Group #11933355 — subgroups

Subgroups — C₅×#10635 #11933355

Order 1280.

294 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1960	C₂	1	1	yes	maximal, characteristic
2	C₅×#1838	C₂	1	1	yes	maximal, characteristic
3	C₅×#1546	C₂	1	2	yes	maximal
4	C₅×#1286	C₂	1	2	yes	maximal
5	C₅×#1281	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₅×#431	C₂²	1	2	yes	—
8	C₅×#423	C₂²	1	2	yes	—
9	C₂×C₅×#103	—	2	2	no	—
10	C₂×C₅×#97	C₂²	1	1	yes	characteristic
11	C₅×#382	C₂²	1	1	yes	characteristic
12	C₅×#341	—	2	2	no	—
13	C₅×#332	—	2	4	no	—
14	#10635	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₅×Q₈	—	2	1	no	—
16	C₂×C₅×M₁₆	—	2	2	no	—
17	C₂²×C₅×C₈	D₄	1	2	yes	—
18	C₅×C₄⋊Q₈	—	2	2	no	—
19	C₅×C₄⋊Q₈	—	2	1	no	—
20	C₅×C₄⋊Q₈	D₄	1	2	yes	—
21	C₂×C₅×C₄⋊C₄	—	2	2	no	—
22	C₂×C₅×C₄⋊C₄	—	2	1	no	—
23	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
24	C₅×C₄⋊C₈	—	2	2	no	—
25	C₅×C₄⋊C₈	—	2	2	no	—
26	C₅×C₄⋊C₈	—	2	2	no	—
27	C₅×#103	—	4	4	no	—
28	C₅×C₂²⋊C₈	—	2	2	no	—
29	C₅×#97	—	2	2	no	—
30	C₄×C₅×C₈	—	2	2	no	—
31	C₅×#95	—	2	2	no	—
32	#1960	C₂×C₅	1	1	yes	characteristic
33	#1838	C₂×C₅	1	1	yes	characteristic
34	#1546	C₂×C₅	1	2	yes	—
35	#1286	C₂×C₅	1	2	yes	—
36	#1281	C₂×C₅	1	1	yes	characteristic
37	C₂×C₅×Q₈	—	2	2	no	—
38	C₂×C₅×Q₈	—	4	1	no	—
39	C₂×C₅×Q₈	—	4	2	no	—
40	C₂×C₅×Q₈	—	4	2	no	—
41	C₂²×C₄×C₅	—	4	1	no	—
42	C₂²×C₄×C₅	—	4	1	no	—
43	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₅	#41	1	2	yes	—
45	C₅×M₁₆	—	4	2	no	—
46	C₅×M₁₆	—	4	2	no	—
47	C₂×C₅×C₈	—	2	2	no	—
48	C₂×C₅×C₈	—	2	2	no	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	4	2	no	—
51	C₂×C₅×C₈	—	4	2	no	—
52	C₅×C₄⋊C₄	—	2	4	no	—
53	C₅×C₄⋊C₄	—	4	2	no	—
54	C₅×C₄⋊C₄	—	4	2	no	—
55	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₅	#41	1	1	yes	characteristic
57	C₄²×C₅	#41	1	2	yes	—
58	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
59	#431	C₂²×C₅	1	2	yes	—
60	#423	C₂²×C₅	1	2	yes	—
61	C₂×#103	—	2	2	no	—
62	C₂×#97	C₂²×C₅	1	1	yes	characteristic
63	#382	C₂²×C₅	1	1	yes	characteristic
64	#341	—	2	2	no	—
65	#332	—	2	4	no	—
66	C₂³×C₅	#124	1	1	yes	characteristic
67	C₅×Q₈	—	4	4	no	—
68	C₅×Q₈	—	8	2	no	—
69	C₂×C₄×C₅	—	4	2	no	—
70	C₂×C₄×C₅	—	4	2	no	—
71	C₂×C₄×C₅	—	8	1	no	—
72	C₂×C₄×C₅	—	8	1	no	—
73	C₂×C₄×C₅	—	8	2	no	—
74	C₂×C₄×C₅	—	8	1	no	—
75	C₂×C₄×C₅	#121	1	1	yes	characteristic
76	C₂×C₄×C₅	#123	1	2	yes	—
77	C₂×C₄×C₅	#123	1	1	yes	characteristic
78	C₂×C₄×C₅	#126	1	2	yes	—
79	C₂×C₄×C₅	#135	1	2	yes	—
80	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
81	C₅×C₈	—	4	2	no	—
82	C₅×C₈	—	8	2	no	—
83	C₅×C₈	—	8	2	no	—
84	C₂²×Q₈	—	2	1	no	—
85	C₂×M₁₆	—	2	2	no	—
86	C₂²×C₈	C₅×D₄	1	2	yes	—
87	C₄⋊Q₈	—	2	2	no	—
88	C₄⋊Q₈	—	2	1	no	—
89	C₄⋊Q₈	C₅×D₄	1	2	yes	—
90	C₂×C₄⋊C₄	—	2	2	no	—
91	C₂×C₄⋊C₄	—	2	1	no	—
92	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
93	C₄⋊C₈	—	2	2	no	—
94	C₄⋊C₈	—	2	2	no	—
95	C₄⋊C₈	—	2	2	no	—
96	#103	—	4	4	no	—
97	C₂²⋊C₈	—	2	2	no	—
98	#97	—	2	2	no	—
99	C₄×C₈	—	2	2	no	—
100	#95	—	2	2	no	—
101	C₂²×C₅	—	2	2	no	—
102	C₂²×C₅	#397	1	1	yes	characteristic
103	C₂²×C₅	#488	1	1	yes	characteristic
104	C₂²×C₅	#490	1	1	yes	characteristic
105	C₄×C₅	—	2	2	no	—
106	C₄×C₅	—	2	2	no	—
107	C₄×C₅	—	8	2	no	—
108	C₄×C₅	—	16	1	no	—
109	C₄×C₅	#463	1	2	yes	—
110	C₄×C₅	#482	1	2	yes	—
111	C₂×Q₈	—	2	2	no	—
112	C₂×Q₈	—	4	1	no	—
113	C₂×Q₈	—	4	2	no	—
114	C₂×Q₈	—	4	2	no	—
115	C₂²×C₄	—	4	1	no	—
116	C₂²×C₄	—	4	1	no	—
117	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
118	C₂²×C₄	C₅×#41	1	2	yes	—
119	M₁₆	—	4	2	no	—
120	M₁₆	—	4	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	2	2	no	—
124	C₂×C₈	—	4	2	no	—
125	C₂×C₈	—	4	2	no	—
126	C₄⋊C₄	—	2	4	no	—
127	C₄⋊C₄	—	4	2	no	—
128	C₄⋊C₄	—	4	2	no	—
129	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
130	C₄²	C₅×#41	1	1	yes	characteristic
131	C₄²	C₅×#41	1	2	yes	—
132	C₂×C₅	—	2	1	no	—
133	C₂×C₅	—	2	1	no	—
134	C₂×C₅	#2073	1	1	yes	characteristic
135	C₂×C₅	#2082	1	2	yes	—
136	C₂³	C₅×#124	1	1	yes	characteristic
137	Q₈	—	4	4	no	—
138	Q₈	—	8	2	no	—
139	C₂×C₄	—	4	2	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	8	1	no	—
142	C₂×C₄	—	8	1	no	—
143	C₂×C₄	—	8	2	no	—
144	C₂×C₄	—	8	1	no	—
145	C₂×C₄	C₅×#121	1	1	yes	characteristic
146	C₂×C₄	C₅×#123	1	2	yes	—
147	C₂×C₄	C₅×#123	1	1	yes	characteristic
148	C₂×C₄	C₅×#126	1	2	yes	—
149	C₂×C₄	C₅×#135	1	2	yes	—
150	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
151	C₈	—	4	2	no	—
152	C₈	—	8	2	no	—
153	C₈	—	8	2	no	—
154	C₅	#10635	1	1	yes	characteristic, direct product factor, Sylow
155	C₂²	—	2	2	no	—
156	C₂²	C₅×#397	1	1	yes	characteristic
157	C₂²	C₅×#488	1	1	yes	characteristic
158	C₂²	C₅×#490	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	2	no	—
161	C₄	—	8	2	no	—
162	C₄	—	16	1	no	—
163	C₄	C₅×#463	1	2	yes	—
164	C₄	C₅×#482	1	2	yes	—
165	C₂	—	2	1	no	—
166	C₂	—	2	1	no	—
167	C₂	C₅×#2073	1	1	yes	characteristic
168	C₂	C₅×#2082	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1960

C₂

yes

maximal, characteristic

C₅×#1838

C₂

yes

maximal, characteristic

C₅×#1546

C₂

yes

maximal

C₅×#1286

C₂

yes

maximal

C₅×#1281

C₂

yes

maximal, characteristic

C₂×C₅×C₄⋊Q₈

C₂²

yes

characteristic

C₅×#431

C₂²

yes

—

C₅×#423

C₂²

yes

—

C₂×C₅×#103

—

C₂×C₅×#97

C₂²

yes

characteristic

C₅×#382

C₂²

yes

—

—

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

—

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

D₄

yes

—

C₅×C₄⋊Q₈

—

C₅×C₄⋊Q₈

—

C₅×C₄⋊Q₈

D₄

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×#103

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₄×C₅×C₈

—

C₅×#95

—

#1960

C₂×C₅

yes

characteristic

#1838

C₂×C₅

yes

characteristic

#1546

C₂×C₅

yes

—

#1286

C₂×C₅

yes

—

#1281

C₂×C₅

yes

characteristic

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

#41

yes

—

C₅×M₁₆

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×D₄

yes

C₄²×C₅

yes

C₄²×C₅

yes

—

C₂×C₄⋊Q₈

C₂²×C₅

yes

characteristic

#431

C₂²×C₅

yes

—

#423

C₂²×C₅

yes

—

C₂×#103

—

C₂×#97

C₂²×C₅

yes

characteristic

#382

C₂²×C₅

yes

characteristic

#341

—

#332

—

C₂³×C₅

#124

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#121

yes

characteristic

C₂×C₄×C₅

#123

yes

—

C₂×C₄×C₅

#123

yes

characteristic

C₂×C₄×C₅

#126

yes

—

C₂×C₄×C₅

#135

yes

—

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂²×C₈

C₅×D₄

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₅×D₄

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

100

#95

—

101

C₂²×C₅

—

102

C₂²×C₅

#397

yes

characteristic

103

C₂²×C₅

#488

yes

characteristic

104

C₂²×C₅

#490

yes

characteristic

105

C₄×C₅

—

106

C₄×C₅

—

107

C₄×C₅

—

108

C₄×C₅

—

109

C₄×C₅

#463

yes

—

110

C₄×C₅

#482

yes

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

118

C₂²×C₄

C₅×#41

yes

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄²

C₂×C₅×D₄

yes

characteristic

130

C₄²

C₅×#41

yes

characteristic

131

C₄²

C₅×#41

yes

—

132

C₂×C₅

—

133

C₂×C₅

—

134

C₂×C₅

#2073

yes

characteristic

135

C₂×C₅

#2082

yes

—

136

C₂³

C₅×#124

yes

characteristic

137

Q₈

—

138

Q₈

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

C₅×#121

yes

characteristic

146

C₂×C₄

C₅×#123

yes

—

147

C₂×C₄

C₅×#123

yes

characteristic

148

C₂×C₄

C₅×#126

yes

—

149

C₂×C₄

C₅×#135

yes

—

150

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

151

C₈

—

152

C₈

—

153

C₈

—

154

C₅

#10635

yes

characteristic, direct product factor, Sylow

155

C₂²

—

156

C₂²

C₅×#397

yes

characteristic

157

C₂²

C₅×#488

yes

characteristic

158

C₂²

C₅×#490

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

C₅×#463

yes

—

164

C₄

C₅×#482

yes

—

165

C₂

—

166

C₂

—

167

C₂

C₅×#2073

yes

characteristic

168

C₂

C₅×#2082

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	#124
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#397

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂³×C₅

#124

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
14. #10635	C₅	direct (N × H)
154. C₅	#10635	direct (N × H)

H ≅ G/N

type

14. #10635

C₅

direct (N × H)

154. C₅

#10635

direct (N × H)

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

subgroup	index
C₅×#1960	2
C₅×#1838	2
C₅×#1546	2
C₅×#1286	2
C₅×#1281	2
#10635	5

subgroup

index

Subgroups — C₅×#10635 #11933355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10635 #11933355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10635 #11933355