Group #11930542 — subgroups

Subgroups — C₅×#7822 #11930542

Order 1280.

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2679	C₂	1	1	yes	maximal, characteristic
2	C₅×#2094	C₂	1	3	yes	maximal, complemented
3	C₅×#1270	C₂	1	3	yes	maximal, complemented
4	C₂×C₅×#120	—	2	3	no	—
5	C₂×C₅×#106	—	2	3	no	—
6	C₂×C₅×#102	—	2	3	no	—
7	C₅×#394	—	2	3	no	—
8	C₅×#390	C₂²	1	3	yes	—
9	C₅×#384	C₂²	1	1	yes	characteristic, complemented
10	C₅×#336	C₂²	1	3	yes	complemented
11	#7822	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁵×C₅	—	2	1	no	—
13	C₂²×C₅×D₄	—	2	3	no	—
14	C₂²×C₅×D₄	D₄	1	3	yes	—
15	C₂²×C₅×C₈	—	2	3	no	—
16	C₅×#120	—	4	6	no	—
17	C₅×#120	—	4	6	no	—
18	C₂×C₅×C₄⋊C₄	—	2	3	no	—
19	C₂×C₅×C₄⋊C₄	D₄	1	3	yes	—
20	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
21	C₂×C₅×C₂²⋊C₄	—	2	6	no	—
22	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
23	C₅×#106	—	4	6	no	—
24	C₅×#102	—	4	6	no	—
25	C₅×#95	—	2	1	no	—
26	#2679	C₂×C₅	1	1	yes	characteristic
27	#2094	C₂×C₅	1	3	yes	complemented
28	#1270	C₂×C₅	1	3	yes	complemented
29	C₂⁴×C₅	—	2	3	no	—
30	C₂⁴×C₅	—	4	6	no	—
31	C₂⁴×C₅	—	8	3	no	—
32	C₂⁴×C₅	—	8	1	no	—
33	C₂×C₅×D₄	—	2	3	no	—
34	C₂×C₅×D₄	—	4	3	no	—
35	C₂×C₅×D₄	—	4	3	no	—
36	C₂×C₅×D₄	—	4	12	no	—
37	C₂×C₅×D₄	—	8	3	no	—
38	C₂×C₅×D₄	SD₁₆	1	6	yes	—
39	C₂²×C₄×C₅	—	2	3	no	—
40	C₂²×C₄×C₅	—	4	1	no	—
41	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
42	C₂×C₅×C₈	—	2	6	no	—
43	C₂×C₅×C₈	—	4	3	no	—
44	C₂×C₅×C₈	—	4	3	no	—
45	C₅×C₄⋊C₄	—	4	3	no	—
46	C₅×C₄⋊C₄	—	4	3	no	—
47	C₅×C₄⋊C₄	—	4	3	no	—
48	C₅×C₂²⋊C₄	—	4	6	no	—
49	C₅×C₂²⋊C₄	—	4	6	no	—
50	C₅×C₂²⋊C₄	—	4	6	no	—
51	C₄²×C₅	—	4	1	no	—
52	C₂×#120	—	2	3	no	—
53	C₂×#106	—	2	3	no	—
54	C₂×#102	—	2	3	no	—
55	#394	—	2	3	no	—
56	#390	C₂²×C₅	1	3	yes	—
57	#384	C₂²×C₅	1	1	yes	characteristic, complemented
58	#336	C₂²×C₅	1	3	yes	complemented
59	C₂³×C₅	—	2	6	no	—
60	C₂³×C₅	—	4	6	no	—
61	C₂³×C₅	—	4	3	no	—
62	C₂³×C₅	—	4	6	no	—
63	C₂³×C₅	—	4	3	no	—
64	C₂³×C₅	—	8	12	no	—
65	C₂³×C₅	—	8	12	no	—
66	C₂³×C₅	—	8	4	no	—
67	C₂³×C₅	#120	1	1	yes	characteristic
68	C₅×D₄	—	4	6	no	—
69	C₅×D₄	—	8	3	no	—
70	C₅×D₄	—	8	12	no	—
71	C₂×C₄×C₅	—	2	3	no	—
72	C₂×C₄×C₅	—	2	3	no	—
73	C₂×C₄×C₅	—	4	6	no	—
74	C₂×C₄×C₅	—	4	3	no	—
75	C₂×C₄×C₅	—	8	3	no	—
76	C₂×C₄×C₅	C₂×SD₁₆	1	3	yes	—
77	C₂×C₄×C₅	AGL(1,ℤ/8)	1	3	yes	—
78	C₅×C₈	—	4	6	no	—
79	C₂⁵	—	2	1	no	—
80	C₂²×D₄	—	2	3	no	—
81	C₂²×D₄	C₅×D₄	1	3	yes	—
82	C₂²×C₈	—	2	3	no	—
83	#120	—	4	6	no	—
84	#120	—	4	6	no	—
85	C₂×C₄⋊C₄	—	2	3	no	—
86	C₂×C₄⋊C₄	C₅×D₄	1	3	yes	—
87	C₂×C₂²⋊C₄	—	2	3	no	—
88	C₂×C₂²⋊C₄	—	2	6	no	—
89	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
90	#106	—	4	6	no	—
91	#102	—	4	6	no	—
92	#95	—	2	1	no	—
93	C₂²×C₅	—	4	6	no	—
94	C₂²×C₅	—	4	12	no	—
95	C₂²×C₅	—	8	16	no	—
96	C₂²×C₅	—	8	6	no	—
97	C₂²×C₅	—	8	3	no	—
98	C₂²×C₅	—	8	3	no	—
99	C₂²×C₅	#450	1	3	yes	—
100	C₂²×C₅	#453	1	3	yes	—
101	C₂²×C₅	#458	1	1	yes	characteristic
102	C₄×C₅	—	2	3	no	—
103	C₄×C₅	—	2	3	no	—
104	C₄×C₅	—	8	3	no	—
105	C₄×C₅	—	16	1	no	—
106	C₂⁴	—	2	3	no	—
107	C₂⁴	—	4	6	no	—
108	C₂⁴	—	8	3	no	—
109	C₂⁴	—	8	1	no	—
110	C₂×D₄	—	2	3	no	—
111	C₂×D₄	—	4	3	no	—
112	C₂×D₄	—	4	3	no	—
113	C₂×D₄	—	4	12	no	—
114	C₂×D₄	—	8	3	no	—
115	C₂×D₄	C₅×SD₁₆	1	6	yes	—
116	C₂²×C₄	—	2	3	no	—
117	C₂²×C₄	—	4	1	no	—
118	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
119	C₂×C₈	—	2	6	no	—
120	C₂×C₈	—	4	3	no	—
121	C₂×C₈	—	4	3	no	—
122	C₄⋊C₄	—	4	3	no	—
123	C₄⋊C₄	—	4	3	no	—
124	C₄⋊C₄	—	4	3	no	—
125	C₂²⋊C₄	—	4	6	no	—
126	C₂²⋊C₄	—	4	6	no	—
127	C₂²⋊C₄	—	4	6	no	—
128	C₄²	—	4	1	no	—
129	C₂×C₅	—	8	6	no	—
130	C₂×C₅	#1613	1	3	yes	—
131	C₂×C₅	#1629	1	3	yes	—
132	C₂×C₅	#1655	1	1	yes	characteristic
133	C₂³	—	2	6	no	—
134	C₂³	—	4	6	no	—
135	C₂³	—	4	3	no	—
136	C₂³	—	4	6	no	—
137	C₂³	—	4	3	no	—
138	C₂³	—	8	12	no	—
139	C₂³	—	8	12	no	—
140	C₂³	—	8	4	no	—
141	C₂³	C₅×#120	1	1	yes	characteristic
142	D₄	—	4	6	no	—
143	D₄	—	8	3	no	—
144	D₄	—	8	12	no	—
145	C₂×C₄	—	2	3	no	—
146	C₂×C₄	—	2	3	no	—
147	C₂×C₄	—	4	6	no	—
148	C₂×C₄	—	4	3	no	—
149	C₂×C₄	—	8	3	no	—
150	C₂×C₄	C₂×C₅×SD₁₆	1	3	yes	—
151	C₂×C₄	C₅×AGL(1,ℤ/8)	1	3	yes	—
152	C₈	—	4	6	no	—
153	C₅	#7822	1	1	yes	characteristic, direct product factor, Sylow
154	C₂²	—	4	6	no	—
155	C₂²	—	4	12	no	—
156	C₂²	—	8	16	no	—
157	C₂²	—	8	6	no	—
158	C₂²	—	8	3	no	—
159	C₂²	—	8	3	no	—
160	C₂²	C₅×#450	1	3	yes	—
161	C₂²	C₅×#453	1	3	yes	—
162	C₂²	C₅×#458	1	1	yes	characteristic
163	C₄	—	2	3	no	—
164	C₄	—	2	3	no	—
165	C₄	—	8	3	no	—
166	C₄	—	16	1	no	—
167	C₂	—	8	6	no	—
168	C₂	C₅×#1613	1	3	yes	—
169	C₂	C₅×#1629	1	3	yes	—
170	C₂	C₅×#1655	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2679

C₂

yes

maximal, characteristic

C₅×#2094

C₂

yes

maximal, complemented

C₅×#1270

C₂

yes

maximal, complemented

C₂×C₅×#120

—

C₂×C₅×#106

—

C₂×C₅×#102

—

C₅×#394

—

C₅×#390

C₂²

yes

—

C₅×#384

C₂²

yes

characteristic, complemented

C₅×#336

C₂²

yes

complemented

#7822

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂⁵×C₅

—

C₂²×C₅×D₄

—

C₂²×C₅×D₄

D₄

yes

—

C₂²×C₅×C₈

—

C₅×#120

—

C₅×#120

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

D₄

yes

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#106

—

C₅×#102

—

C₅×#95

—

#2679

C₂×C₅

yes

characteristic

#2094

C₂×C₅

yes

complemented

#1270

C₂×C₅

yes

complemented

C₂⁴×C₅

—

C₂⁴×C₅

—

C₂⁴×C₅

—

C₂⁴×C₅

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

SD₁₆

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

—

—

—

—

C₂²×C₅

yes

—

#384

C₂²×C₅

yes

characteristic, complemented

#336

C₂²×C₅

yes

complemented

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#120

yes

characteristic

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₅×C₈

—

C₂⁵

—

C₂²×D₄

—

C₂²×D₄

C₅×D₄

yes

—

C₂²×C₈

—

#120

—

#120

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₅×D₄

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂³×C₅

yes

—

—

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#450

yes

—

100

C₂²×C₅

#453

yes

—

101

C₂²×C₅

#458

yes

characteristic

102

C₄×C₅

—

103

C₄×C₅

—

104

C₄×C₅

—

105

C₄×C₅

—

106

C₂⁴

—

107

C₂⁴

—

108

C₂⁴

—

109

C₂⁴

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

C₅×SD₁₆

yes

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂×C₅×D₄

yes

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₂×C₅

—

130

C₂×C₅

#1613

yes

—

131

C₂×C₅

#1629

yes

—

132

C₂×C₅

#1655

yes

characteristic

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

C₅×#120

yes

characteristic

142

D₄

—

143

D₄

—

144

D₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₂×C₅×SD₁₆

yes

—

151

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

152

C₈

—

153

C₅

#7822

yes

characteristic, direct product factor, Sylow

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

C₅×#450

yes

—

161

C₂²

C₅×#453

yes

—

162

C₂²

C₅×#458

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₂

—

168

C₂

C₅×#1613

yes

—

169

C₂

C₅×#1629

yes

—

170

C₂

C₅×#1655

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₅×#2679	C₂
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂³×C₅

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₅×#2679

C₂

LCS

G ▷ C₂×C₄² ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
2. C₅×#2094	C₂	semidirect
3. C₅×#1270	C₂	semidirect
9. C₅×#384	C₂²	semidirect
10. C₅×#336	C₂²	semidirect
11. #7822	C₅	direct (N × H)
27. #2094	C₂×C₅	semidirect
28. #1270	C₂×C₅	semidirect
57. #384	C₂²×C₅	semidirect
58. #336	C₂²×C₅	semidirect
153. C₅	#7822	direct (N × H)

H ≅ G/N

type

2. C₅×#2094

C₂

semidirect

3. C₅×#1270

C₂

semidirect

9. C₅×#384

C₂²

semidirect

10. C₅×#336

C₂²

semidirect

11. #7822

C₅

direct (N × H)

27. #2094

C₂×C₅

semidirect

28. #1270

C₂×C₅

semidirect

57. #384

C₂²×C₅

semidirect

58. #336

C₂²×C₅

semidirect

153. C₅

#7822

direct (N × H)

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

subgroup	index
C₅×#2679	2
C₅×#2094	2
C₅×#1270	2
#7822	5

subgroup

index

Subgroups — C₅×#7822 #11930542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#7822 #11930542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7822 #11930542