Group #11955520 — subgroups

Subgroups — C₅×#32800 #11955520

Order 1280.

816 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 238 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×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2860	C₂	1	1	yes	maximal, characteristic
3	C₅×#2043	C₂	1	6	yes	maximal, complemented
4	C₅×#2013	C₂	1	6	yes	maximal
5	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×SD₁₆	C₂²	1	4	yes	—
7	C₂×C₅×C₄⋊Q₈	C₂²	1	6	yes	—
8	C₂×C₅×#126	—	2	1	no	—
9	C₂×C₅×#103	C₂²	1	12	yes	—
10	C₅×#390	C₂²	1	3	yes	—
11	C₅×#389	C₂²	1	3	yes	—
12	C₅×#388	—	2	3	no	—
13	C₅×#384	—	2	3	no	—
14	C₅×#384	—	2	1	no	—
15	C₄³×C₅	C₂²	1	1	yes	characteristic
16	C₅×#336	C₂²	1	6	yes	—
17	#32800	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×Q₈	C₂³	1	4	yes	—
19	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
20	C₂×C₅×SD₁₆	—	4	12	no	—
21	C₂²×C₅×C₈	C₂³	1	4	yes	—
22	C₅×C₄⋊Q₈	—	4	12	no	—
23	C₅×#126	—	4	4	no	—
24	C₂×C₅×C₄⋊C₄	—	2	6	no	—
25	C₂×C₅×C₄⋊C₄	—	2	6	no	—
26	C₂×C₅×C₄⋊C₄	—	2	3	no	—
27	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
28	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
29	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
30	C₂×C₄²×C₅	D₄	1	3	yes	—
31	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₅	C₂³	1	3	yes	—
33	C₅×#103	—	4	12	no	—
34	C₅×#95	—	2	3	no	—
35	#2868	C₂×C₅	1	1	yes	characteristic, complemented
36	#2860	C₂×C₅	1	1	yes	characteristic
37	#2043	C₂×C₅	1	6	yes	complemented
38	#2013	C₂×C₅	1	6	yes	—
39	#1839	C₂×C₅	1	1	yes	characteristic, complemented
40	C₂⁴×C₅	—	2	1	no	—
41	C₂×C₅×Q₈	—	2	12	no	—
42	C₂×C₅×Q₈	—	2	12	no	—
43	C₂×C₅×D₄	—	2	6	no	—
44	C₂²×C₄×C₅	—	2	3	no	—
45	C₂²×C₄×C₅	—	2	4	no	—
46	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
47	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
48	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
49	C₅×SD₁₆	—	4	16	no	—
50	C₂×C₅×C₈	—	2	12	no	—
51	C₅×C₄⋊C₄	—	2	6	no	—
52	C₅×C₄⋊C₄	—	4	12	no	—
53	C₅×C₄⋊C₄	—	4	12	no	—
54	C₅×C₄⋊C₄	—	4	6	no	—
55	C₅×C₂²⋊C₄	—	4	6	no	—
56	C₅×C₂²⋊C₄	—	4	6	no	—
57	C₄²×C₅	—	2	6	no	—
58	C₄²×C₅	—	2	6	no	—
59	C₄²×C₅	SD₁₆	1	4	yes	complemented
60	C₂²×SD₁₆	C₂²×C₅	1	4	yes	—
61	C₂×C₄⋊Q₈	C₂²×C₅	1	6	yes	—
62	C₂×#126	—	2	1	no	—
63	C₂×#103	C₂²×C₅	1	12	yes	—
64	#390	C₂²×C₅	1	3	yes	—
65	#389	C₂²×C₅	1	3	yes	—
66	#388	—	2	3	no	—
67	#384	—	2	3	no	—
68	#384	—	2	1	no	—
69	C₄³	C₂²×C₅	1	1	yes	characteristic
70	#336	C₂²×C₅	1	6	yes	—
71	C₂³×C₅	—	4	3	no	—
72	C₂³×C₅	—	4	1	no	—
73	C₂³×C₅	—	4	3	no	—
74	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
75	C₅×Q₈	—	4	4	no	—
76	C₅×Q₈	—	4	12	no	—
77	C₅×D₄	—	4	4	no	—
78	C₂×C₄×C₅	—	2	3	no	—
79	C₂×C₄×C₅	—	2	3	no	—
80	C₂×C₄×C₅	—	2	3	no	—
81	C₂×C₄×C₅	—	2	3	no	—
82	C₂×C₄×C₅	—	4	3	no	—
83	C₂×C₄×C₅	—	4	12	no	—
84	C₂×C₄×C₅	—	4	3	no	—
85	C₂×C₄×C₅	—	4	3	no	—
86	C₂×C₄×C₅	C₂×SD₁₆	1	6	yes	—
87	C₂×C₄×C₅	#137	1	6	yes	—
88	C₂×C₄×C₅	H(5,𝔽₂)	1	6	yes	—
89	C₅×C₈	—	4	4	no	—
90	C₂²×Q₈	C₂³×C₅	1	4	yes	—
91	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
92	C₂×SD₁₆	—	4	12	no	—
93	C₂²×C₈	C₂³×C₅	1	4	yes	—
94	C₄⋊Q₈	—	4	12	no	—
95	#126	—	4	4	no	—
96	C₂×C₄⋊C₄	—	2	3	no	—
97	C₂×C₄⋊C₄	—	2	6	no	—
98	C₂×C₄⋊C₄	—	2	6	no	—
99	C₂×C₄⋊C₄	C₂³×C₅	1	3	yes	—
100	C₂×C₂²⋊C₄	—	2	3	no	—
101	C₂×C₂²⋊C₄	—	2	3	no	—
102	C₂×C₄²	C₅×D₄	1	3	yes	—
103	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
104	C₂×C₄²	C₂³×C₅	1	3	yes	—
105	#103	—	4	12	no	—
106	#95	—	2	3	no	—
107	C₂²×C₅	—	8	1	no	—
108	C₂²×C₅	—	8	3	no	—
109	C₂²×C₅	—	8	3	no	—
110	C₂²×C₅	#535	1	3	yes	—
111	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
112	C₂²×C₅	C₂×#137	1	3	yes	—
113	C₄×C₅	—	2	6	no	—
114	C₄×C₅	—	2	6	no	—
115	C₄×C₅	—	8	4	no	—
116	C₄×C₅	—	8	3	no	—
117	C₄×C₅	#560	1	4	yes	—
118	C₂⁴	—	2	1	no	—
119	C₂×Q₈	—	2	12	no	—
120	C₂×Q₈	—	2	12	no	—
121	C₂×D₄	—	2	6	no	—
122	C₂²×C₄	—	2	3	no	—
123	C₂²×C₄	—	2	4	no	—
124	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
125	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
126	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
127	SD₁₆	—	4	16	no	—
128	C₂×C₈	—	2	12	no	—
129	C₄⋊C₄	—	2	6	no	—
130	C₄⋊C₄	—	4	12	no	—
131	C₄⋊C₄	—	4	12	no	—
132	C₄⋊C₄	—	4	6	no	—
133	C₂²⋊C₄	—	4	6	no	—
134	C₂²⋊C₄	—	4	6	no	—
135	C₄²	—	2	6	no	—
136	C₄²	—	2	6	no	—
137	C₄²	C₅×SD₁₆	1	4	yes	complemented
138	C₂×C₅	—	16	1	no	—
139	C₂×C₅	#2818	1	1	yes	characteristic
140	C₂×C₅	#3206	1	3	yes	—
141	C₂×C₅	#3218	1	3	yes	—
142	C₂³	—	4	3	no	—
143	C₂³	—	4	1	no	—
144	C₂³	—	4	3	no	—
145	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
146	Q₈	—	4	4	no	—
147	Q₈	—	4	12	no	—
148	D₄	—	4	4	no	—
149	C₂×C₄	—	2	3	no	—
150	C₂×C₄	—	2	3	no	—
151	C₂×C₄	—	2	3	no	—
152	C₂×C₄	—	2	3	no	—
153	C₂×C₄	—	4	3	no	—
154	C₂×C₄	—	4	12	no	—
155	C₂×C₄	—	4	3	no	—
156	C₂×C₄	—	4	3	no	—
157	C₂×C₄	C₂×C₅×SD₁₆	1	6	yes	—
158	C₂×C₄	C₅×#137	1	6	yes	—
159	C₂×C₄	C₅×H(5,𝔽₂)	1	6	yes	—
160	C₈	—	4	4	no	—
161	C₅	#32800	1	1	yes	characteristic, direct product factor, Sylow
162	C₂²	—	8	1	no	—
163	C₂²	—	8	3	no	—
164	C₂²	—	8	3	no	—
165	C₂²	C₅×#535	1	3	yes	—
166	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
167	C₂²	C₂×C₅×#137	1	3	yes	—
168	C₄	—	2	6	no	—
169	C₄	—	2	6	no	—
170	C₄	—	8	4	no	—
171	C₄	—	8	3	no	—
172	C₄	C₅×#560	1	4	yes	—
173	C₂	—	16	1	no	—
174	C₂	C₅×#2818	1	1	yes	characteristic
175	C₂	C₅×#3206	1	3	yes	—
176	C₂	C₅×#3218	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2868

C₂

yes

maximal, characteristic, complemented

C₅×#2860

C₂

yes

maximal, characteristic

C₅×#2043

C₂

yes

maximal, complemented

C₅×#2013

C₂

yes

maximal

C₅×#1839

C₂

yes

maximal, characteristic, complemented

C₂²×C₅×SD₁₆

C₂²

yes

—

C₂×C₅×C₄⋊Q₈

C₂²

yes

—

C₂×C₅×#126

—

C₂×C₅×#103

C₂²

yes

—

C₅×#390

C₂²

yes

—

C₅×#389

C₂²

yes

—

C₅×#388

—

C₅×#384

—

C₅×#384

—

C₄³×C₅

C₂²

yes

characteristic

C₅×#336

C₂²

yes

—

#32800

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

C₂³

yes

—

C₂²×C₅×D₄

C₂³

yes

characteristic

C₂×C₅×SD₁₆

—

C₂²×C₅×C₈

C₂³

yes

—

C₅×C₄⋊Q₈

—

C₅×#126

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

C₂³

yes

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₄²×C₅

D₄

yes

—

C₂×C₄²×C₅

D₄

yes

characteristic

C₂×C₄²×C₅

C₂³

yes

—

C₅×#103

—

C₅×#95

—

#2868

C₂×C₅

yes

characteristic, complemented

#2860

C₂×C₅

yes

characteristic

#2043

C₂×C₅

yes

complemented

#2013

C₂×C₅

yes

—

#1839

C₂×C₅

yes

characteristic, complemented

C₂⁴×C₅

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

C₂⁴

yes

characteristic

C₅×SD₁₆

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

SD₁₆

yes

complemented

C₂²×SD₁₆

C₂²×C₅

yes

—

C₂×C₄⋊Q₈

C₂²×C₅

yes

—

C₂×#126

—

C₂×#103

C₂²×C₅

yes

—

#390

C₂²×C₅

yes

—

#389

C₂²×C₅

yes

—

#388

—

#384

—

#384

—

C₄³

C₂²×C₅

yes

characteristic

#336

C₂²×C₅

yes

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

C₂²×D₄

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₅×D₄

—

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×SD₁₆

yes

—

C₂×C₄×C₅

#137

yes

—

C₂×C₄×C₅

H(5,𝔽₂)

yes

—

C₅×C₈

—

C₂²×Q₈

C₂³×C₅

yes

—

C₂²×D₄

C₂³×C₅

yes

characteristic

C₂×SD₁₆

—

C₂²×C₈

C₂³×C₅

yes

—

C₄⋊Q₈

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂³×C₅

yes

—

100

C₂×C₂²⋊C₄

—

101

C₂×C₂²⋊C₄

—

102

C₂×C₄²

C₅×D₄

yes

—

103

C₂×C₄²

C₅×D₄

yes

characteristic

104

C₂×C₄²

C₂³×C₅

yes

—

105

#103

—

106

#95

—

107

C₂²×C₅

—

108

C₂²×C₅

—

109

C₂²×C₅

—

110

C₂²×C₅

#535

yes

—

111

C₂²×C₅

C₂²×SD₁₆

yes

characteristic

112

C₂²×C₅

C₂×#137

yes

—

113

C₄×C₅

—

114

C₄×C₅

—

115

C₄×C₅

—

116

C₄×C₅

—

117

C₄×C₅

#560

yes

—

118

C₂⁴

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×D₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂×C₅×D₄

yes

—

125

C₂²×C₄

C₂×C₅×D₄

yes

—

126

C₂²×C₄

C₂⁴×C₅

yes

characteristic

127

SD₁₆

—

128

C₂×C₈

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

—

136

C₄²

—

137

C₄²

C₅×SD₁₆

yes

complemented

138

C₂×C₅

—

139

C₂×C₅

#2818

yes

characteristic

140

C₂×C₅

#3206

yes

—

141

C₂×C₅

#3218

yes

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

C₂²×C₅×D₄

yes

characteristic

146

Q₈

—

147

Q₈

—

148

D₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×C₅×SD₁₆

yes

—

158

C₂×C₄

C₅×#137

yes

—

159

C₂×C₄

C₅×H(5,𝔽₂)

yes

—

160

C₈

—

161

C₅

#32800

yes

characteristic, direct product factor, Sylow

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

C₅×#535

yes

—

166

C₂²

C₂²×C₅×SD₁₆

yes

characteristic

167

C₂²

C₂×C₅×#137

yes

—

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

C₅×#560

yes

—

173

C₂

—

174

C₂

C₅×#2818

yes

characteristic

175

C₂

C₅×#3206

yes

—

176

C₂

C₅×#3218

yes

—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

subgroup

G/H

center, socle

C₂³×C₅

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₅

prime radical

C₂²×C₅×D₄

C₂³

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

N	H ≅ G/N	type
1. C₅×#2868	C₂	semidirect
3. C₅×#2043	C₂	semidirect
5. C₅×#1839	C₂	semidirect
17. #32800	C₅	direct (N × H)
35. #2868	C₂×C₅	semidirect
37. #2043	C₂×C₅	semidirect
39. #1839	C₂×C₅	semidirect
59. C₄²×C₅	SD₁₆	semidirect
137. C₄²	C₅×SD₁₆	semidirect
161. C₅	#32800	direct (N × H)

H ≅ G/N

type

1. C₅×#2868

C₂

semidirect

3. C₅×#2043

C₂

semidirect

5. C₅×#1839

C₂

semidirect

17. #32800

C₅

direct (N × H)

35. #2868

C₂×C₅

semidirect

37. #2043

C₂×C₅

semidirect

39. #1839

C₂×C₅

semidirect

59. C₄²×C₅

SD₁₆

semidirect

137. C₄²

C₅×SD₁₆

semidirect

161. C₅

#32800

direct (N × H)

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

subgroup	index
C₅×#2868	2
C₅×#2860	2
C₅×#2043	2
C₅×#2013	2
C₅×#1839	2
#32800	5

subgroup

index

Subgroups — C₅×#32800 #11955520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#32800 #11955520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32800 #11955520