Group #20283076 — subgroups

Subgroups — #20283076

Order 6784.

472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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×#13133208	C₂	1	2	yes	maximal
2	#16810522	C₂	1	4	yes	maximal
3	#16810519	C₂	1	4	yes	maximal
4	#16810493	C₂	1	1	yes	maximal, characteristic
5	#16810488	C₂	1	2	yes	maximal
6	C₄²×Dic₅₃	C₂	1	1	yes	maximal, characteristic
7	C₅₃×#384	C₂	1	1	yes	maximal, characteristic
8	#13133208	—	2	8	no	—
9	C₂×C₄⋊Dic₅₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₅₃	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	—
12	C₂×#11719919	C₂²	1	4	yes	—
13	C₂×C₄×Dic₅₃	C₂²	1	2	yes	—
14	C₂×C₄×Dic₅₃	C₂²	1	2	yes	—
15	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
17	#13133124	C₂²	1	8	yes	—
18	C₂×C₄⋊C₄×C₅₃	C₂²	1	4	yes	—
19	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
20	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
22	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
24	C₂²×Dic₅₃	C₂³	1	4	yes	—
25	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₅₃	C₂³	1	2	yes	—
28	C₄⋊C₄×C₅₃	—	2	4	no	—
29	C₄⋊C₄×C₅₃	—	2	8	no	—
30	C₄²×C₅₃	Q₈	1	4	yes	—
31	C₄⋊Dic₅₃	—	2	4	no	—
32	C₄⋊Dic₅₃	—	2	8	no	—
33	C₄⋊Dic₅₃	—	2	8	no	—
34	#11719919	—	2	8	no	—
35	C₄×Dic₅₃	—	2	4	no	—
36	C₄×Dic₅₃	—	2	4	no	—
37	C₄×Dic₅₃	D₄	1	4	yes	—
38	C₄×Dic₅₃	Q₈	1	4	yes	—
39	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₅₃	—	2	4	no	—
41	C₂×C₄×C₅₃	—	2	8	no	—
42	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₅₃	C₂×Q₈	1	4	yes	—
44	C₂×C₄×C₅₃	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₅₃	C₂×Q₈	1	2	yes	—
46	C₂×C₄×C₅₃	#41	1	4	yes	—
47	C₂×C₄×C₅₃	#41	1	4	yes	—
48	C₂×Dic₅₃	—	2	2	no	—
49	C₂×Dic₅₃	—	2	2	no	—
50	C₂×Dic₅₃	—	2	2	no	—
51	C₂×Dic₅₃	—	2	2	no	—
52	C₂×Dic₅₃	—	2	4	no	—
53	C₂×Dic₅₃	—	2	8	no	—
54	C₂×Dic₅₃	C₂×D₄	1	2	yes	—
55	C₂×Dic₅₃	C₂×D₄	1	2	yes	—
56	C₂×Dic₅₃	C₂×Q₈	1	4	yes	—
57	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
58	C₂²×C₅₃	C₂²×Q₈	1	1	yes	characteristic
59	C₂²×C₅₃	C₂²×Q₈	1	1	yes	characteristic
60	C₂²×C₅₃	C₂×#41	1	2	yes	—
61	C₂²×C₅₃	C₂×#41	1	2	yes	—
62	C₄×C₅₃	—	4	4	no	—
63	C₄×C₅₃	#125	1	8	yes	complemented
64	C₄×C₅₃	C₄⋊Q₈	1	4	yes	—
65	Dic₅₃	—	2	2	no	—
66	Dic₅₃	—	2	2	no	—
67	Dic₅₃	—	2	4	no	—
68	Dic₅₃	—	4	4	no	—
69	#2859	—	53	1	no	maximal, Sylow
70	C₂×C₅₃	C₂×#125	1	2	yes	—
71	C₂×C₅₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₅₃	#532	1	1	yes	characteristic
73	C₂×C₅₃	#532	1	1	yes	characteristic
74	C₂×C₅₃	#533	1	2	yes	—
75	C₂×#125	—	53	2	no	—
76	#389	—	53	4	no	—
77	#389	—	53	4	no	—
78	#384	—	53	1	no	—
79	#384	D₅₃	1	1	yes	characteristic
80	#382	—	53	2	no	—
81	C₄³	—	53	1	no	—
82	C₅₃	#2859	1	1	yes	characteristic, complemented, Sylow
83	#125	—	106	8	no	—
84	C₂×C₄⋊C₄	—	53	4	no	—
85	C₂×C₄⋊C₄	—	53	2	no	—
86	C₂×C₄⋊C₄	—	53	4	no	—
87	C₂×C₄⋊C₄	—	53	4	no	—
88	C₂×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
89	C₂×C₄⋊C₄	C₂×D₅₃	1	4	yes	—
90	C₂×C₄²	—	53	1	no	—
91	C₂×C₄²	—	53	1	no	—
92	C₂×C₄²	—	53	2	no	—
93	C₂×C₄²	—	53	2	no	—
94	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
95	#95	—	53	8	no	—
96	C₂²×C₄	—	53	2	no	—
97	C₂²×C₄	—	53	1	no	—
98	C₂²×C₄	—	53	1	no	—
99	C₂²×C₄	—	53	4	no	—
100	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
101	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
103	C₄⋊C₄	—	2	4	no	—
104	C₄⋊C₄	—	2	8	no	—
105	C₄⋊C₄	—	106	8	no	—
106	C₄⋊C₄	—	106	8	no	—
107	C₄⋊C₄	—	106	4	no	—
108	C₄⋊C₄	—	106	8	no	—
109	C₄²	—	53	4	no	—
110	C₄²	—	53	4	no	—
111	C₄²	—	106	4	no	—
112	C₄²	—	106	4	no	—
113	C₄²	Dic₁₀₆	1	4	yes	—
114	C₂³	C₂³×D₅₃	1	1	yes	characteristic
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	8	no	—
117	C₂×C₄	—	53	2	no	—
118	C₂×C₄	—	53	2	no	—
119	C₂×C₄	—	53	4	no	—
120	C₂×C₄	—	106	2	no	—
121	C₂×C₄	—	106	2	no	—
122	C₂×C₄	—	106	2	no	—
123	C₂×C₄	—	106	2	no	—
124	C₂×C₄	—	106	4	no	—
125	C₂×C₄	—	106	8	no	—
126	C₂×C₄	C₂×Dic₁₀₆	1	4	yes	—
127	C₂×C₄	C₂×Dic₁₀₆	1	2	yes	—
128	C₂×C₄	D₄×D₅₃	1	2	yes	—
129	C₂×C₄	#11719947	1	4	yes	—
130	C₂×C₄	Q₈×D₅₃	1	2	yes	—
131	C₂×C₄	#11719949	1	4	yes	—
132	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
133	C₂²	C₂×Q₈×D₅₃	1	1	yes	characteristic
134	C₂²	C₂²×Dic₁₀₆	1	1	yes	characteristic
135	C₂²	C₂×#11719947	1	2	yes	—
136	C₂²	C₂×#11719949	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	106	2	no	—
139	C₄	—	106	2	no	—
140	C₄	—	106	4	no	—
141	C₄	—	212	4	no	—
142	C₄	#13133208	1	8	yes	complemented
143	C₄	#13133216	1	4	yes	—
144	C₂	C₂×#13133208	1	2	yes	—
145	C₂	C₂×#13133216	1	1	yes	characteristic
146	C₂	#16811171	1	1	yes	characteristic
147	C₂	#16811174	1	1	yes	characteristic
148	C₂	#16811178	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13133208

C₂

yes

maximal

#16810522

C₂

yes

maximal

#16810519

C₂

yes

maximal

#16810493

C₂

yes

maximal, characteristic

#16810488

C₂

yes

maximal

C₄²×Dic₅₃

C₂

yes

maximal, characteristic

C₅₃×#384

C₂

yes

maximal, characteristic

#13133208

—

C₂×C₄⋊Dic₅₃

C₂²

yes

—

C₂×C₄⋊Dic₅₃

C₂²

yes

—

C₂×C₄⋊Dic₅₃

C₂²

yes

—

C₂×#11719919

C₂²

yes

—

C₂×C₄×Dic₅₃

C₂²

yes

—

C₂×C₄×Dic₅₃

C₂²

yes

—

C₂×C₄×Dic₅₃

C₂²

yes

characteristic

C₂×C₄×Dic₅₃

C₂²

yes

characteristic

#13133124

C₂²

yes

—

C₂×C₄⋊C₄×C₅₃

C₂²

yes

—

C₂×C₄⋊C₄×C₅₃

C₂²

yes

—

C₂×C₄²×C₅₃

C₂²

yes

characteristic

C₂²×C₄×C₅₃

C₂³

yes

—

C₂²×C₄×C₅₃

C₂³

yes

characteristic

C₂²×C₄×C₅₃

C₂³

yes

—

C₂²×Dic₅₃

C₂³

yes

—

C₂²×Dic₅₃

C₂³

yes

characteristic

C₂²×Dic₅₃

C₂³

yes

characteristic

C₂²×Dic₅₃

C₂³

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄²×C₅₃

Q₈

yes

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

#11719919

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

D₄

yes

—

C₄×Dic₅₃

Q₈

yes

—

C₂³×C₅₃

C₂⁴

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×D₄

yes

—

C₂×C₄×C₅₃

C₂×Q₈

yes

—

C₂×C₄×C₅₃

C₂×Q₈

yes

—

C₂×C₄×C₅₃

C₂×Q₈

yes

—

C₂×C₄×C₅₃

#41

yes

—

C₂×C₄×C₅₃

#41

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂×D₄

yes

—

C₂×Dic₅₃

C₂×D₄

yes

—

C₂×Dic₅₃

C₂×Q₈

yes

—

C₂²×C₅₃

C₂²×D₄

yes

characteristic

C₂²×C₅₃

C₂²×Q₈

yes

characteristic

C₂²×C₅₃

C₂²×Q₈

yes

characteristic

C₂²×C₅₃

C₂×#41

yes

—

C₂²×C₅₃

C₂×#41

yes

—

C₄×C₅₃

—

C₄×C₅₃

#125

yes

complemented

C₄×C₅₃

C₄⋊Q₈

yes

—

Dic₅₃

—

Dic₅₃

—

Dic₅₃

—

Dic₅₃

—

#2859

—

maximal, Sylow

C₂×C₅₃

C₂×#125

yes

—

C₂×C₅₃

C₂×C₄⋊Q₈

yes

C₂×C₅₃

yes

C₂×C₅₃

yes

C₂×C₅₃

yes

—

—

—

—

—

D₅₃

yes

characteristic

#382

—

C₄³

—

C₅₃

#2859

yes

characteristic, complemented, Sylow

#125

—

106

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅₃

yes

—

C₂×C₄⋊C₄

C₂×D₅₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₃

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₅₃

yes

—

101

C₂²×C₄

C₂²×D₅₃

yes

characteristic

102

C₂²×C₄

C₂²×D₅₃

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

—

106

C₄⋊C₄

—

106

—

107

C₄⋊C₄

—

106

—

108

C₄⋊C₄

—

106

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

106

—

112

C₄²

—

106

—

113

C₄²

Dic₁₀₆

yes

—

114

C₂³

C₂³×D₅₃

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

106

—

121

C₂×C₄

—

106

—

122

C₂×C₄

—

106

—

123

C₂×C₄

—

106

—

124

C₂×C₄

—

106

—

125

C₂×C₄

—

106

—

126

C₂×C₄

C₂×Dic₁₀₆

yes

—

127

C₂×C₄

C₂×Dic₁₀₆

yes

—

128

C₂×C₄

D₄×D₅₃

yes

—

129

C₂×C₄

#11719947

yes

—

130

C₂×C₄

Q₈×D₅₃

yes

—

131

C₂×C₄

#11719949

yes

—

132

C₂²

C₂×D₄×D₅₃

yes

characteristic

133

C₂²

C₂×Q₈×D₅₃

yes

characteristic

134

C₂²

C₂²×Dic₁₀₆

yes

characteristic

135

C₂²

C₂×#11719947

yes

—

136

C₂²

C₂×#11719949

yes

—

137

C₄

—

138

C₄

—

106

—

139

C₄

—

106

—

140

C₄

—

106

—

141

C₄

—

212

—

142

C₄

#13133208

yes

complemented

143

C₄

#13133216

yes

—

144

C₂

C₂×#13133208

yes

—

145

C₂

C₂×#13133216

yes

characteristic

146

C₂

#16811171

yes

characteristic

147

C₂

#16811174

yes

characteristic

148

C₂

#16811178

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₃
commutator, socle	C₂³×C₅₃	C₂⁴
Fitting	C₅₃×#384	C₂
hypercenter	#384	D₅₃
hypocenter	C₅₃	#2859
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₃

commutator, socle

C₂³×C₅₃

C₂⁴

Fitting

C₅₃×#384

C₂

D₅₃

C₅₃

G ▷ C₂³×C₅₃ ▷ C₅₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
63. C₄×C₅₃	#125	semidirect
82. C₅₃	#2859	semidirect
142. C₄	#13133208	semidirect

H ≅ G/N

type

63. C₄×C₅₃

#125

semidirect

82. C₅₃

#2859

semidirect

142. C₄

#13133208

semidirect

Subgroups — #20283076

Conjugacy classes of subgroups

Complements