Group #14571980 — subgroups

Subgroups — #14571980

Order 2432.

924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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	C₂×#10597320	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597376	C₂	1	6	yes	maximal, complemented
3	#11926446	C₂	1	6	yes	maximal, complemented
4	#11926414	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
7	C₂²×C₂²⋊D₁₉	C₂²	1	4	yes	—
8	C₂²×D₇₆	C₂²	1	6	yes	—
9	C₂×C₄²×C₁₉	—	2	4	no	—
10	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	#10597376	—	2	24	no	—
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	12	yes	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	6	yes	—
15	#10597320	—	2	4	no	—
16	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
17	C₂³×D₁₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₉	—	2	6	no	—
19	C₂²×C₄×C₁₉	—	2	6	no	—
20	C₂²×C₄×C₁₉	D₄	1	12	yes	complemented
21	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂×C₂²⋊D₁₉	—	2	24	no	—
24	C₂²×Dic₁₉	C₂³	1	4	yes	—
25	C₂×D₇₆	—	2	12	no	—
26	C₂×D₇₆	—	2	12	no	—
27	C₂×D₇₆	—	2	12	no	—
28	C₄²×C₁₉	—	2	6	no	—
29	C₄²×C₁₉	D₄	1	4	yes	complemented
30	(C₂×D₁₉)⋊C₄	—	2	24	no	—
31	C₄⋊Dic₁₉	—	2	12	no	—
32	C₂³×C₁₉	—	2	1	no	—
33	C₂³×C₁₉	—	2	3	no	—
34	C₂³×C₁₉	C₂×D₄	1	6	yes	—
35	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
36	C₂²×D₁₉	—	2	12	no	—
37	C₂²×D₁₉	—	2	4	no	—
38	C₂²×D₁₉	—	2	12	no	—
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×C₄×C₁₉	—	2	3	no	—
41	C₂×C₄×C₁₉	—	2	24	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
43	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
45	C₂×C₄×C₁₉	#41	1	6	yes	—
46	C₂²⋊D₁₉	—	4	16	no	—
47	C₂×Dic₁₉	—	2	12	no	—
48	D₇₆	—	4	24	no	—
49	#2856	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	2	6	no	—
51	C₂²×C₁₉	—	2	6	no	—
52	C₂²×C₁₉	#127	1	4	yes	complemented
53	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
54	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
55	C₂²×C₁₉	C₂×#41	1	3	yes	—
56	C₂×D₁₉	—	4	12	no	—
57	C₂×D₁₉	—	4	4	no	—
58	C₂×D₁₉	—	4	12	no	—
59	C₄×C₁₉	—	2	6	no	—
60	C₄×C₁₉	#121	1	12	yes	complemented
61	Dic₁₉	—	4	4	no	—
62	C₂×#127	—	19	1	no	—
63	C₂×#121	—	19	6	no	—
64	C₂²×C₄²	D₁₉	1	1	yes	characteristic, complemented
65	#390	—	19	6	no	—
66	#384	—	19	1	no	—
67	C₂×C₁₉	—	2	4	no	—
68	C₂×C₁₉	C₂×#121	1	3	yes	—
69	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
70	C₂×C₁₉	#532	1	3	yes	—
71	D₁₉	—	8	4	no	—
72	C₂²×D₄	—	19	4	no	—
73	C₂²×D₄	—	19	6	no	—
74	C₂³×C₄	C₂×D₁₉	1	3	yes	—
75	#127	—	38	4	no	—
76	#121	—	38	24	no	—
77	C₂×C₄⋊C₄	—	19	6	no	—
78	C₂×C₂²⋊C₄	—	19	12	no	—
79	C₂×C₄²	—	2	4	no	—
80	C₂×C₄²	C₂×D₁₉	1	3	yes	—
81	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
82	C₁₉	#2856	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	—	19	4	no	—
84	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
85	C₂×D₄	—	38	24	no	—
86	C₂×D₄	—	38	12	no	—
87	C₂×D₄	—	38	12	no	—
88	C₂×D₄	—	38	12	no	—
89	C₂²×C₄	—	2	6	no	—
90	C₂²×C₄	—	2	6	no	—
91	C₂²×C₄	—	19	4	no	—
92	C₂²×C₄	D₇₆	1	12	yes	complemented
93	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
94	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
95	C₄⋊C₄	—	38	12	no	—
96	C₂²⋊C₄	—	38	24	no	—
97	C₄²	—	2	6	no	—
98	C₄²	C₂²⋊D₁₉	1	4	yes	complemented
99	C₂³	—	2	3	no	—
100	C₂³	—	2	1	no	—
101	C₂³	—	38	12	no	—
102	C₂³	—	38	12	no	—
103	C₂³	—	38	4	no	—
104	C₂³	C₂×D₇₆	1	6	yes	—
105	C₂³	C₂³×D₁₉	1	1	yes	characteristic
106	D₄	—	76	16	no	—
107	D₄	—	76	24	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	2	3	no	—
110	C₂×C₄	—	2	24	no	—
111	C₂×C₄	—	38	12	no	—
112	C₂×C₄	C₂×D₇₆	1	6	yes	—
113	C₂×C₄	C₂×D₇₆	1	6	yes	—
114	C₂×C₄	#64541	1	6	yes	—
115	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
116	C₂²	—	2	6	no	—
117	C₂²	—	2	6	no	—
118	C₂²	—	76	4	no	—
119	C₂²	—	76	12	no	—
120	C₂²	—	76	12	no	—
121	C₂²	#10597320	1	4	yes	complemented
122	C₂²	C₂²×D₇₆	1	3	yes	—
123	C₂²	C₂×#64541	1	3	yes	—
124	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₄	—	2	6	no	—
126	C₄	—	76	4	no	—
127	C₄	#10597376	1	12	yes	complemented
128	C₂	—	2	4	no	—
129	C₂	—	152	4	no	—
130	C₂	C₂×#10597376	1	3	yes	—
131	C₂	C₂×#10597320	1	1	yes	characteristic
132	C₂	#11927094	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic, complemented

C₂×#10597376

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal, complemented

#11926414

C₂

yes

maximal, characteristic, complemented

C₂²×C₄²×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597320

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

complemented

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2856

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

complemented

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

complemented

Dic₁₉

—

C₂×#127

—

C₂×#121

—

C₂²×C₄²

D₁₉

yes

characteristic, complemented

#390

—

#384

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#121

yes

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#532

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

C₂×D₁₉

yes

—

#127

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₁₉

#2856

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

complemented

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

complemented

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₂×D₇₆

yes

—

105

C₂³

C₂³×D₁₉

yes

characteristic

106

D₄

—

107

D₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₂×D₇₆

yes

—

113

C₂×C₄

C₂×D₇₆

yes

—

114

C₂×C₄

#64541

yes

—

115

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#10597320

yes

complemented

122

C₂²

C₂²×D₇₆

yes

—

123

C₂²

C₂×#64541

yes

—

124

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

#10597376

yes

complemented

128

C₂

—

129

C₂

—

152

—

130

C₂

C₂×#10597376

yes

—

131

C₂

C₂×#10597320

yes

characteristic

132

C₂

#11927094

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂²×C₄²×C₁₉	C₂
hypercenter	C₂²×C₄²	D₁₉
hypocenter	C₁₉	#2856
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂²×C₄²×C₁₉

C₂

hypercenter

C₂²×C₄²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂²×C₄²

N	H ≅ G/N	type
1. C₂×#10597320	C₂	semidirect
2. C₂×#10597376	C₂	semidirect
3. #11926446	C₂	semidirect
4. #11926414	C₂	semidirect
5. C₂²×C₄²×C₁₉	C₂	semidirect
20. C₂²×C₄×C₁₉	D₄	semidirect
29. C₄²×C₁₉	D₄	semidirect
52. C₂²×C₁₉	#127	semidirect
60. C₄×C₁₉	#121	semidirect
64. C₂²×C₄²	D₁₉	semidirect
82. C₁₉	#2856	semidirect
92. C₂²×C₄	D₇₆	semidirect
98. C₄²	C₂²⋊D₁₉	semidirect
121. C₂²	#10597320	semidirect
127. C₄	#10597376	semidirect

H ≅ G/N

type

1. C₂×#10597320

C₂

semidirect

2. C₂×#10597376

C₂

semidirect

3. #11926446

C₂

semidirect

4. #11926414

C₂

semidirect

5. C₂²×C₄²×C₁₉

C₂

semidirect

20. C₂²×C₄×C₁₉

D₄

semidirect

29. C₄²×C₁₉

D₄

semidirect

52. C₂²×C₁₉

#127

semidirect

60. C₄×C₁₉

#121

semidirect

64. C₂²×C₄²

D₁₉

semidirect

82. C₁₉

#2856

semidirect

92. C₂²×C₄

D₇₆

semidirect

98. C₄²

C₂²⋊D₁₉

semidirect

121. C₂²

#10597320

semidirect

127. C₄

#10597376

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597376	2
#11926446	2
#11926414	2
C₂²×C₄²×C₁₉	2
#2856	19

subgroup

index

C₂²×C₄²×C₁₉

Subgroups — #14571980

Conjugacy classes of subgroups

Complements

Maximal subgroups