Group #11934781 — subgroups

Subgroups — C₅×#12061 #11934781

Order 1280.

200 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2183	C₂	1	2	yes	maximal
2	C₅×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#1367	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₈⋊C₁₆	C₂	1	2	yes	maximal
5	C₅×#1312	C₂	1	1	yes	maximal, characteristic
6	C₅×C₈×Q₈	C₂²	1	2	yes	—
7	C₄×C₅×Q₁₆	C₄	1	1	yes	characteristic
8	C₅×C₄⋊C₁₆	—	2	2	no	—
9	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
10	C₅×#346	—	2	2	no	—
11	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
12	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
13	C₅×#335	C₄	1	1	yes	characteristic
14	C₅×Q₈⋊C₈	C₄	1	2	yes	—
15	C₅×C₈²	C₂²	1	1	yes	characteristic
16	#12061	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₅×Q₁₆	C₈	1	1	yes	characteristic
18	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
19	C₂×C₅×C₁₆	—	2	2	no	—
20	C₂×C₅×C₁₆	—	2	1	no	—
21	C₂×C₅×C₁₆	D₄	1	2	yes	—
22	C₅×#107	C₈	1	1	yes	characteristic
23	C₅×C₄⋊C₈	—	2	2	no	—
24	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
25	C₅×#103	C₈	1	2	yes	—
26	C₄×C₅×C₈	—	2	2	no	—
27	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
28	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
29	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
30	#2183	C₂×C₅	1	2	yes	—
31	C₈×Q₁₆	C₂×C₅	1	1	yes	characteristic
32	#1367	C₂×C₅	1	1	yes	characteristic
33	Q₈⋊C₁₆	C₂×C₅	1	2	yes	—
34	#1312	C₂×C₅	1	1	yes	characteristic
35	C₂×C₅×Q₈	C₂×C₈	1	2	yes	—
36	C₅×Q₁₆	—	2	2	no	—
37	C₂×C₅×C₈	—	2	2	no	—
38	C₂×C₅×C₈	—	2	1	no	—
39	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
40	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
41	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
42	C₂×C₅×C₈	#41	1	1	yes	characteristic
43	C₅×C₄⋊C₄	—	2	2	no	—
44	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
45	C₄²×C₅	—	2	2	no	—
46	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
47	C₅×C₁₆	—	2	2	no	—
48	C₅×C₁₆	—	4	1	no	—
49	C₅×C₁₆	—	4	2	no	—
50	C₈×Q₈	C₂²×C₅	1	2	yes	—
51	C₄×Q₁₆	C₄×C₅	1	1	yes	characteristic
52	C₄⋊C₁₆	—	2	2	no	—
53	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
54	#346	—	2	2	no	—
55	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
56	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
57	#335	C₄×C₅	1	1	yes	characteristic
58	Q₈⋊C₈	C₄×C₅	1	2	yes	—
59	C₈²	C₂²×C₅	1	1	yes	characteristic
60	C₅×Q₈	—	2	2	no	—
61	C₅×Q₈	—	2	2	no	—
62	C₂×C₄×C₅	—	2	2	no	—
63	C₂×C₄×C₅	—	2	2	no	—
64	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
65	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
66	C₂×C₄×C₅	#131	1	1	yes	characteristic
67	C₅×C₈	—	2	1	no	—
68	C₅×C₈	—	2	1	no	—
69	C₅×C₈	—	4	1	no	—
70	C₅×C₈	—	4	2	no	—
71	C₅×C₈	M₃₂	1	2	yes	—
72	C₅×C₈	#137	1	2	yes	—
73	C₂×Q₁₆	C₅×C₈	1	1	yes	characteristic
74	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
75	C₂×C₁₆	—	2	2	no	—
76	C₂×C₁₆	—	2	1	no	—
77	C₂×C₁₆	C₅×D₄	1	2	yes	—
78	#107	C₅×C₈	1	1	yes	characteristic
79	C₄⋊C₈	—	2	2	no	—
80	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
81	#103	C₅×C₈	1	2	yes	—
82	C₄×C₈	—	2	2	no	—
83	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
84	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
85	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
86	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
87	C₄×C₅	—	2	1	no	—
88	C₄×C₅	—	4	2	no	—
89	C₄×C₅	—	4	2	no	—
90	C₄×C₅	#441	1	1	yes	characteristic
91	C₄×C₅	#444	1	1	yes	characteristic
92	C₄×C₅	C₂×M₃₂	1	1	yes	characteristic
93	C₄×C₅	#504	1	1	yes	characteristic
94	C₂×Q₈	C₂×C₅×C₈	1	2	yes	—
95	Q₁₆	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
99	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
100	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
101	C₂×C₈	C₅×#41	1	1	yes	characteristic
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
104	C₄²	—	2	2	no	—
105	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
106	C₁₆	—	2	2	no	—
107	C₁₆	—	4	1	no	—
108	C₁₆	—	4	2	no	—
109	C₂×C₅	#1579	1	1	yes	characteristic
110	C₂×C₅	#2169	1	1	yes	characteristic
111	C₂×C₅	#2171	1	1	yes	characteristic
112	Q₈	—	2	2	no	—
113	Q₈	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
117	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
118	C₂×C₄	C₅×#131	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	—	2	1	no	—
121	C₈	—	4	1	no	—
122	C₈	—	4	2	no	—
123	C₈	C₅×M₃₂	1	2	yes	—
124	C₈	C₅×#137	1	2	yes	—
125	C₅	#12061	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	4	2	no	—
129	C₄	—	4	2	no	—
130	C₄	C₅×#441	1	1	yes	characteristic
131	C₄	C₅×#444	1	1	yes	characteristic
132	C₄	C₂×C₅×M₃₂	1	1	yes	characteristic
133	C₄	C₅×#504	1	1	yes	characteristic
134	C₂	C₅×#1579	1	1	yes	characteristic
135	C₂	C₅×#2169	1	1	yes	characteristic
136	C₂	C₅×#2171	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2183

C₂

yes

maximal

C₅×C₈×Q₁₆

C₂

yes

maximal, characteristic

C₅×#1367

C₂

yes

maximal, characteristic

C₅×Q₈⋊C₁₆

C₂

yes

maximal

C₅×#1312

C₂

yes

maximal, characteristic

C₅×C₈×Q₈

C₂²

yes

—

C₄×C₅×Q₁₆

C₄

yes

characteristic

C₅×C₄⋊C₁₆

—

C₅×C₄⋊C₁₆

C₂²

yes

—

C₅×#346

—

C₄×C₅×C₁₆

C₂²

yes

characteristic

C₄×C₅×C₁₆

C₂²

yes

characteristic

C₅×#335

C₄

yes

characteristic

C₅×Q₈⋊C₈

C₄

yes

—

C₅×C₈²

C₂²

yes

characteristic

#12061

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×Q₁₆

C₈

yes

characteristic

C₄×C₅×Q₈

C₂×C₄

yes

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

D₄

yes

—

C₅×#107

C₈

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

C₂×C₄

yes

—

C₅×#103

C₈

yes

—

C₄×C₅×C₈

—

C₄×C₅×C₈

C₂×C₄

yes

characteristic

C₄×C₅×C₈

C₂×C₄

yes

characteristic

C₄×C₅×C₈

C₂³

yes

characteristic

#2183

C₂×C₅

yes

—

C₈×Q₁₆

C₂×C₅

yes

characteristic

#1367

C₂×C₅

yes

characteristic

Q₈⋊C₁₆

C₂×C₅

yes

—

#1312

C₂×C₅

yes

characteristic

C₂×C₅×Q₈

C₂×C₈

yes

—

C₅×Q₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂×C₈

yes

characteristic

C₂×C₅×C₈

C₂×C₈

yes

characteristic

C₂×C₅×C₈

C₂×D₄

yes

characteristic

C₂×C₅×C₈

#41

yes

characteristic

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

C₂×C₈

yes

—

C₄²×C₅

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₅×C₁₆

—

C₅×C₁₆

—

C₅×C₁₆

—

C₈×Q₈

C₂²×C₅

yes

—

C₄×Q₁₆

C₄×C₅

yes

characteristic

C₄⋊C₁₆

—

C₄⋊C₁₆

C₂²×C₅

yes

—

#346

—

C₄×C₁₆

C₂²×C₅

yes

characteristic

C₄×C₁₆

C₂²×C₅

yes

characteristic

#335

C₄×C₅

yes

characteristic

Q₈⋊C₈

C₄×C₅

yes

—

C₈²

C₂²×C₅

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄×D₄

yes

characteristic

C₂×C₄×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

#131

yes

characteristic

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

M₃₂

yes

—

C₅×C₈

#137

yes

—

C₂×Q₁₆

C₅×C₈

yes

characteristic

C₄×Q₈

C₂×C₄×C₅

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₅×D₄

yes

—

#107

C₅×C₈

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂×C₄×C₅

yes

—

#103

C₅×C₈

yes

—

C₄×C₈

—

C₄×C₈

C₂×C₄×C₅

yes

characteristic

C₄×C₈

C₂×C₄×C₅

yes

characteristic

C₄×C₈

C₂³×C₅

yes

characteristic

C₂²×C₅

C₈×D₄

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

C₂×M₃₂

yes

characteristic

C₄×C₅

#504

yes

characteristic

C₂×Q₈

C₂×C₅×C₈

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₅×C₈

yes

characteristic

C₂×C₈

C₂×C₅×C₈

yes

characteristic

100

C₂×C₈

C₂×C₅×D₄

yes

characteristic

101

C₂×C₈

C₅×#41

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

C₂×C₅×C₈

yes

—

104

C₄²

—

105

C₄²

C₂²×C₄×C₅

yes

characteristic

106

C₁₆

—

107

C₁₆

—

108

C₁₆

—

109

C₂×C₅

#1579

yes

characteristic

110

C₂×C₅

#2169

yes

characteristic

111

C₂×C₅

#2171

yes

characteristic

112

Q₈

—

113

Q₈

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₄×C₅×D₄

yes

characteristic

117

C₂×C₄

C₂²×C₅×C₈

yes

characteristic

118

C₂×C₄

C₅×#131

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₈

C₅×M₃₂

yes

—

124

C₈

C₅×#137

yes

—

125

C₅

#12061

yes

characteristic, direct product factor, Sylow

126

C₂²

C₅×C₈×D₄

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

C₅×#441

yes

characteristic

131

C₄

C₅×#444

yes

characteristic

132

C₄

C₂×C₅×M₃₂

yes

characteristic

133

C₄

C₅×#504

yes

characteristic

134

C₂

C₅×#1579

yes

characteristic

135

C₂

C₅×#2169

yes

characteristic

136

C₂

C₅×#2171

yes

characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₂×C₄	C₂²×C₅×C₈
Frattini, cosocle	C₄×C₈	C₂³×C₅
socle, prime radical	C₂²×C₅	C₈×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₄×C₅×C₁₆ ◁ G

subgroup

G/H

center

C₂×C₅×C₈

C₂×D₄

commutator

C₂×C₄

C₂²×C₅×C₈

Frattini, cosocle

C₄×C₈

C₂³×C₅

socle, prime radical

C₂²×C₅

C₈×D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₅×C₈ ◁ C₄×C₅×C₁₆ ◁ G

N	H ≅ G/N	type
16. #12061	C₅	direct (N × H)
125. C₅	#12061	direct (N × H)

H ≅ G/N

type

16. #12061

C₅

direct (N × H)

125. C₅

#12061

direct (N × H)

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

subgroup	index
C₅×#2183	2
C₅×C₈×Q₁₆	2
C₅×#1367	2
C₅×Q₈⋊C₁₆	2
C₅×#1312	2
#12061	5

subgroup

index

C₅×C₈×Q₁₆

C₅×Q₈⋊C₁₆

Subgroups — C₅×#12061 #11934781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#12061 #11934781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12061 #11934781