Group #11931475 — subgroups

Subgroups — C₅×#8755 #11931475

Order 1280.

398 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 110 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	C₅×#2313	C₂	1	1	yes	maximal, characteristic
2	C₅×#1821	C₂	1	2	yes	maximal
3	C₅×#1306	C₂	1	4	yes	maximal
4	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
5	C₅×#407	C₂²	1	4	yes	—
6	C₅×#387	—	2	4	no	—
7	C₅×#381	C₂²	1	2	yes	—
8	C₅×#380	C₄	1	2	yes	—
9	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
10	C₅×#343	—	2	4	no	—
11	#8755	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₂×C₅×M₁₆	—	2	4	no	—
16	C₂×C₅×C₄⋊C₄	—	2	4	no	—
17	C₂×C₅×C₄⋊C₄	—	2	2	no	—
18	C₂×C₅×C₄⋊C₄	D₄	1	4	yes	—
19	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₅	—	2	2	no	—
21	C₅×C₂²⋊C₈	—	2	8	no	—
22	C₅×#95	—	2	2	no	—
23	C₅×#95	—	2	2	no	—
24	C₅×#95	—	2	4	no	—
25	#2313	C₂×C₅	1	1	yes	characteristic
26	#1821	C₂×C₅	1	2	yes	—
27	#1306	C₂×C₅	1	4	yes	—
28	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₅	—	2	2	no	—
30	C₂²×C₄×C₅	—	2	2	no	—
31	C₂²×C₄×C₅	—	2	4	no	—
32	C₂²×C₄×C₅	—	4	2	no	—
33	C₂²×C₄×C₅	—	8	1	no	—
34	C₂²×C₄×C₅	—	8	1	no	—
35	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
38	C₂²×C₄×C₅	#41	1	4	yes	—
39	C₅×M₁₆	—	4	8	no	—
40	C₂×C₅×C₈	—	4	4	no	—
41	C₅×C₄⋊C₄	—	2	8	no	—
42	C₅×C₄⋊C₄	—	8	2	no	—
43	C₅×C₂²⋊C₄	—	4	4	no	—
44	C₄²×C₅	—	8	2	no	—
45	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
46	#407	C₂²×C₅	1	4	yes	—
47	#387	—	2	4	no	—
48	#381	C₂²×C₅	1	2	yes	—
49	#380	C₄×C₅	1	2	yes	—
50	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
51	#343	—	2	4	no	—
52	C₂³×C₅	—	2	2	no	—
53	C₂³×C₅	—	4	1	no	—
54	C₂³×C₅	—	4	1	no	—
55	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂³×C₅	#117	1	2	yes	—
57	C₂×C₄×C₅	—	2	4	no	—
58	C₂×C₄×C₅	—	2	2	no	—
59	C₂×C₄×C₅	—	2	2	no	—
60	C₂×C₄×C₅	—	4	4	no	—
61	C₂×C₄×C₅	—	4	2	no	—
62	C₂×C₄×C₅	—	4	2	no	—
63	C₂×C₄×C₅	—	4	4	no	—
64	C₂×C₄×C₅	—	4	4	no	—
65	C₂×C₄×C₅	—	4	4	no	—
66	C₂×C₄×C₅	—	8	2	no	—
67	C₂×C₄×C₅	—	8	2	no	—
68	C₂×C₄×C₅	#123	1	4	yes	—
69	C₅×C₈	—	8	4	no	—
70	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
71	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
72	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
73	C₂×M₁₆	—	2	4	no	—
74	C₂×C₄⋊C₄	—	2	4	no	—
75	C₂×C₄⋊C₄	—	2	2	no	—
76	C₂×C₄⋊C₄	C₅×D₄	1	4	yes	—
77	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
78	C₂×C₄²	—	2	2	no	—
79	C₂²⋊C₈	—	2	8	no	—
80	#95	—	2	2	no	—
81	#95	—	2	2	no	—
82	#95	—	2	4	no	—
83	C₂²×C₅	—	2	1	no	—
84	C₂²×C₅	—	2	1	no	—
85	C₂²×C₅	—	2	2	no	—
86	C₂²×C₅	—	2	2	no	—
87	C₂²×C₅	—	2	2	no	—
88	C₂²×C₅	—	4	4	no	—
89	C₂²×C₅	#381	1	1	yes	characteristic
90	C₂²×C₅	#410	1	2	yes	—
91	C₄×C₅	—	2	4	no	—
92	C₄×C₅	—	4	2	no	—
93	C₄×C₅	—	4	2	no	—
94	C₄×C₅	—	8	4	no	—
95	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
96	C₂²×C₄	—	2	2	no	—
97	C₂²×C₄	—	2	2	no	—
98	C₂²×C₄	—	2	4	no	—
99	C₂²×C₄	—	4	2	no	—
100	C₂²×C₄	—	8	1	no	—
101	C₂²×C₄	—	8	1	no	—
102	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
105	C₂²×C₄	C₅×#41	1	4	yes	—
106	M₁₆	—	4	8	no	—
107	C₂×C₈	—	4	4	no	—
108	C₄⋊C₄	—	2	8	no	—
109	C₄⋊C₄	—	8	2	no	—
110	C₂²⋊C₄	—	4	4	no	—
111	C₄²	—	8	2	no	—
112	C₂×C₅	—	2	2	no	—
113	C₂×C₅	—	4	2	no	—
114	C₂×C₅	#1820	1	1	yes	characteristic
115	C₂×C₅	#1829	1	1	yes	characteristic
116	C₂×C₅	#1830	1	1	yes	characteristic
117	C₂³	—	2	2	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	4	1	no	—
120	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³	C₅×#117	1	2	yes	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	8	2	no	—
132	C₂×C₄	—	8	2	no	—
133	C₂×C₄	C₅×#123	1	4	yes	—
134	C₈	—	8	4	no	—
135	C₅	#8755	1	1	yes	characteristic, direct product factor, Sylow
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	2	no	—
139	C₂²	—	2	2	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	4	4	no	—
142	C₂²	C₅×#381	1	1	yes	characteristic
143	C₂²	C₅×#410	1	2	yes	—
144	C₄	—	2	4	no	—
145	C₄	—	4	2	no	—
146	C₄	—	4	2	no	—
147	C₄	—	8	4	no	—
148	C₂	—	2	2	no	—
149	C₂	—	4	2	no	—
150	C₂	C₅×#1820	1	1	yes	characteristic
151	C₂	C₅×#1829	1	1	yes	characteristic
152	C₂	C₅×#1830	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2313

C₂

yes

maximal, characteristic

C₅×#1821

C₂

yes

maximal

C₅×#1306

C₂

yes

maximal

C₂²×C₅×C₄⋊C₄

C₂²

yes

characteristic

C₅×#407

C₂²

yes

—

C₅×#387

—

C₅×#381

C₂²

yes

—

C₅×#380

C₄

yes

—

C₄×C₅×C₂²⋊C₄

C₄

yes

—

C₅×#343

—

#8755

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₄×C₅

C₂×C₄

yes

characteristic

C₂³×C₄×C₅

C₂×C₄

yes

characteristic

C₂³×C₄×C₅

C₂³

yes

characteristic

C₂×C₅×M₁₆

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

D₄

yes

—

C₂×C₅×C₂²⋊C₄

C₂×C₄

yes

—

C₂×C₄²×C₅

—

C₅×C₂²⋊C₈

—

C₅×#95

—

C₅×#95

—

C₅×#95

—

#2313

C₂×C₅

yes

characteristic

#1821

C₂×C₅

yes

—

#1306

C₂×C₅

yes

—

C₂⁴×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

#41

yes

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

C₂²×C₄⋊C₄

C₂²×C₅

yes

characteristic

#407

C₂²×C₅

yes

—

#387

—

#381

C₂²×C₅

yes

—

#380

C₄×C₅

yes

—

C₄×C₂²⋊C₄

C₄×C₅

yes

—

#343

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₅

#117

yes

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#123

yes

—

C₅×C₈

—

C₂³×C₄

C₂×C₄×C₅

yes

characteristic

C₂³×C₄

C₂×C₄×C₅

yes

characteristic

C₂³×C₄

C₂³×C₅

yes

characteristic

C₂×M₁₆

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₅×D₄

yes

—

C₂×C₂²⋊C₄

C₂×C₄×C₅

yes

—

C₂×C₄²

—

C₂²⋊C₈

—

#95

—

#95

—

#95

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#381

yes

characteristic

C₂²×C₅

#410

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂⁴

C₂²×C₄×C₅

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

103

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

104

C₂²×C₄

C₂×C₅×D₄

yes

—

105

C₂²×C₄

C₅×#41

yes

—

106

M₁₆

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₂×C₅

—

113

C₂×C₅

—

114

C₂×C₅

#1820

yes

characteristic

115

C₂×C₅

#1829

yes

characteristic

116

C₂×C₅

#1830

yes

characteristic

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂×C₅×C₂²⋊C₄

yes

characteristic

121

C₂³

C₅×#117

yes

—

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

—

133

C₂×C₄

C₅×#123

yes

—

134

C₈

—

135

C₅

#8755

yes

characteristic, direct product factor, Sylow

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₅×#381

yes

characteristic

143

C₂²

C₅×#410

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₂

—

149

C₂

—

150

C₂

C₅×#1820

yes

characteristic

151

C₂

C₅×#1829

yes

characteristic

152

C₂

C₅×#1830

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#381
commutator	C₂⁴	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#381

commutator

C₂⁴

C₂²×C₄×C₅

Frattini, cosocle

C₂³×C₄

C₂³×C₅

prime radical

C₂⁴×C₅

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

N	H ≅ G/N	type
11. #8755	C₅	direct (N × H)
135. C₅	#8755	direct (N × H)

H ≅ G/N

type

11. #8755

C₅

direct (N × H)

135. C₅

#8755

direct (N × H)

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

subgroup	index
C₅×#2313	2
C₅×#1821	2
C₅×#1306	2
#8755	5

subgroup

index

Subgroups — C₅×#8755 #11931475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8755 #11931475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8755 #11931475