Group #50313630 — subgroups

Subgroups — C₁₅₁×#8705 #50313630

Order 38656.

486 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 142 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×#383×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#1817×C₁₅₁	C₂	1	2	yes	maximal
3	#1280×C₁₅₁	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊C₈×C₁₅₁	C₂²	1	4	yes	—
6	#383×C₁₅₁	—	2	4	no	—
7	C₂×#95×C₁₅₁	C₄	1	2	yes	—
8	C₂×#95×C₁₅₁	C₄	1	2	yes	—
9	C₂×#95×C₁₅₁	C₂²	1	2	yes	—
10	#336×C₁₅₁	—	2	4	no	—
11	C₂³×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₅₁	C₂×C₄	1	4	yes	—
13	C₂³×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
15	C₂²×C₈×C₁₅₁	—	2	4	no	—
16	C₂×C₄²×C₁₅₁	—	2	4	no	—
17	C₂×C₄²×C₁₅₁	D₄	1	4	yes	—
18	C₂²⋊C₈×C₁₅₁	—	2	8	no	—
19	#95×C₁₅₁	—	2	4	no	—
20	#95×C₁₅₁	—	2	4	no	—
21	#95×C₁₅₁	—	2	4	no	—
22	C₂⁴×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₅₁	—	2	2	no	—
24	C₂²×C₄×C₁₅₁	—	2	2	no	—
25	C₂²×C₄×C₁₅₁	—	2	4	no	—
26	C₂²×C₄×C₁₅₁	—	2	4	no	—
27	C₂²×C₄×C₁₅₁	—	2	8	no	—
28	C₂²×C₄×C₁₅₁	—	4	2	no	—
29	C₂²×C₄×C₁₅₁	—	4	2	no	—
30	C₂²×C₄×C₁₅₁	—	4	4	no	—
31	C₂²×C₄×C₁₅₁	—	4	4	no	—
32	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₁₅₁	#41	1	4	yes	—
36	C₂×C₈×C₁₅₁	—	4	8	no	—
37	C₂×C₈×C₁₅₁	—	4	4	no	—
38	C₄²×C₁₅₁	—	2	8	no	—
39	C₂³×C₁₅₁	—	2	2	no	—
40	C₂³×C₁₅₁	—	2	2	no	—
41	C₂³×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂³×C₁₅₁	#117	1	2	yes	—
43	C₂³×C₁₅₁	#131	1	4	yes	—
44	C₂×C₄×C₁₅₁	—	2	4	no	—
45	C₂×C₄×C₁₅₁	—	2	2	no	—
46	C₂×C₄×C₁₅₁	—	2	2	no	—
47	C₂×C₄×C₁₅₁	—	2	4	no	—
48	C₂×C₄×C₁₅₁	—	2	4	no	—
49	C₂×C₄×C₁₅₁	—	4	4	no	—
50	C₂×C₄×C₁₅₁	—	4	4	no	—
51	C₂×C₄×C₁₅₁	—	4	4	no	—
52	C₂×C₄×C₁₅₁	—	4	4	no	—
53	C₂×C₄×C₁₅₁	—	4	4	no	—
54	C₂×C₄×C₁₅₁	—	4	4	no	—
55	C₂×C₄×C₁₅₁	—	8	8	no	—
56	C₂×C₄×C₁₅₁	#123	1	4	yes	—
57	C₈×C₁₅₁	—	8	4	no	—
58	C₂²×C₁₅₁	—	2	2	no	—
59	C₂²×C₁₅₁	—	2	2	no	—
60	C₂²×C₁₅₁	—	2	8	no	—
61	C₂²×C₁₅₁	#381	1	1	yes	characteristic
62	C₂²×C₁₅₁	#408	1	2	yes	—
63	C₂²×C₁₅₁	#410	1	2	yes	—
64	C₂²×C₁₅₁	#413	1	2	yes	—
65	C₂²×C₁₅₁	#433	1	4	yes	—
66	C₄×C₁₅₁	—	2	4	no	—
67	C₄×C₁₅₁	—	4	2	no	—
68	C₄×C₁₅₁	—	4	2	no	—
69	C₄×C₁₅₁	—	8	4	no	—
70	C₂×C₁₅₁	—	2	4	no	—
71	C₂×C₁₅₁	#1473	1	4	yes	—
72	C₂×C₁₅₁	#1818	1	1	yes	characteristic
73	C₂×C₁₅₁	#1820	1	1	yes	characteristic
74	C₂×C₁₅₁	#1822	1	1	yes	characteristic
75	#8705	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₁₅₁	#8705	1	1	yes	characteristic, direct product factor, Sylow
77	C₂×#383	C₂×C₁₅₁	1	1	yes	characteristic
78	#1817	C₂×C₁₅₁	1	2	yes	—
79	#1280	C₂×C₁₅₁	1	4	yes	—
80	C₂²×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
81	C₂×C₂²⋊C₈	C₂²×C₁₅₁	1	4	yes	—
82	#383	—	2	4	no	—
83	C₂×#95	C₄×C₁₅₁	1	2	yes	—
84	C₂×#95	C₄×C₁₅₁	1	2	yes	—
85	C₂×#95	C₂²×C₁₅₁	1	2	yes	—
86	#336	—	2	4	no	—
87	C₂³×C₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
88	C₂³×C₄	C₂×C₄×C₁₅₁	1	4	yes	—
89	C₂³×C₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
90	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
91	C₂²×C₈	—	2	4	no	—
92	C₂×C₄²	—	2	4	no	—
93	C₂×C₄²	D₄×C₁₅₁	1	4	yes	—
94	C₂²⋊C₈	—	2	8	no	—
95	#95	—	2	4	no	—
96	#95	—	2	4	no	—
97	#95	—	2	4	no	—
98	C₂⁴	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
99	C₂²×C₄	—	2	2	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	—	2	4	no	—
102	C₂²×C₄	—	2	4	no	—
103	C₂²×C₄	—	2	8	no	—
104	C₂²×C₄	—	4	2	no	—
105	C₂²×C₄	—	4	2	no	—
106	C₂²×C₄	—	4	4	no	—
107	C₂²×C₄	—	4	4	no	—
108	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
109	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
110	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
111	C₂²×C₄	#41×C₁₅₁	1	4	yes	—
112	C₂×C₈	—	4	8	no	—
113	C₂×C₈	—	4	4	no	—
114	C₄²	—	2	8	no	—
115	C₂³	—	2	2	no	—
116	C₂³	—	2	2	no	—
117	C₂³	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
118	C₂³	#117×C₁₅₁	1	2	yes	—
119	C₂³	#131×C₁₅₁	1	4	yes	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	8	8	no	—
132	C₂×C₄	#123×C₁₅₁	1	4	yes	—
133	C₈	—	8	4	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	8	no	—
137	C₂²	#381×C₁₅₁	1	1	yes	characteristic
138	C₂²	#408×C₁₅₁	1	2	yes	—
139	C₂²	#410×C₁₅₁	1	2	yes	—
140	C₂²	#413×C₁₅₁	1	2	yes	—
141	C₂²	#433×C₁₅₁	1	4	yes	—
142	C₄	—	2	4	no	—
143	C₄	—	4	2	no	—
144	C₄	—	4	2	no	—
145	C₄	—	8	4	no	—
146	C₂	—	2	4	no	—
147	C₂	#1473×C₁₅₁	1	4	yes	—
148	C₂	#1818×C₁₅₁	1	1	yes	characteristic
149	C₂	#1820×C₁₅₁	1	1	yes	characteristic
150	C₂	#1822×C₁₅₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#383×C₁₅₁

C₂

yes

maximal, characteristic

#1817×C₁₅₁

C₂

yes

maximal

#1280×C₁₅₁

C₂

yes

maximal

C₂²×C₄²×C₁₅₁

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₁₅₁

C₂²

yes

—

#383×C₁₅₁

—

C₂×#95×C₁₅₁

C₄

yes

—

C₂×#95×C₁₅₁

C₄

yes

—

C₂×#95×C₁₅₁

C₂²

yes

—

#336×C₁₅₁

—

C₂³×C₄×C₁₅₁

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₅₁

C₂×C₄

yes

—

C₂³×C₄×C₁₅₁

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₅₁

C₂³

yes

characteristic

C₂²×C₈×C₁₅₁

—

C₂×C₄²×C₁₅₁

—

C₂×C₄²×C₁₅₁

D₄

yes

—

C₂²⋊C₈×C₁₅₁

—

#95×C₁₅₁

—

#95×C₁₅₁

—

#95×C₁₅₁

—

C₂⁴×C₁₅₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

—

C₂²×C₄×C₁₅₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₅₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₅₁

C₂×D₄

yes

—

C₂²×C₄×C₁₅₁

#41

yes

—

C₂×C₈×C₁₅₁

—

C₂×C₈×C₁₅₁

—

C₄²×C₁₅₁

—

C₂³×C₁₅₁

—

C₂³×C₁₅₁

—

C₂³×C₁₅₁

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₅₁

#117

yes

—

C₂³×C₁₅₁

#131

yes

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

#123

yes

—

C₈×C₁₅₁

—

C₂²×C₁₅₁

—

C₂²×C₁₅₁

—

C₂²×C₁₅₁

—

C₂²×C₁₅₁

#381

yes

characteristic

C₂²×C₁₅₁

#408

yes

—

C₂²×C₁₅₁

#410

yes

—

C₂²×C₁₅₁

#413

yes

—

C₂²×C₁₅₁

#433

yes

—

C₄×C₁₅₁

—

C₄×C₁₅₁

—

C₄×C₁₅₁

—

C₄×C₁₅₁

—

C₂×C₁₅₁

—

C₂×C₁₅₁

#1473

yes

—

C₂×C₁₅₁

yes

C₂×C₁₅₁

yes

C₂×C₁₅₁

yes

C₁₅₁

yes

maximal, characteristic, direct product factor, Sylow

C₁₅₁

#8705

yes

characteristic, direct product factor, Sylow

C₂×#383

C₂×C₁₅₁

yes

characteristic

#1817

C₂×C₁₅₁

yes

—

#1280

C₂×C₁₅₁

yes

—

C₂²×C₄²

C₂²×C₁₅₁

yes

characteristic

C₂×C₂²⋊C₈

C₂²×C₁₅₁

yes

—

#383

—

C₂×#95

C₄×C₁₅₁

yes

—

C₂×#95

C₄×C₁₅₁

yes

—

C₂×#95

C₂²×C₁₅₁

yes

—

#336

—

C₂³×C₄

C₂×C₄×C₁₅₁

yes

characteristic

C₂³×C₄

C₂×C₄×C₁₅₁

yes

—

C₂³×C₄

C₂×C₄×C₁₅₁

yes

characteristic

C₂³×C₄

C₂³×C₁₅₁

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

D₄×C₁₅₁

yes

—

C₂²⋊C₈

—

#95

—

#95

—

#95

—

C₂⁴

C₂²×C₄×C₁₅₁

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊C₄×C₁₅₁

yes

—

109

C₂²×C₄

C₂²⋊C₄×C₁₅₁

yes

—

110

C₂²×C₄

C₂×D₄×C₁₅₁

yes

—

111

C₂²×C₄

#41×C₁₅₁

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄²

—

115

C₂³

—

116

C₂³

—

117

C₂³

C₂×C₂²⋊C₄×C₁₅₁

yes

characteristic

118

C₂³

#117×C₁₅₁

yes

—

119

C₂³

#131×C₁₅₁

yes

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#123×C₁₅₁

yes

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

#381×C₁₅₁

yes

characteristic

138

C₂²

#408×C₁₅₁

yes

—

139

C₂²

#410×C₁₅₁

yes

—

140

C₂²

#413×C₁₅₁

yes

—

141

C₂²

#433×C₁₅₁

yes

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₂

—

147

C₂

#1473×C₁₅₁

yes

—

148

C₂

#1818×C₁₅₁

yes

characteristic

149

C₂

#1820×C₁₅₁

yes

characteristic

150

C₂

#1822×C₁₅₁

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₅₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₅₁
prime radical	C₂⁴×C₁₅₁	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₂²×C₄²×C₁₅₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₅₁

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₁₅₁

Frattini, cosocle

C₂³×C₄

C₂³×C₁₅₁

prime radical

C₂⁴×C₁₅₁

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₅₁ ◁ C₂²×C₄²×C₁₅₁ ◁ G

N	H ≅ G/N	type
75. #8705	C₁₅₁	direct (N × H)
76. C₁₅₁	#8705	direct (N × H)

H ≅ G/N

type

75. #8705

C₁₅₁

direct (N × H)

76. C₁₅₁

#8705

direct (N × H)

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

subgroup	index
C₂×#383×C₁₅₁	2
#1817×C₁₅₁	2
#1280×C₁₅₁	2
#8705	151

subgroup

index

C₂×#383×C₁₅₁

#1817×C₁₅₁

#1280×C₁₅₁

#8705

151

Subgroups — C₁₅₁×#8705 #50313630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C151×#8705 #50313630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#8705 #50313630