Group #11935605 — subgroups

Subgroups — C₅×#12885 #11935605

Order 1280.

234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2153	C₂	1	1	yes	maximal, characteristic
2	C₅×#2151	C₂	1	1	yes	maximal, characteristic
3	C₅×#1747	C₂	1	1	yes	maximal, characteristic
4	C₅×#1379	C₂	1	2	yes	maximal
5	C₅×#1378	C₂	1	2	yes	maximal
6	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₅×M₃₂	C₂²	1	2	yes	—
8	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	C₅×#405	C₂²	1	2	yes	—
10	C₅×#405	C₂²	1	1	yes	characteristic
11	C₅×#364	—	2	2	no	—
12	C₅×C₄⋊C₁₆	—	2	2	no	—
13	C₅×#338	C₄	1	1	yes	characteristic
14	C₅×H(3,ℤ/4)	C₄	1	1	yes	characteristic
15	C₅×H(3,ℤ/4)	C₄	1	2	yes	—
16	#12885	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
18	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
20	C₅×#117	C₂×C₄	1	2	yes	—
21	C₅×#117	C₂×C₄	1	1	yes	characteristic
22	C₅×M₃₂	—	2	2	no	—
23	C₅×M₃₂	—	2	2	no	—
24	C₅×M₃₂	—	2	2	no	—
25	C₂×C₅×C₁₆	—	2	1	no	—
26	C₂×C₅×C₁₆	—	2	1	no	—
27	C₂×C₅×C₁₆	—	2	2	no	—
28	C₂×C₅×C₁₆	—	2	2	no	—
29	C₅×#97	—	2	2	no	—
30	C₅×#97	Q₈	1	2	yes	—
31	C₄×C₅×C₈	—	2	2	no	—
32	C₄×C₅×C₈	D₄	1	2	yes	—
33	#2153	C₂×C₅	1	1	yes	characteristic
34	#2151	C₂×C₅	1	1	yes	characteristic
35	#1747	C₂×C₅	1	1	yes	characteristic
36	#1379	C₂×C₅	1	2	yes	—
37	#1378	C₂×C₅	1	2	yes	—
38	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₅×M₁₆	—	2	2	no	—
40	C₅×M₁₆	—	2	2	no	—
41	C₅×M₁₆	—	2	2	no	—
42	C₂×C₅×C₈	—	2	2	no	—
43	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
44	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
45	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₅×C₈	#41	1	2	yes	—
47	C₂×C₅×C₈	#41	1	2	yes	—
48	C₅×C₄⋊C₄	—	2	1	no	—
49	C₅×C₄⋊C₄	—	2	2	no	—
50	C₅×C₂²⋊C₄	—	2	1	no	—
51	C₅×C₂²⋊C₄	—	2	2	no	—
52	C₄²×C₅	—	2	2	no	—
53	C₄²×C₅	C₄⋊C₄	1	2	yes	—
54	C₅×C₁₆	—	4	1	no	—
55	C₅×C₁₆	—	4	1	no	—
56	C₅×C₁₆	—	4	2	no	—
57	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
58	C₂×M₃₂	C₂²×C₅	1	2	yes	—
59	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
60	#405	C₂²×C₅	1	2	yes	—
61	#405	C₂²×C₅	1	1	yes	characteristic
62	#364	—	2	2	no	—
63	C₄⋊C₁₆	—	2	2	no	—
64	#338	C₄×C₅	1	1	yes	characteristic
65	H(3,ℤ/4)	C₄×C₅	1	1	yes	characteristic
66	H(3,ℤ/4)	C₄×C₅	1	2	yes	—
67	C₂³×C₅	#131	1	1	yes	characteristic
68	C₂×C₄×C₅	—	2	2	no	—
69	C₂×C₄×C₅	—	4	2	no	—
70	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₅	#117	1	2	yes	—
72	C₂×C₄×C₅	#131	1	2	yes	—
73	C₂×C₄×C₅	#131	1	1	yes	characteristic
74	C₅×C₈	—	2	2	no	—
75	C₅×C₈	—	4	2	no	—
76	C₅×C₈	#124	1	1	yes	characteristic
77	C₅×C₈	#124	1	1	yes	characteristic
78	C₅×C₈	#125	1	2	yes	—
79	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
80	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
81	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
82	#117	C₂×C₄×C₅	1	2	yes	—
83	#117	C₂×C₄×C₅	1	1	yes	characteristic
84	M₃₂	—	2	2	no	—
85	M₃₂	—	2	2	no	—
86	M₃₂	—	2	2	no	—
87	C₂×C₁₆	—	2	1	no	—
88	C₂×C₁₆	—	2	1	no	—
89	C₂×C₁₆	—	2	2	no	—
90	C₂×C₁₆	—	2	2	no	—
91	#97	—	2	2	no	—
92	#97	C₅×Q₈	1	2	yes	—
93	C₄×C₈	—	2	2	no	—
94	C₄×C₈	C₅×D₄	1	2	yes	—
95	C₂²×C₅	—	4	1	no	—
96	C₂²×C₅	#424	1	1	yes	characteristic
97	C₂²×C₅	#433	1	2	yes	—
98	C₄×C₅	—	4	2	no	—
99	C₄×C₅	—	8	2	no	—
100	C₄×C₅	#382	1	1	yes	characteristic
101	C₄×C₅	#424	1	1	yes	characteristic
102	C₄×C₅	#433	1	2	yes	—
103	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
104	M₁₆	—	2	2	no	—
105	M₁₆	—	2	2	no	—
106	M₁₆	—	2	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
109	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
110	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
111	C₂×C₈	C₅×#41	1	2	yes	—
112	C₂×C₈	C₅×#41	1	2	yes	—
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	—	2	2	no	—
115	C₂²⋊C₄	—	2	1	no	—
116	C₂²⋊C₄	—	2	2	no	—
117	C₄²	—	2	2	no	—
118	C₄²	C₅×C₄⋊C₄	1	2	yes	—
119	C₁₆	—	4	1	no	—
120	C₁₆	—	4	1	no	—
121	C₁₆	—	4	2	no	—
122	C₂×C₅	—	2	1	no	—
123	C₂×C₅	—	2	2	no	—
124	C₂×C₅	#1832	1	1	yes	characteristic
125	C₂³	C₅×#131	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄	C₅×#117	1	2	yes	—
130	C₂×C₄	C₅×#131	1	2	yes	—
131	C₂×C₄	C₅×#131	1	1	yes	characteristic
132	C₈	—	2	2	no	—
133	C₈	—	4	2	no	—
134	C₈	C₅×#124	1	1	yes	characteristic
135	C₈	C₅×#124	1	1	yes	characteristic
136	C₈	C₅×#125	1	2	yes	—
137	C₅	#12885	1	1	yes	characteristic, direct product factor, Sylow
138	C₂²	—	4	1	no	—
139	C₂²	C₅×#424	1	1	yes	characteristic
140	C₂²	C₅×#433	1	2	yes	—
141	C₄	—	4	2	no	—
142	C₄	—	8	2	no	—
143	C₄	C₅×#382	1	1	yes	characteristic
144	C₄	C₅×#424	1	1	yes	characteristic
145	C₄	C₅×#433	1	2	yes	—
146	C₂	—	2	1	no	—
147	C₂	—	2	2	no	—
148	C₂	C₅×#1832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2153

C₂

yes

maximal, characteristic

C₅×#2151

C₂

yes

maximal, characteristic

C₅×#1747

C₂

yes

maximal, characteristic

C₅×#1379

C₂

yes

maximal

C₅×#1378

C₂

yes

maximal

C₂×C₅×M₃₂

C₂²

yes

characteristic

C₂×C₅×M₃₂

C₂²

yes

—

C₂²×C₅×C₁₆

C₂²

yes

characteristic

C₅×#405

C₂²

yes

—

C₅×#405

C₂²

yes

characteristic

C₅×#364

—

C₅×C₄⋊C₁₆

—

C₅×#338

C₄

yes

characteristic

C₅×H(3,ℤ/4)

C₄

yes

characteristic

C₅×H(3,ℤ/4)

C₄

yes

—

#12885

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×M₁₆

C₂×C₄

yes

—

C₂×C₅×M₁₆

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂³

yes

characteristic

C₅×#117

C₂×C₄

yes

—

C₅×#117

C₂×C₄

yes

characteristic

C₅×M₃₂

—

C₅×M₃₂

—

C₅×M₃₂

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

—

C₅×#97

—

C₅×#97

Q₈

yes

—

C₄×C₅×C₈

—

C₄×C₅×C₈

D₄

yes

—

#2153

C₂×C₅

yes

characteristic

#2151

C₂×C₅

yes

characteristic

#1747

C₂×C₅

yes

characteristic

#1379

C₂×C₅

yes

—

#1378

C₂×C₅

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₅×M₁₆

—

C₅×M₁₆

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₂×D₄

yes

characteristic

C₂×C₅×C₈

C₂×Q₈

yes

characteristic

C₂×C₅×C₈

#41

yes

—

C₂×C₅×C₈

#41

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

C₄²×C₅

C₄⋊C₄

yes

—

C₅×C₁₆

—

C₅×C₁₆

—

C₅×C₁₆

—

C₂×M₃₂

C₂²×C₅

yes

characteristic

C₂×M₃₂

C₂²×C₅

yes

—

C₂²×C₁₆

C₂²×C₅

yes

characteristic

#405

C₂²×C₅

yes

—

#405

C₂²×C₅

yes

characteristic

#364

—

C₄⋊C₁₆

—

#338

C₄×C₅

yes

characteristic

H(3,ℤ/4)

C₄×C₅

yes

characteristic

H(3,ℤ/4)

C₄×C₅

yes

—

C₂³×C₅

#131

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#131

yes

—

C₂×C₄×C₅

#131

yes

characteristic

C₅×C₈

—

C₅×C₈

—

C₅×C₈

yes

C₅×C₈

yes

C₅×C₈

yes

—

C₂×M₁₆

C₂×C₄×C₅

yes

—

C₂×M₁₆

C₂×C₄×C₅

yes

characteristic

C₂²×C₈

C₂³×C₅

yes

characteristic

#117

C₂×C₄×C₅

yes

—

#117

C₂×C₄×C₅

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

C₅×Q₈

yes

—

C₄×C₈

—

C₄×C₈

C₅×D₄

yes

—

C₂²×C₅

—

C₂²×C₅

#424

yes

characteristic

C₂²×C₅

#433

yes

—

C₄×C₅

—

C₄×C₅

—

100

C₄×C₅

#382

yes

characteristic

101

C₄×C₅

#424

yes

characteristic

102

C₄×C₅

#433

yes

—

103

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

C₅×C₄⋊C₄

yes

—

109

C₂×C₈

C₂×C₅×D₄

yes

characteristic

110

C₂×C₈

C₂×C₅×Q₈

yes

characteristic

111

C₂×C₈

C₅×#41

yes

—

112

C₂×C₈

C₅×#41

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

C₅×C₄⋊C₄

yes

—

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

C₂×C₅

—

123

C₂×C₅

—

124

C₂×C₅

#1832

yes

characteristic

125

C₂³

C₅×#131

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

129

C₂×C₄

C₅×#117

yes

—

130

C₂×C₄

C₅×#131

yes

—

131

C₂×C₄

C₅×#131

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

C₅×#124

yes

characteristic

135

C₈

C₅×#124

yes

characteristic

136

C₈

C₅×#125

yes

—

137

C₅

#12885

yes

characteristic, direct product factor, Sylow

138

C₂²

—

139

C₂²

C₅×#424

yes

characteristic

140

C₂²

C₅×#433

yes

—

141

C₄

—

142

C₄

—

143

C₄

C₅×#382

yes

characteristic

144

C₄

C₅×#424

yes

characteristic

145

C₄

C₅×#433

yes

—

146

C₂

—

147

C₂

—

148

C₂

C₅×#1832

yes

characteristic

	subgroup	G/H
center	C₅×C₈	#124
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂×C₅	#1832
prime radical	C₂³×C₅	#131
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₅×C₈ ◁ C₂²×C₅×C₈ ◁ G

subgroup

G/H

center

C₅×C₈

#124

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂²×C₈

C₂³×C₅

C₂×C₅

C₂³×C₅

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₅×C₈ ◁ C₂²×C₅×C₈ ◁ G

N	H ≅ G/N	type
16. #12885	C₅	direct (N × H)
137. C₅	#12885	direct (N × H)

H ≅ G/N

type

16. #12885

C₅

direct (N × H)

137. C₅

#12885

direct (N × H)

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

subgroup	index
C₅×#2153	2
C₅×#2151	2
C₅×#1747	2
C₅×#1379	2
C₅×#1378	2
#12885	5

subgroup

index

Subgroups — C₅×#12885 #11935605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12885 #11935605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12885 #11935605