Group #11989753 — subgroups

Subgroups — #11989753

Order 1280.

330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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×#1726	C₂	1	1	yes	maximal, characteristic
2	#10600519	C₂	1	2	yes	maximal
3	#10598151	C₂	1	2	yes	maximal
4	#10598105	C₂	1	2	yes	maximal
5	C₂×C₅×#97	C₄	1	2	yes	—
6	C₂×C₅×#97	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₅×#376	C₂²	1	1	yes	characteristic
10	#65214	C₂²	1	4	yes	—
11	#64674	C₄	1	8	yes	complemented
12	#8140	—	5	1	no	maximal, Sylow
13	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
18	C₅×#97	—	2	4	no	—
19	C₅×#97	—	2	2	no	—
20	C₄×C₅×C₈	—	2	4	no	—
21	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
22	C₅×#95	—	2	2	no	—
23	C₂²⋊#168	—	2	4	no	—
24	C₄⋊#168	—	2	4	no	—
25	C₄×#168	C₂×C₄	1	8	yes	—
26	#1726	D₅	1	1	yes	characteristic
27	#1452	—	5	2	no	—
28	#1275	—	5	2	no	—
29	#1274	—	5	2	no	—
30	C₂²×C₄×C₅	—	2	2	no	—
31	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₅	#41	1	2	yes	—
33	C₂×C₅×C₈	—	2	2	no	—
34	C₂×C₅×C₈	—	2	2	no	—
35	C₂×C₅×C₈	—	2	2	no	—
36	C₂×C₅×C₈	—	2	2	no	—
37	C₂×C₅×C₈	C₄²	1	2	yes	—
38	C₂×C₅×C₈	C₄²	1	2	yes	—
39	C₂×C₅×C₈	M₁₆	1	4	yes	—
40	C₄²×C₅	—	2	2	no	—
41	C₄²×C₅	M₁₆	1	4	yes	—
42	C₄²×C₅	C₂²×C₄	1	2	yes	—
43	C₄²×C₅	#41	1	2	yes	—
44	C₂×#168	—	2	8	no	—
45	#431	—	5	4	no	—
46	C₂×#97	Dic₅	1	2	yes	—
47	C₂×#97	C₂×D₅	1	1	yes	characteristic
48	C₂×C₄×C₈	Dic₅	1	2	yes	—
49	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
50	#376	C₂×D₅	1	1	yes	characteristic
51	#322	—	5	8	no	—
52	C₂³×C₅	#117	1	1	yes	characteristic
53	C₂×C₄×C₅	—	2	4	no	—
54	C₂×C₄×C₅	—	4	2	no	—
55	C₂×C₄×C₅	—	4	4	no	—
56	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₅	#117	1	4	yes	—
58	C₂×C₄×C₅	#117	1	1	yes	characteristic
59	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
60	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
61	C₅×C₈	—	2	2	no	—
62	C₅×C₈	—	2	2	no	—
63	C₅×C₈	—	2	4	no	—
64	#168	—	4	8	no	—
65	C₂²×C₈	C₂×Dic₅	1	2	yes	—
66	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
67	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
68	C₂×C₄²	C₂×Dic₅	1	2	yes	—
69	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
70	C₄⋊C₈	—	10	4	no	—
71	C₂²⋊C₈	—	10	4	no	—
72	#97	—	2	4	no	—
73	#97	—	2	2	no	—
74	C₄×C₈	—	2	4	no	—
75	C₄×C₈	—	5	8	no	—
76	C₄×C₈	C₄×D₅	1	4	yes	—
77	#95	—	2	2	no	—
78	C₂²×C₅	—	2	2	no	—
79	C₂²×C₅	#376	1	1	yes	characteristic
80	C₂²×C₅	#432	1	2	yes	—
81	C₄×C₅	—	2	4	no	—
82	C₄×C₅	—	4	4	no	—
83	C₄×C₅	C₄×M₁₆	1	1	yes	characteristic
84	C₄×C₅	C₄×M₁₆	1	1	yes	characteristic
85	C₄×C₅	#432	1	2	yes	—
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	#709	1	2	yes	—
88	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	10	8	no	—
94	C₂×C₈	#681	1	4	yes	—
95	C₂×C₈	C₄×Dic₅	1	2	yes	—
96	C₂×C₈	C₄×Dic₅	1	2	yes	—
97	C₄²	—	2	2	no	—
98	C₄²	#681	1	4	yes	—
99	C₄²	C₂×C₄×D₅	1	2	yes	—
100	C₄²	#709	1	2	yes	—
101	C₂×C₅	—	2	2	no	—
102	C₂×C₅	#1745	1	1	yes	characteristic
103	C₂×C₅	#1747	1	2	yes	—
104	C₂³	#4072	1	1	yes	characteristic
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	4	4	no	—
108	C₂×C₄	#4018	1	4	yes	—
109	C₂×C₄	C₂×#681	1	2	yes	—
110	C₂×C₄	C₂×#681	1	2	yes	—
111	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
112	C₂×C₄	#4072	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	2	2	no	—
115	C₈	—	2	4	no	—
116	C₈	—	20	8	no	—
117	C₅	#8140	1	1	yes	characteristic, complemented, Sylow
118	C₂²	—	2	2	no	—
119	C₂²	#65215	1	2	yes	—
120	C₂²	#65221	1	1	yes	characteristic
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₄×#681	1	1	yes	characteristic
124	C₄	C₄×#681	1	1	yes	characteristic
125	C₄	#65215	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	#10600182	1	1	yes	characteristic
128	C₂	#10600688	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1726

C₂

yes

maximal, characteristic

#10600519

C₂

yes

maximal

#10598151

C₂

yes

maximal

#10598105

C₂

yes

maximal

C₂×C₅×#97

C₄

yes

—

C₂×C₅×#97

C₂²

yes

characteristic

C₂×C₄×C₅×C₈

C₄

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#376

C₂²

yes

characteristic

#65214

C₂²

yes

—

#64674

C₄

yes

complemented

#8140

—

maximal, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×#97

—

C₅×#97

—

C₄×C₅×C₈

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₅×#95

—

C₂²⋊#168

—

C₄⋊#168

—

C₄×#168

C₂×C₄

yes

—

#1726

D₅

yes

—

—

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

#41

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄²

yes

—

C₂×C₅×C₈

C₄²

yes

—

C₂×C₅×C₈

M₁₆

yes

—

C₄²×C₅

—

C₄²×C₅

M₁₆

yes

—

C₄²×C₅

C₂²×C₄

yes

—

C₄²×C₅

#41

yes

—

C₂×#168

—

#431

—

C₂×#97

Dic₅

yes

—

C₂×#97

C₂×D₅

yes

characteristic

C₂×C₄×C₈

Dic₅

yes

—

C₂×C₄×C₈

C₂×D₅

yes

characteristic

#376

C₂×D₅

yes

characteristic

#322

—

C₂³×C₅

#117

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₄²

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#117

yes

characteristic

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

#168

—

C₂²×C₈

C₂×Dic₅

yes

—

C₂²×C₈

C₂×Dic₅

yes

characteristic

C₂²×C₈

C₂×Dic₅

yes

characteristic

C₂×C₄²

C₂×Dic₅

yes

—

C₂×C₄²

C₂²×D₅

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₅

yes

—

#95

—

C₂²×C₅

—

C₂²×C₅

#376

yes

characteristic

C₂²×C₅

#432

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₄×M₁₆

yes

characteristic

C₄×C₅

C₄×M₁₆

yes

characteristic

C₄×C₅

#432

yes

—

C₂²×C₄

—

C₂²×C₄

#709

yes

—

C₂²×C₄

C₂²×Dic₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#681

yes

—

C₂×C₈

C₄×Dic₅

yes

—

C₂×C₈

C₄×Dic₅

yes

—

C₄²

—

C₄²

#681

yes

—

C₄²

C₂×C₄×D₅

yes

—

100

C₄²

#709

yes

—

101

C₂×C₅

—

102

C₂×C₅

#1745

yes

characteristic

103

C₂×C₅

#1747

yes

—

104

C₂³

#4072

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

#4018

yes

—

109

C₂×C₄

C₂×#681

yes

—

110

C₂×C₄

C₂×#681

yes

—

111

C₂×C₄

C₂×C₄×Dic₅

yes

characteristic

112

C₂×C₄

#4072

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₅

#8140

yes

characteristic, complemented, Sylow

118

C₂²

—

119

C₂²

#65215

yes

—

120

C₂²

#65221

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

C₄×#681

yes

characteristic

124

C₄

C₄×#681

yes

characteristic

125

C₄

#65215

yes

—

126

C₂

—

127

C₂

#10600182

yes

characteristic

128

C₂

#10600688

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₅
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₅×#1726	C₂
socle	C₂²×C₅	#376
prime radical	C₂³×C₅	#117
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1726	D₅
hypocenter	C₅	#8140
LCS	G ▷ C₂×C₄×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #1726

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₅

commutator

C₂×C₄×C₅

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₅

C₂

C₂²×C₅

C₂³×C₅

C₂×C₄²×C₅

C₂³

D₅

C₅

G ▷ C₂×C₄×C₅ ▷ C₅

C₁ ◁ C₂×C₄ ◁ #1726

N	H ≅ G/N	type
11. #64674	C₄	semidirect
117. C₅	#8140	semidirect

H ≅ G/N

type

11. #64674

C₄

semidirect

117. C₅

#8140

semidirect

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

subgroup	index
C₅×#1726	2
#10600519	2
#10598151	2
#10598105	2
#8140	5

subgroup

index

Subgroups — #11989753

Conjugacy classes of subgroups

Complements

Maximal subgroups