Group #11955577 — subgroups

Subgroups — C₅×#32857 #11955577

Order 1280.

510 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 206 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×#2647	C₂	1	2	yes	maximal
2	C₅×#2101	C₂	1	4	yes	maximal
3	C₅×#2088	C₂	1	4	yes	maximal
4	C₅×#2084	C₂	1	4	yes	maximal
5	C₅×#1832	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#106	C₂²	1	4	yes	—
7	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
8	C₅×#400	—	2	4	no	—
9	C₅×#398	—	2	4	no	—
10	C₅×#389	C₂²	1	4	yes	—
11	C₅×#389	C₂²	1	4	yes	—
12	C₅×#384	C₂²	1	2	yes	—
13	C₅×#382	C₂²	1	2	yes	—
14	C₅×#376	C₂²	1	1	yes	characteristic
15	C₅×#340	C₂²	1	8	yes	—
16	C₅×#340	C₂²	1	4	yes	—
17	C₅×#336	C₂²	1	4	yes	—
18	#32857	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₅×C₈	C₂³	1	4	yes	—
20	C₂×C₅×C₄⋊C₄	—	2	4	no	—
21	C₂×C₅×C₄⋊C₄	—	2	4	no	—
22	C₂×C₅×C₄⋊C₄	—	2	4	no	—
23	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
24	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
25	C₂×C₄²×C₅	C₂³	1	2	yes	—
26	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₅×#106	—	4	4	no	—
28	C₅×C₄⋊C₈	—	4	2	no	—
29	C₅×#95	—	2	4	no	—
30	C₅×#95	—	2	4	no	—
31	C₅×#95	—	2	4	no	—
32	C₅×#95	D₄	1	4	yes	—
33	#2647	C₂×C₅	1	2	yes	—
34	#2101	C₂×C₅	1	4	yes	—
35	#2088	C₂×C₅	1	4	yes	—
36	#2084	C₂×C₅	1	4	yes	—
37	#1832	C₂×C₅	1	1	yes	characteristic
38	C₂²×C₄×C₅	—	2	4	no	—
39	C₂²×C₄×C₅	—	2	4	no	—
40	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
41	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
43	C₂×C₅×C₈	—	2	4	no	—
44	C₂×C₅×C₈	—	2	8	no	—
45	C₅×C₄⋊C₄	—	2	4	no	—
46	C₅×C₄⋊C₄	—	2	8	no	—
47	C₅×C₄⋊C₄	—	2	4	no	—
48	C₅×C₄⋊C₄	—	8	4	no	—
49	C₅×C₄⋊C₄	—	8	4	no	—
50	C₅×C₄⋊C₄	—	8	4	no	—
51	C₄²×C₅	—	2	1	no	—
52	C₄²×C₅	—	2	4	no	—
53	C₄²×C₅	—	2	1	no	—
54	C₂×#106	C₂²×C₅	1	4	yes	—
55	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
56	#400	—	2	4	no	—
57	#398	—	2	4	no	—
58	#389	C₂²×C₅	1	4	yes	—
59	#389	C₂²×C₅	1	4	yes	—
60	#384	C₂²×C₅	1	2	yes	—
61	#382	C₂²×C₅	1	2	yes	—
62	#376	C₂²×C₅	1	1	yes	characteristic
63	#340	C₂²×C₅	1	8	yes	—
64	#340	C₂²×C₅	1	4	yes	—
65	#336	C₂²×C₅	1	4	yes	—
66	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
67	C₂×C₄×C₅	—	2	4	no	—
68	C₂×C₄×C₅	—	2	2	no	—
69	C₂×C₄×C₅	—	2	4	no	—
70	C₂×C₄×C₅	—	2	4	no	—
71	C₂×C₄×C₅	—	2	4	no	—
72	C₂×C₄×C₅	—	4	4	no	—
73	C₂×C₄×C₅	—	4	4	no	—
74	C₂×C₄×C₅	—	4	4	no	—
75	C₂×C₄×C₅	—	4	4	no	—
76	C₂×C₄×C₅	—	4	4	no	—
77	C₂×C₄×C₅	—	4	4	no	—
78	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
79	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
80	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
81	C₅×C₈	—	4	4	no	—
82	C₂²×C₈	C₂³×C₅	1	4	yes	—
83	C₂×C₄⋊C₄	—	2	4	no	—
84	C₂×C₄⋊C₄	—	2	4	no	—
85	C₂×C₄⋊C₄	—	2	4	no	—
86	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
87	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
88	C₂×C₄²	C₂³×C₅	1	2	yes	—
89	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
90	#106	—	4	4	no	—
91	C₄⋊C₈	—	4	2	no	—
92	#95	—	2	4	no	—
93	#95	—	2	4	no	—
94	#95	—	2	4	no	—
95	#95	C₅×D₄	1	4	yes	—
96	C₂²×C₅	#536	1	2	yes	—
97	C₂²×C₅	#537	1	1	yes	characteristic
98	C₂²×C₅	#577	1	4	yes	—
99	C₄×C₅	—	4	4	no	—
100	C₄×C₅	—	4	2	no	—
101	C₄×C₅	—	8	4	no	—
102	C₄×C₅	—	8	4	no	—
103	C₄×C₅	#563	1	2	yes	—
104	C₄×C₅	#564	1	2	yes	—
105	C₂²×C₄	—	2	4	no	—
106	C₂²×C₄	—	2	4	no	—
107	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
108	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
109	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
110	C₂×C₈	—	2	4	no	—
111	C₂×C₈	—	2	8	no	—
112	C₄⋊C₄	—	2	4	no	—
113	C₄⋊C₄	—	2	8	no	—
114	C₄⋊C₄	—	2	4	no	—
115	C₄⋊C₄	—	8	4	no	—
116	C₄⋊C₄	—	8	4	no	—
117	C₄⋊C₄	—	8	4	no	—
118	C₄²	—	2	1	no	—
119	C₄²	—	2	4	no	—
120	C₄²	—	2	1	no	—
121	C₂×C₅	#2822	1	1	yes	characteristic
122	C₂×C₅	#3244	1	4	yes	—
123	C₂×C₅	#3260	1	2	yes	—
124	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	4	4	no	—
133	C₂×C₄	—	4	4	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
137	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
138	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
139	C₈	—	4	4	no	—
140	C₅	#32857	1	1	yes	characteristic, direct product factor, Sylow
141	C₂²	C₅×#536	1	2	yes	—
142	C₂²	C₅×#537	1	1	yes	characteristic
143	C₂²	C₅×#577	1	4	yes	—
144	C₄	—	4	4	no	—
145	C₄	—	4	2	no	—
146	C₄	—	8	4	no	—
147	C₄	—	8	4	no	—
148	C₄	C₅×#563	1	2	yes	—
149	C₄	C₅×#564	1	2	yes	—
150	C₂	C₅×#2822	1	1	yes	characteristic
151	C₂	C₅×#3244	1	4	yes	—
152	C₂	C₅×#3260	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2647

C₂

yes

maximal

C₅×#2101

C₂

yes

maximal

C₅×#2088

C₂

yes

maximal

C₅×#2084

C₂

yes

maximal

C₅×#1832

C₂

yes

maximal, characteristic

C₂×C₅×#106

C₂²

yes

—

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₅×#400

—

C₅×#398

—

C₅×#389

C₂²

yes

—

C₅×#389

C₂²

yes

—

C₅×#384

C₂²

yes

—

C₅×#382

C₂²

yes

—

C₅×#376

C₂²

yes

characteristic

C₅×#340

C₂²

yes

—

C₅×#340

C₂²

yes

—

C₅×#336

C₂²

yes

—

#32857

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×C₈

C₂³

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

C₂³

yes

—

C₂×C₅×C₄⋊C₄

C₂³

yes

—

C₂×C₄²×C₅

C₂³

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#106

—

C₅×C₄⋊C₈

—

C₅×#95

—

C₅×#95

—

C₅×#95

—

C₅×#95

D₄

yes

—

#2647

C₂×C₅

yes

—

#2101

C₂×C₅

yes

—

#2088

C₂×C₅

yes

—

#2084

C₂×C₅

yes

—

#1832

C₂×C₅

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×C₄×C₅

C₂⁴

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

—

C₂×#106

C₂²×C₅

yes

—

C₂×C₄⋊C₈

C₂²×C₅

yes

—

#400

—

#398

—

#389

C₂²×C₅

yes

—

#389

C₂²×C₅

yes

—

#384

C₂²×C₅

yes

—

#382

C₂²×C₅

yes

—

#376

C₂²×C₅

yes

characteristic

#340

C₂²×C₅

yes

—

#340

C₂²×C₅

yes

—

#336

C₂²×C₅

yes

—

C₂³×C₅

C₂²×D₄

yes

characteristic

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

H(5,𝔽₂)

yes

characteristic

C₂×C₄×C₅

2₋¹⁺⁴

yes

—

C₂×C₄×C₅

2₋¹⁺⁴

yes

characteristic

C₅×C₈

—

C₂²×C₈

C₂³×C₅

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂³×C₅

yes

—

C₂×C₄⋊C₄

C₂³×C₅

yes

—

C₂×C₄²

C₂³×C₅

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

#106

—

C₄⋊C₈

—

—

—

—

C₅×D₄

yes

—

C₂²×C₅

#536

yes

—

C₂²×C₅

#537

yes

characteristic

C₂²×C₅

#577

yes

—

C₄×C₅

—

100

C₄×C₅

—

101

C₄×C₅

—

102

C₄×C₅

—

103

C₄×C₅

#563

yes

—

104

C₄×C₅

#564

yes

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂×C₅×D₄

yes

—

108

C₂²×C₄

C₂×C₅×D₄

yes

—

109

C₂²×C₄

C₂⁴×C₅

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₂×C₅

#2822

yes

characteristic

122

C₂×C₅

#3244

yes

—

123

C₂×C₅

#3260

yes

—

124

C₂³

C₂²×C₅×D₄

yes

characteristic

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

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₅×H(5,𝔽₂)

yes

characteristic

137

C₂×C₄

C₅×2₋¹⁺⁴

yes

—

138

C₂×C₄

C₅×2₋¹⁺⁴

yes

characteristic

139

C₈

—

140

C₅

#32857

yes

characteristic, direct product factor, Sylow

141

C₂²

C₅×#536

yes

—

142

C₂²

C₅×#537

yes

characteristic

143

C₂²

C₅×#577

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

C₅×#563

yes

—

149

C₄

C₅×#564

yes

—

150

C₂

C₅×#2822

yes

characteristic

151

C₂

C₅×#3244

yes

—

152

C₂

C₅×#3260

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₅

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₅

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

N	H ≅ G/N	type
18. #32857	C₅	direct (N × H)
140. C₅	#32857	direct (N × H)

H ≅ G/N

type

18. #32857

C₅

direct (N × H)

140. C₅

#32857

direct (N × H)

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

subgroup	index
C₅×#2647	2
C₅×#2101	2
C₅×#2088	2
C₅×#2084	2
C₅×#1832	2
#32857	5

subgroup

index

Subgroups — C₅×#32857 #11955577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#32857 #11955577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32857 #11955577