Group #14571900 — subgroups

Subgroups — #14571900

Order 2432.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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	3	yes	maximal, complemented
2	#11926468	C₂	1	2	yes	maximal, complemented
3	#11926466	C₂	1	6	yes	maximal, complemented
4	#11926399	C₂	1	3	yes	maximal
5	C₁₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×D₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	complemented
8	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
10	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
11	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	complemented
13	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	complemented
14	C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
15	C₁₉⋊#95	C₂²	1	3	yes	complemented
16	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
17	C₂³×D₁₉	—	4	3	no	—
18	C₂³×D₁₉	—	4	3	no	—
19	C₂³×D₁₉	Q₈	1	4	yes	—
20	C₂³×D₁₉	C₂³	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂²×Dic₁₉	C₂³	1	6	yes	—
24	C₄⋊C₄×C₁₉	—	4	3	no	—
25	C₂²⋊C₄×C₁₉	—	4	3	no	—
26	C₂²⋊Dic₁₉	—	4	3	no	—
27	(C₂×D₁₉)⋊C₄	—	4	6	no	—
28	(C₂×D₁₉)⋊C₄	—	4	6	no	—
29	C₄⋊Dic₁₉	—	4	3	no	—
30	Dic₁₉⋊C₄	—	4	6	no	—
31	C₂³×C₁₉	—	2	3	no	—
32	C₂³×C₁₉	—	2	3	no	—
33	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
34	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
35	C₂²×D₁₉	—	2	6	no	—
36	C₂²×D₁₉	—	2	6	no	—
37	C₂²×D₁₉	—	4	12	no	—
38	C₂²×D₁₉	—	4	4	no	—
39	C₂²×D₁₉	—	4	12	no	—
40	C₂²×D₁₉	C₂×Q₈	1	4	yes	—
41	C₂×C₄×C₁₉	—	2	6	no	—
42	C₂×C₄×C₁₉	—	2	3	no	—
43	C₂×C₄×C₁₉	—	2	6	no	—
44	C₂×C₄×C₁₉	—	2	3	no	—
45	C₂×Dic₁₉	—	2	6	no	—
46	C₂×Dic₁₉	—	2	6	no	—
47	C₂×Dic₁₉	—	2	6	no	—
48	#2842	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	—	2	6	no	—
50	C₂²×C₁₉	—	4	1	no	—
51	C₂²×C₁₉	—	4	3	no	—
52	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
54	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
55	C₂×D₁₉	—	2	12	no	—
56	C₂×D₁₉	—	4	16	no	—
57	C₂×D₁₉	—	4	2	no	—
58	C₂×D₁₉	—	4	6	no	—
59	C₄×C₁₉	—	4	3	no	—
60	C₄×C₁₉	—	4	3	no	—
61	Dic₁₉	—	4	6	no	—
62	#399	—	19	3	no	—
63	#399	D₁₉	1	1	yes	characteristic, complemented
64	#396	—	19	6	no	—
65	#396	—	19	2	no	—
66	#379	—	19	3	no	—
67	C₂×C₁₉	—	4	2	no	—
68	C₂×C₁₉	#543	1	3	yes	—
69	C₂×C₁₉	#560	1	1	yes	characteristic
70	C₂×C₁₉	#560	1	3	yes	—
71	D₁₉	—	4	4	no	—
72	C₂⁵	—	19	1	no	—
73	C₂×C₄⋊C₄	—	19	6	no	—
74	C₂×C₄⋊C₄	—	19	3	no	—
75	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	complemented
76	C₂×C₂²⋊C₄	—	19	3	no	—
77	C₂×C₂²⋊C₄	—	19	6	no	—
78	C₂×C₂²⋊C₄	—	19	6	no	—
79	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
80	#95	—	19	3	no	—
81	#95	C₂×D₁₉	1	1	yes	characteristic, complemented
82	C₁₉	#2842	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	—	19	2	no	—
84	C₂⁴	—	19	4	no	—
85	C₂⁴	—	76	3	no	—
86	C₂⁴	—	76	3	no	—
87	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
88	C₂²×C₄	—	19	6	no	—
89	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
91	C₄⋊C₄	—	4	3	no	—
92	C₄⋊C₄	—	76	6	no	—
93	C₄⋊C₄	—	76	3	no	—
94	C₂²⋊C₄	—	4	3	no	—
95	C₂²⋊C₄	—	76	6	no	—
96	C₂²⋊C₄	—	76	6	no	—
97	C₂²⋊C₄	—	76	3	no	—
98	C₂³	—	2	3	no	—
99	C₂³	—	2	3	no	—
100	C₂³	—	19	4	no	—
101	C₂³	—	38	6	no	—
102	C₂³	—	38	6	no	—
103	C₂³	—	76	12	no	—
104	C₂³	—	76	4	no	—
105	C₂³	—	76	12	no	—
106	C₂³	Q₈×D₁₉	1	2	yes	—
107	C₂³	C₂³×D₁₉	1	1	yes	characteristic
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	2	3	no	—
110	C₂×C₄	—	2	6	no	—
111	C₂×C₄	—	2	6	no	—
112	C₂×C₄	—	38	6	no	—
113	C₂×C₄	—	38	6	no	—
114	C₂×C₄	—	38	6	no	—
115	C₂²	—	2	6	no	—
116	C₂²	—	4	1	no	—
117	C₂²	—	4	3	no	—
118	C₂²	—	38	12	no	—
119	C₂²	—	76	16	no	—
120	C₂²	—	76	2	no	—
121	C₂²	—	76	6	no	—
122	C₂²	#10597430	1	3	yes	—
123	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
124	C₂²	#10597435	1	3	yes	—
125	C₄	—	4	3	no	—
126	C₄	—	4	3	no	—
127	C₄	—	76	6	no	—
128	C₂	—	4	2	no	—
129	C₂	—	76	4	no	—
130	C₂	#11927169	1	3	yes	—
131	C₂	#11927281	1	1	yes	characteristic
132	C₂	#11927284	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926480

C₂

yes

maximal, complemented

#11926468

C₂

yes

maximal, complemented

#11926466

C₂

yes

maximal, complemented

#11926399

C₂

yes

maximal

C₁₉×#399

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

complemented

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

C₂×Dic₁₉⋊C₄

C₂²

yes

complemented

C₁₉×#95

C₂²

yes

characteristic, complemented

C₁₉⋊#95

C₂²

yes

complemented

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

—

C₂³×D₁₉

—

C₂³×D₁₉

Q₈

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2842

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#399

—

#399

D₁₉

yes

characteristic, complemented

#396

—

#396

—

#379

—

C₂×C₁₉

—

C₂×C₁₉

#543

yes

—

C₂×C₁₉

#560

yes

characteristic

C₂×C₁₉

#560

yes

—

D₁₉

—

C₂⁵

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

#95

C₂×D₁₉

yes

characteristic, complemented

C₁₉

#2842

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

Q₈×D₁₉

yes

—

107

C₂³

C₂³×D₁₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

#10597430

yes

—

123

C₂²

C₂×Q₈×D₁₉

yes

characteristic

124

C₂²

#10597435

yes

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₂

—

129

C₂

—

130

C₂

#11927169

yes

—

131

C₂

#11927281

yes

characteristic

132

C₂

#11927284

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#399	C₂
prime radical	C₂⁴×D₁₉	C₂²
hypercenter	#399	D₁₉
hypocenter	C₁₉	#2842
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #399

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#399

C₂

prime radical

C₂⁴×D₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #399

N	H ≅ G/N	type
1. #11926480	C₂	semidirect
2. #11926468	C₂	semidirect
3. #11926466	C₂	semidirect
5. C₁₉×#399	C₂	semidirect
7. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
12. C₂×C₄⋊Dic₁₉	C₂²	semidirect
13. C₂×Dic₁₉⋊C₄	C₂²	semidirect
14. C₁₉×#95	C₂²	semidirect
15. C₁₉⋊#95	C₂²	semidirect
63. #399	D₁₉	semidirect
75. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
81. #95	C₂×D₁₉	semidirect
82. C₁₉	#2842	semidirect

H ≅ G/N

type

1. #11926480

C₂

semidirect

2. #11926468

C₂

semidirect

3. #11926466

C₂

semidirect

5. C₁₉×#399

C₂

semidirect

7. C₂×C₄⋊C₄×C₁₉

C₂²

semidirect

12. C₂×C₄⋊Dic₁₉

C₂²

semidirect

13. C₂×Dic₁₉⋊C₄

C₂²

semidirect

14. C₁₉×#95

C₂²

semidirect

15. C₁₉⋊#95

C₂²

semidirect

63. #399

D₁₉

semidirect

75. C₂×C₄⋊C₄

C₂×D₁₉

semidirect

81. #95

C₂×D₁₉

semidirect

82. C₁₉

#2842

semidirect

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

subgroup	index
#11926480	2
#11926468	2
#11926466	2
#11926399	2
C₁₉×#399	2
#2842	19

subgroup

index

C₁₉×#399

Subgroups — #14571900

Conjugacy classes of subgroups

Complements

Maximal subgroups