Group #11988690 — subgroups

Subgroups — #11988690

Order 1280.

610 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 207 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×#64974	C₂	1	3	yes	maximal
2	C₅×#1273	C₂	1	1	yes	maximal, characteristic, complemented
3	#10598144	C₂	1	3	yes	maximal, complemented
4	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
6	C₂×#3952	C₄	1	6	yes	—
7	C₂×#3946	C₄	1	6	yes	—
8	C₂×C₄×#168	C₂²	1	3	yes	—
9	#64974	—	2	12	no	—
10	#7851	—	5	1	no	maximal, Sylow
11	C₂²×C₄×D₅	C₂×C₄	1	3	yes	—
12	C₂²×C₅×C₈	C₂×C₄	1	6	yes	—
13	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
14	C₂×C₄×Dic₅	C₂×C₄	1	3	yes	—
15	C₂²×#168	C₂×C₄	1	6	yes	—
16	C₄²×D₅	D₄	1	6	yes	—
17	C₄²×D₅	Q₈	1	2	yes	—
18	C₄×C₅×C₈	—	2	6	no	—
19	#3952	—	2	12	no	—
20	#3946	—	2	12	no	—
21	C₄×#168	—	2	6	no	—
22	C₂×#431	—	5	3	no	—
23	#1273	—	5	3	no	—
24	#1273	D₅	1	1	yes	characteristic, complemented
25	C₂³×D₅	C₄²	1	1	yes	characteristic
26	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
27	C₂²×Dic₅	C₄²	1	3	yes	—
28	C₂×C₄×D₅	—	2	6	no	—
29	C₂×C₄×D₅	—	2	6	no	—
30	C₂×C₄×D₅	C₂²⋊C₄	1	6	yes	—
31	C₂×C₄×D₅	C₄⋊C₄	1	6	yes	—
32	C₂×C₅×C₈	—	2	6	no	—
33	C₂×C₅×C₈	—	2	6	no	—
34	C₂×C₅×C₈	—	2	6	no	—
35	C₄²×C₅	C₂×D₄	1	3	yes	—
36	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
37	C₄×Dic₅	C₂²⋊C₄	1	6	yes	—
38	C₄×Dic₅	C₄⋊C₄	1	6	yes	—
39	C₂×#168	—	2	6	no	—
40	C₂×#168	—	2	6	no	—
41	C₂×#168	—	2	6	no	—
42	C₂²×C₄²	—	5	1	no	—
43	#431	—	10	12	no	—
44	C₂×C₄⋊C₈	—	5	6	no	—
45	C₂×C₂²⋊C₈	—	5	6	no	—
46	C₂×C₄×C₈	—	5	3	no	—
47	C₂×C₄×C₈	C₂×D₅	1	3	yes	—
48	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
49	C₂²×D₅	—	2	3	no	—
50	C₂²×D₅	—	2	3	no	—
51	C₂²×D₅	#95	1	2	yes	—
52	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
53	C₂×C₄×C₅	C₂×C₄⋊C₄	1	3	yes	—
54	C₂×C₄×C₅	#131	1	6	yes	—
55	C₂×C₄×C₅	#131	1	6	yes	—
56	C₂×Dic₅	—	2	3	no	—
57	C₂×Dic₅	—	2	3	no	—
58	C₂×Dic₅	#95	1	6	yes	—
59	C₄×D₅	—	2	12	no	—
60	C₄×D₅	—	2	12	no	—
61	C₅×C₈	—	4	6	no	—
62	#168	—	4	6	no	—
63	C₂³×C₄	—	5	3	no	—
64	C₂²×C₈	—	5	6	no	—
65	C₂²×C₈	C₄×D₅	1	6	yes	—
66	C₂×C₄²	—	5	3	no	—
67	C₂×C₄²	—	5	6	no	—
68	C₂×C₄²	—	5	2	no	—
69	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
70	C₄⋊C₈	—	10	12	no	—
71	C₂²⋊C₈	—	10	12	no	—
72	C₄×C₈	—	2	6	no	—
73	C₄×C₈	—	10	6	no	—
74	C₂²×C₅	C₂×#95	1	1	yes	characteristic
75	C₂²×C₅	#405	1	3	yes	—
76	C₂²×C₅	#405	1	3	yes	—
77	C₂×D₅	—	2	6	no	—
78	C₂×D₅	—	4	1	no	—
79	C₂×D₅	—	4	3	no	—
80	C₄×C₅	#408	1	6	yes	—
81	C₄×C₅	#424	1	6	yes	—
82	Dic₅	—	2	6	no	—
83	C₂⁴	—	5	1	no	—
84	C₂²×C₄	—	5	3	no	—
85	C₂²×C₄	—	5	6	no	—
86	C₂²×C₄	—	5	6	no	—
87	C₂²×C₄	—	10	6	no	—
88	C₂²×C₄	—	10	6	no	—
89	C₂²×C₄	C₂×C₄×D₅	1	3	yes	—
90	C₂×C₈	—	2	6	no	—
91	C₂×C₈	—	2	6	no	—
92	C₂×C₈	—	2	6	no	—
93	C₂×C₈	—	10	6	no	—
94	C₂×C₈	—	10	6	no	—
95	C₂×C₈	—	10	6	no	—
96	C₄²	—	5	6	no	—
97	C₄²	—	5	6	no	—
98	C₄²	D₄×D₅	1	3	yes	—
99	C₄²	Q₈×D₅	1	1	yes	characteristic
100	C₂×C₅	#1454	1	1	yes	characteristic
101	C₂×C₅	#1454	1	3	yes	—
102	C₂×C₅	#1729	1	3	yes	—
103	D₅	—	4	2	no	—
104	C₂³	—	5	2	no	—
105	C₂³	—	10	3	no	—
106	C₂³	—	10	3	no	—
107	C₂³	C₄²×D₅	1	1	yes	characteristic
108	C₂×C₄	—	5	6	no	—
109	C₂×C₄	—	10	3	no	—
110	C₂×C₄	—	10	3	no	—
111	C₂×C₄	—	10	12	no	—
112	C₂×C₄	—	10	12	no	—
113	C₂×C₄	D₅×C₂²⋊C₄	1	3	yes	—
114	C₂×C₄	D₅×C₄⋊C₄	1	3	yes	—
115	C₂×C₄	#4047	1	6	yes	—
116	C₂×C₄	#4053	1	6	yes	—
117	C₈	—	4	6	no	—
118	C₈	—	20	6	no	—
119	C₅	#7851	1	1	yes	characteristic, complemented, Sylow
120	C₂²	—	10	6	no	—
121	C₂²	—	20	1	no	—
122	C₂²	—	20	3	no	—
123	C₂²	D₅×#95	1	1	yes	characteristic
124	C₂²	#64978	1	3	yes	—
125	C₂²	#64997	1	3	yes	—
126	C₄	—	10	6	no	—
127	C₄	#65016	1	6	yes	—
128	C₄	#65128	1	6	yes	—
129	C₂	—	20	2	no	—
130	C₂	#10598842	1	1	yes	characteristic
131	C₂	#10598867	1	3	yes	—
132	C₂	#10599454	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#64974

C₂

yes

maximal

C₅×#1273

C₂

yes

maximal, characteristic, complemented

#10598144

C₂

yes

maximal, complemented

C₂×C₄²×D₅

C₂²

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×#3952

C₄

yes

—

C₂×#3946

C₄

yes

—

C₂×C₄×#168

C₂²

yes

—

#64974

—

#7851

—

maximal, Sylow

C₂²×C₄×D₅

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₂×C₄×Dic₅

C₂×C₄

yes

—

C₂²×#168

C₂×C₄

yes

—

C₄²×D₅

D₄

yes

—

C₄²×D₅

Q₈

yes

—

C₄×C₅×C₈

—

—

—

—

—

—

D₅

yes

characteristic, complemented

C₂³×D₅

C₄²

yes

characteristic

C₂²×C₄×C₅

C₂²×C₄

yes

—

C₂²×Dic₅

C₄²

yes

—

C₂×C₄×D₅

—

C₂×C₄×D₅

—

C₂×C₄×D₅

C₂²⋊C₄

yes

—

C₂×C₄×D₅

C₄⋊C₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄×Dic₅

C₂²⋊C₄

yes

—

C₄×Dic₅

C₄⋊C₄

yes

—

C₂×#168

—

C₂×#168

—

C₂×#168

—

C₂²×C₄²

—

#431

—

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₅

yes

—

C₂³×C₅

C₂×C₄²

yes

characteristic

C₂²×D₅

—

C₂²×D₅

—

C₂²×D₅

#95

yes

—

C₂×C₄×C₅

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

#131

yes

—

C₂×C₄×C₅

#131

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

#95

yes

—

C₄×D₅

—

C₄×D₅

—

C₅×C₈

—

#168

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₄×D₅

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₅

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₅

C₂×#95

yes

characteristic

C₂²×C₅

#405

yes

—

C₂²×C₅

#405

yes

—

C₂×D₅

—

C₂×D₅

—

C₂×D₅

—

C₄×C₅

#408

yes

—

C₄×C₅

#424

yes

—

Dic₅

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₅

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

D₄×D₅

yes

—

C₄²

Q₈×D₅

yes

characteristic

100

C₂×C₅

#1454

yes

characteristic

101

C₂×C₅

#1454

yes

—

102

C₂×C₅

#1729

yes

—

103

D₅

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₄²×D₅

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

D₅×C₂²⋊C₄

yes

—

114

C₂×C₄

D₅×C₄⋊C₄

yes

—

115

C₂×C₄

#4047

yes

—

116

C₂×C₄

#4053

yes

—

117

C₈

—

118

C₈

—

119

C₅

#7851

yes

characteristic, complemented, Sylow

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

D₅×#95

yes

characteristic

124

C₂²

#64978

yes

—

125

C₂²

#64997

yes

—

126

C₄

—

127

C₄

#65016

yes

—

128

C₄

#65128

yes

—

129

C₂

—

130

C₂

#10598842

yes

characteristic

131

C₂

#10598867

yes

—

132

C₂

#10599454

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₅
commutator, socle	C₂³×C₅	C₂×C₄²
Fitting	C₅×#1273	C₂
prime radical	C₂³×D₅	C₄²
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1273	D₅
hypocenter	C₅	#7851
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₅

commutator, socle

C₂³×C₅

C₂×C₄²

Fitting

C₅×#1273

C₂

prime radical

C₂³×D₅

C₄²

cosocle

C₂×C₄²×C₅

C₂³

D₅

C₅

G ▷ C₂³×C₅ ▷ C₅

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. C₅×#1273	C₂	semidirect
3. #10598144	C₂	semidirect
24. #1273	D₅	semidirect
119. C₅	#7851	semidirect

H ≅ G/N

type

2. C₅×#1273

C₂

semidirect

3. #10598144

C₂

semidirect

24. #1273

D₅

semidirect

119. C₅

#7851

semidirect

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

subgroup	index
C₂×#64974	2
C₅×#1273	2
#10598144	2
#7851	5

subgroup

index

Subgroups — #11988690

Conjugacy classes of subgroups

Complements

Maximal subgroups