Group #13013907 — subgroups

Subgroups — #13013907

Order 1280.

208 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 78 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	C₂×#64861	C₂	1	2	yes	maximal
2	#10601311	C₂	1	1	yes	maximal, characteristic
3	C₂×#3998	—	2	2	no	—
4	C₅×#423	C₄	1	1	yes	characteristic
5	C₂×#3954	—	2	2	no	—
6	#65213	C₄	1	1	yes	characteristic
7	C₂×C₄×#168	C₂²	1	1	yes	characteristic
8	#64861	—	2	2	no	—
9	#64861	C₄	1	4	yes	—
10	#7273	—	5	1	no	maximal, Sylow
11	C₂×C₅×M₁₆	—	2	1	no	—
12	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×#681	—	2	1	no	—
14	C₂²×#168	D₄	1	2	yes	—
15	#3998	—	2	4	no	—
16	#3998	—	4	2	no	—
17	C₂×#674	—	4	2	no	—
18	C₅×C₄⋊C₈	—	4	1	no	—
19	#3954	—	4	2	no	—
20	#3954	—	4	2	no	—
21	C₄⋊#168	—	4	1	no	—
22	C₄×#168	C₂×C₄	1	2	yes	—
23	C₄×#168	D₄	1	1	yes	characteristic
24	C₄×#168	Q₈	1	1	yes	characteristic
25	C₂×#364	—	5	2	no	—
26	#1848	—	5	1	no	—
27	C₂²×C₄×C₅	—	2	1	no	—
28	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
29	C₅×M₁₆	—	4	2	no	—
30	C₂×C₅×C₈	—	4	1	no	—
31	C₄²×C₅	—	2	1	no	—
32	C₄²×C₅	C₄²	1	1	yes	characteristic
33	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
34	#681	—	4	2	no	—
35	C₂×#168	—	4	1	no	—
36	C₂×#168	C₂²⋊C₄	1	2	yes	—
37	C₂×#168	C₄⋊C₄	1	2	yes	—
38	C₂×#168	D₈	1	2	yes	—
39	C₂×#168	SD₁₆	1	2	yes	—
40	C₂×#168	SD₁₆	1	2	yes	—
41	C₂×#168	Q₁₆	1	2	yes	—
42	#674	—	4	4	no	—
43	C₂×M₃₂	—	10	2	no	—
44	C₂×#108	—	10	2	no	—
45	#423	—	5	1	no	—
46	#423	AGL(1,𝔽₅)	1	1	yes	characteristic
47	C₂×C₄×C₈	—	5	1	no	—
48	#364	—	5	4	no	—
49	#364	—	10	2	no	—
50	C₂³×C₅	#101	1	1	yes	characteristic
51	C₂×C₄×C₅	—	2	1	no	—
52	C₂×C₄×C₅	—	2	1	no	—
53	C₂×C₄×C₅	—	4	2	no	—
54	C₂×C₄×C₅	#95	1	1	yes	characteristic
55	C₂×C₄×C₅	#100	1	1	yes	characteristic
56	C₂×C₄×C₅	#102	1	2	yes	—
57	C₂×C₄×C₅	#103	1	2	yes	—
58	C₅×C₈	—	8	1	no	—
59	#168	—	8	1	no	—
60	#168	#102	1	2	yes	—
61	#168	#103	1	2	yes	—
62	#168	#106	1	2	yes	—
63	#168	#107	1	2	yes	—
64	C₂×M₁₆	—	2	1	no	—
65	C₂×M₁₆	—	10	1	no	—
66	C₂²×C₈	—	5	2	no	—
67	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
68	M₃₂	—	10	4	no	—
69	M₃₂	—	20	2	no	—
70	C₂×C₁₆	—	20	2	no	—
71	#108	—	20	2	no	—
72	#108	—	20	2	no	—
73	C₄⋊C₈	—	4	1	no	—
74	C₄⋊C₈	—	20	1	no	—
75	C₄×C₈	—	5	2	no	—
76	C₄×C₈	—	5	1	no	—
77	C₄×C₈	—	5	1	no	—
78	C₂²×C₅	—	4	1	no	—
79	C₂²×C₅	#332	1	2	yes	—
80	C₂²×C₅	#343	1	1	yes	characteristic
81	C₄×C₅	—	2	2	no	—
82	C₄×C₅	—	4	1	no	—
83	C₄×C₅	#331	1	1	yes	characteristic
84	C₄×C₅	#333	1	1	yes	characteristic
85	C₄×C₅	#340	1	2	yes	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
88	M₁₆	—	4	2	no	—
89	M₁₆	—	20	2	no	—
90	C₂×C₈	—	4	1	no	—
91	C₂×C₈	—	5	2	no	—
92	C₂×C₈	—	5	2	no	—
93	C₂×C₈	—	5	2	no	—
94	C₂×C₈	—	5	2	no	—
95	C₂×C₈	—	5	2	no	—
96	C₂×C₈	—	5	2	no	—
97	C₂×C₈	—	20	1	no	—
98	C₄²	—	2	1	no	—
99	C₄²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
100	C₄²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
101	C₁₆	—	20	4	no	—
102	C₂×C₅	—	2	1	no	—
103	C₂×C₅	—	2	2	no	—
104	C₂×C₅	#1296	1	1	yes	characteristic
105	C₂³	#4005	1	1	yes	characteristic
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
110	C₂×C₄	#4007	1	2	yes	—
111	C₂×C₄	#4009	1	2	yes	—
112	C₂×C₄	#4013	1	1	yes	characteristic
113	C₈	—	5	2	no	—
114	C₈	—	5	2	no	—
115	C₈	—	5	2	no	—
116	C₈	—	5	2	no	—
117	C₈	—	8	1	no	—
118	C₈	—	40	1	no	—
119	C₅	#7273	1	1	yes	characteristic, complemented, Sylow
120	C₂²	—	4	1	no	—
121	C₂²	#64873	1	2	yes	—
122	C₂²	#64919	1	1	yes	characteristic
123	C₄	—	2	2	no	—
124	C₄	—	4	1	no	—
125	C₄	#64874	1	2	yes	—
126	C₄	#64925	1	1	yes	characteristic
127	C₄	#64931	1	1	yes	characteristic
128	C₂	—	2	1	no	—
129	C₂	—	2	2	no	—
130	C₂	#10598725	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#64861

C₂

yes

maximal

#10601311

C₂

yes

maximal, characteristic

C₂×#3998

—

C₅×#423

C₄

yes

characteristic

C₂×#3954

—

#65213

C₄

yes

characteristic

C₂×C₄×#168

C₂²

yes

characteristic

#64861

—

#64861

C₄

yes

—

#7273

—

maximal, Sylow

C₂×C₅×M₁₆

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×#681

—

C₂²×#168

D₄

yes

—

#3998

—

#3998

—

C₂×#674

—

C₅×C₄⋊C₈

—

—

—

—

C₂×C₄

yes

—

C₄×#168

D₄

yes

characteristic

C₄×#168

Q₈

yes

characteristic

C₂×#364

—

#1848

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

characteristic

C₅×M₁₆

—

C₂×C₅×C₈

—

C₄²×C₅

—

C₄²×C₅

C₄²

yes

characteristic

C₄²×C₅

C₄⋊C₄

yes

—

—

C₂²⋊C₄

yes

—

C₂×#168

C₄⋊C₄

yes

—

C₂×#168

D₈

yes

—

C₂×#168

SD₁₆

yes

—

C₂×#168

SD₁₆

yes

—

C₂×#168

Q₁₆

yes

—

#674

—

C₂×M₃₂

—

—

—

yes

C₂×C₄×C₈

—

#364

—

#364

—

C₂³×C₅

#101

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

#103

yes

—

C₅×C₈

—

#168

—

#168

#102

yes

—

#168

#103

yes

—

#168

#106

yes

—

#168

#107

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

#332

yes

—

C₂²×C₅

#343

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊AGL(1,𝔽₅)

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

C₄×AGL(1,𝔽₅)

yes

characteristic

100

C₄²

C₄⋊AGL(1,𝔽₅)

yes

characteristic

101

C₁₆

—

102

C₂×C₅

—

103

C₂×C₅

—

104

C₂×C₅

#1296

yes

characteristic

105

C₂³

#4005

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

(C₂×AGL(1,𝔽₅))⋊C₄

yes

characteristic

110

C₂×C₄

#4007

yes

—

111

C₂×C₄

#4009

yes

—

112

C₂×C₄

#4013

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

—

119

C₅

#7273

yes

characteristic, complemented, Sylow

120

C₂²

—

121

C₂²

#64873

yes

—

122

C₂²

#64919

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

#64874

yes

—

126

C₄

#64925

yes

characteristic

127

C₄

#64931

yes

characteristic

128

C₂

—

129

C₂

—

130

C₂

#10598725

yes

characteristic

	subgroup	G/H
center	C₄	#64931
commutator	C₄²×C₅	C₄²
Frattini	C₂×C₄²	C₂×AGL(1,𝔽₅)
Fitting	C₅×#423	C₄
socle	C₂×C₅	#1296
prime radical	C₂³×C₅	#101
cosocle	C₂×C₄×#168	C₂²
hypercenter	#423	AGL(1,𝔽₅)
hypocenter	C₅	#7273
LCS	G ▷ C₄²×C₅ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₄

#64931

commutator

C₄²×C₅

C₄²

C₂×C₄²

C₄

C₂×C₅

C₂³×C₅

C₂×C₄×#168

C₂²

C₅

G ▷ C₄²×C₅ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
119. C₅	#7273	semidirect

H ≅ G/N

type

119. C₅

#7273

semidirect

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

subgroup	index
C₂×#64861	2
#10601311	2
#7273	5

subgroup

index

C₂×#64861

#10601311

#7273

Subgroups — #13013907

Conjugacy classes of subgroups

Complements

Maximal subgroups