G/N	type
1. #11926480	C₂	semidirect
2. #11926467	C₂	semidirect
11. C₂×C₄⋊Dic₁₉	C₂²	semidirect
12. C₂×Dic₁₉⋊C₄	C₂²	semidirect
13. C₁₉⋊#95	C₂²	semidirect
76. C₁₉	#2842	semidirect

H ≅ G/N

type

1. #11926480

C₂

semidirect

2. #11926467

C₂

semidirect

11. C₂×C₄⋊Dic₁₉

C₂²

semidirect

12. C₂×Dic₁₉⋊C₄

C₂²

semidirect

13. C₁₉⋊#95

C₂²

semidirect

76. C₁₉

#2842

semidirect

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

subgroup	index
#11926480	2
#11926467	2
#11926400	2
C₁₉×#379	2
#2842	19

subgroup

index

C₁₉×#379

Subgroups — #14571899

Conjugacy classes of subgroups

Complements

Maximal subgroups