Group #13013449 — subgroups

Subgroups — #13013449

Order 1280.

206 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 62 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	#10602534	C₂	1	1	yes	maximal, characteristic
2	#10598699	C₂	1	2	yes	maximal
3	C₂×C₅×#125	C₄	1	1	yes	characteristic
4	C₂×#3998	—	2	2	no	—
5	#65224	C₄	1	1	yes	characteristic
6	C₂×#3935	C₂²	1	1	yes	characteristic
7	#64749	—	2	2	no	—
8	#7130	—	5	1	no	maximal, Sylow
9	C₅×#125	—	2	1	no	—
10	C₅×#125	—	4	1	no	—
11	C₅×#125	C₈	1	2	yes	—
12	C₂×C₅×C₄⋊C₄	—	2	1	no	—
13	C₂×C₅×C₄⋊C₄	—	4	1	no	—
14	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₅	—	2	1	no	—
16	C₂×C₄⋊Dic₅	—	4	1	no	—
17	C₂²×#168	D₄	1	2	yes	—
18	#3998	—	4	2	no	—
19	#3998	—	4	2	no	—
20	C₂×#674	—	2	4	no	—
21	#3935	—	4	1	no	—
22	#1992	—	5	1	no	—
23	#1375	—	5	2	no	—
24	C₂²×C₄×C₅	—	2	1	no	—
25	C₂²×C₄×C₅	—	4	1	no	—
26	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×Dic₅	—	4	1	no	—
28	C₅×C₄⋊C₄	—	2	2	no	—
29	C₅×C₄⋊C₄	—	4	2	no	—
30	C₅×C₄⋊C₄	—	4	2	no	—
31	C₅×C₄⋊C₄	—	4	1	no	—
32	C₄²×C₅	—	2	1	no	—
33	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
34	C₄²×C₅	M₁₆	1	1	yes	characteristic
35	C₄⋊Dic₅	—	4	2	no	—
36	C₄⋊Dic₅	—	8	2	no	—
37	C₂×#168	—	2	2	no	—
38	C₂×#168	—	2	2	no	—
39	C₂×#168	SD₁₆	1	2	yes	—
40	C₂×#168	Q₁₆	1	2	yes	—
41	#674	—	4	4	no	—
42	C₂×#125	AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₂×M₃₂	—	10	2	no	—
44	C₂×#97	—	5	1	no	—
45	#384	—	5	1	no	—
46	#340	—	10	2	no	—
47	C₂³×C₅	#100	1	1	yes	characteristic
48	C₂×C₄×C₅	—	2	1	no	—
49	C₂×C₄×C₅	—	2	1	no	—
50	C₂×C₄×C₅	—	4	1	no	—
51	C₂×C₄×C₅	—	4	1	no	—
52	C₂×C₄×C₅	—	4	2	no	—
53	C₂×C₄×C₅	—	8	1	no	—
54	C₂×C₄×C₅	—	8	1	no	—
55	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₅	#99	1	1	yes	characteristic
57	C₂×C₄×C₅	#103	1	2	yes	—
58	C₂×C₄×C₅	#104	1	2	yes	—
59	C₂×Dic₅	—	8	2	no	—
60	C₂×Dic₅	—	8	1	no	—
61	#168	—	2	2	no	—
62	#168	—	2	2	no	—
63	C₂²×C₈	—	5	2	no	—
64	#125	—	2	1	no	—
65	#125	—	4	1	no	—
66	#125	#170	1	2	yes	—
67	C₂×C₄⋊C₄	—	2	1	no	—
68	C₂×C₄⋊C₄	—	4	1	no	—
69	C₂×C₄⋊C₄	—	10	1	no	—
70	C₂×C₄⋊C₄	—	20	1	no	—
71	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
72	M₃₂	—	20	2	no	—
73	M₃₂	—	20	2	no	—
74	C₂×C₁₆	—	10	4	no	—
75	#97	—	20	1	no	—
76	C₂²×C₅	—	2	1	no	—
77	C₂²×C₅	—	2	1	no	—
78	C₂²×C₅	#323	1	1	yes	characteristic
79	C₂²×C₅	#329	1	1	yes	characteristic
80	C₂²×C₅	#333	1	1	yes	characteristic
81	C₄×C₅	—	4	1	no	—
82	C₄×C₅	—	4	1	no	—
83	C₄×C₅	—	8	2	no	—
84	C₄×C₅	Q₈⋊C₈	1	2	yes	—
85	C₄×C₅	#328	1	2	yes	—
86	Dic₅	—	16	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	4	1	no	—
89	C₂²×C₄	—	20	1	no	—
90	C₂²×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
91	C₂×C₈	—	5	2	no	—
92	C₂×C₈	—	5	2	no	—
93	C₂×C₈	—	10	2	no	—
94	C₂×C₈	—	10	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	4	2	no	—
97	C₄⋊C₄	—	4	2	no	—
98	C₄⋊C₄	—	4	1	no	—
99	C₄⋊C₄	—	20	2	no	—
100	C₄⋊C₄	—	40	2	no	—
101	C₄²	—	2	1	no	—
102	C₄²	C₂×#170	1	1	yes	characteristic
103	C₄²	#704	1	1	yes	characteristic
104	C₁₆	—	20	4	no	—
105	C₂×C₅	—	2	1	no	—
106	C₂×C₅	—	2	1	no	—
107	C₂×C₅	#1272	1	1	yes	characteristic
108	C₂×C₅	#1355	1	1	yes	characteristic
109	C₂×C₅	#1356	1	1	yes	characteristic
110	C₂³	#4013	1	1	yes	characteristic
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	8	1	no	—
117	C₂×C₄	—	8	1	no	—
118	C₂×C₄	—	40	2	no	—
119	C₂×C₄	—	40	1	no	—
120	C₂×C₄	#4009	1	2	yes	—
121	C₂×C₄	#4010	1	2	yes	—
122	C₂×C₄	#4011	1	1	yes	characteristic
123	C₂×C₄	C₂²⋊#170	1	1	yes	characteristic
124	C₈	—	10	2	no	—
125	C₈	—	10	2	no	—
126	C₅	#7130	1	1	yes	characteristic, complemented, Sylow
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	#64927	1	1	yes	characteristic
130	C₂²	#64931	1	1	yes	characteristic
131	C₂²	#64933	1	1	yes	characteristic
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	8	2	no	—
135	C₄	—	80	1	no	—
136	C₄	#64926	1	2	yes	—
137	C₄	Q₈⋊#170	1	2	yes	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	#10598735	1	1	yes	characteristic
141	C₂	#10598736	1	1	yes	characteristic
142	C₂	#10598828	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10602534

C₂

yes

maximal, characteristic

#10598699

C₂

yes

maximal

C₂×C₅×#125

C₄

yes

characteristic

C₂×#3998

—

#65224

C₄

yes

characteristic

C₂×#3935

C₂²

yes

—

—

—

—

C₈

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₅

—

C₂×C₄⋊Dic₅

—

C₂²×#168

D₄

yes

—

—

—

—

—

—

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

characteristic

C₂²×Dic₅

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

—

C₄²×C₅

C₂×C₈

yes

characteristic

C₄²×C₅

M₁₆

yes

characteristic

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₂×#168

—

C₂×#168

—

C₂×#168

SD₁₆

yes

—

C₂×#168

Q₁₆

yes

—

—

yes

C₂×M₃₂

—

C₂×#97

—

#384

—

#340

—

C₂³×C₅

#100

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

C₂²⋊C₈

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

#104

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

#168

—

#168

—

C₂²×C₈

—

—

—

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#97

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

Q₈⋊C₈

yes

—

C₄×C₅

#328

yes

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊AGL(1,𝔽₅)

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

—

102

C₄²

C₂×#170

yes

characteristic

103

C₄²

#704

yes

characteristic

104

C₁₆

—

105

C₂×C₅

—

106

C₂×C₅

—

107

C₂×C₅

#1272

yes

characteristic

108

C₂×C₅

#1355

yes

characteristic

109

C₂×C₅

#1356

yes

characteristic

110

C₂³

#4013

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

#4009

yes

—

121

C₂×C₄

#4010

yes

—

122

C₂×C₄

#4011

yes

characteristic

123

C₂×C₄

C₂²⋊#170

yes

characteristic

124

C₈

—

125

C₈

—

126

C₅

#7130

yes

characteristic, complemented, Sylow

127

C₂²

—

128

C₂²

—

129

C₂²

#64927

yes

characteristic

130

C₂²

#64931

yes

characteristic

131

C₂²

#64933

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#64926

yes

—

137

C₄

Q₈⋊#170

yes

—

138

C₂

—

139

C₂

—

140

C₂

#10598735

yes

characteristic

141

C₂

#10598736

yes

characteristic

142

C₂

#10598828

yes

characteristic

	subgroup	G/H
center	C₂²	#64927
commutator	C₄²×C₅	C₂×C₈
Frattini	C₂×C₄²	C₂×AGL(1,𝔽₅)
Fitting	C₂×C₅×#125	C₄
socle	C₂²×C₅	#329
prime radical	C₂³×C₅	#100
cosocle	C₂×#3935	C₂²
hypercenter	C₂×#125	AGL(1,𝔽₅)
hypocenter	C₅	#7130
LCS	G ▷ C₄²×C₅ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

#64927

commutator

C₄²×C₅

C₂×C₈

Frattini

C₂×C₄²

C₂×AGL(1,𝔽₅)

Fitting

C₂×C₅×#125

C₄

C₂²×C₅

C₂³×C₅

C₂²

C₅

G ▷ C₄²×C₅ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
126. C₅	#7130	semidirect

H ≅ G/N

type

126. C₅

#7130

semidirect

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

subgroup	index
#10602534	2
#10598699	2
#7130	5

subgroup

index

#10602534

#10598699

#7130

Subgroups — #13013449

Conjugacy classes of subgroups

Complements

Maximal subgroups