Group #11993077 — subgroups

Subgroups — #11993077

Order 1280.

422 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 227 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×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
2	#10600558	C₂	1	2	yes	maximal
3	#10600555	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
5	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂×#3950	—	2	4	no	—
7	#65224	C₂²	1	4	yes	—
8	C₅×C₈²	C₄	1	4	yes	complemented
9	#64771	—	2	8	no	—
10	#8816	—	5	1	no	maximal, Sylow
11	C₂²×C₅×C₈	D₄	1	4	yes	—
12	C₂²×C₅×C₈	D₄	1	2	yes	—
13	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
14	C₂×C₄⋊Dic₅	—	2	8	no	—
15	C₂×C₄⋊Dic₅	—	2	4	no	—
16	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
17	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
18	C₄×C₅×C₈	Q₈	1	4	yes	—
19	C₄×C₅×C₈	Q₈	1	2	yes	—
20	#3950	—	4	8	no	—
21	#1845	—	5	2	no	—
22	#1834	—	5	4	no	—
23	C₂×C₈²	D₅	1	1	yes	characteristic
24	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
26	C₂²×Dic₅	—	4	4	no	—
27	C₂×C₅×C₈	—	2	8	no	—
28	C₂×C₅×C₈	C₄⋊C₄	1	8	yes	—
29	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
30	C₂×C₅×C₈	D₈	1	4	yes	—
31	C₂×C₅×C₈	Q₁₆	1	4	yes	—
32	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
34	C₄²×C₅	C₂×Q₈	1	2	yes	—
35	C₄⋊Dic₅	—	4	8	no	—
36	C₄⋊Dic₅	—	4	16	no	—
37	C₂×#107	—	10	4	no	—
38	C₂×C₄×C₈	C₂×D₅	1	2	yes	—
39	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
40	#384	—	5	4	no	—
41	#340	—	10	8	no	—
42	C₈²	Dic₅	1	4	yes	complemented
43	C₂³×C₅	#127	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
46	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
47	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
49	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
50	C₂×C₄×C₅	#135	1	8	yes	—
51	C₂×Dic₅	—	8	4	no	—
52	C₂×Dic₅	—	8	8	no	—
53	C₅×C₈	—	2	8	no	—
54	C₅×C₈	#107	1	8	yes	—
55	C₂²×C₈	D₂₀	1	4	yes	—
56	C₂²×C₈	D₂₀	1	2	yes	—
57	C₂×C₄⋊C₄	—	10	8	no	—
58	C₂×C₄⋊C₄	—	10	4	no	—
59	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
60	#107	—	20	8	no	—
61	C₄×C₈	Dic₁₀	1	4	yes	—
62	C₄×C₈	Dic₁₀	1	2	yes	—
63	C₄×C₈	C₂×Dic₅	1	4	yes	—
64	C₄×C₈	C₂×Dic₅	1	2	yes	—
65	C₂²×C₅	#384	1	1	yes	characteristic
66	C₂²×C₅	#493	1	1	yes	characteristic
67	C₂²×C₅	#494	1	1	yes	characteristic
68	C₂²×C₅	#495	1	4	yes	—
69	C₄×C₅	C₂×#107	1	2	yes	—
70	C₄×C₅	#427	1	4	yes	—
71	C₄×C₅	#499	1	4	yes	—
72	C₄×C₅	#500	1	2	yes	—
73	Dic₅	—	16	4	no	—
74	C₂²×C₄	—	20	4	no	—
75	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
76	C₂²×C₄	C₂×D₂₀	1	2	yes	—
77	C₂×C₈	—	2	8	no	—
78	C₂×C₈	D₄₀	1	4	yes	—
79	C₂×C₈	Dic₂₀	1	4	yes	—
80	C₂×C₈	C₄⋊Dic₅	1	8	yes	—
81	C₂×C₈	C₄⋊Dic₅	1	4	yes	—
82	C₄⋊C₄	—	20	8	no	—
83	C₄⋊C₄	—	20	16	no	—
84	C₄²	C₂×Dic₁₀	1	2	yes	—
85	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
86	C₄²	C₂²×Dic₅	1	1	yes	characteristic
87	C₂×C₅	#1709	1	2	yes	—
88	C₂×C₅	#1710	1	2	yes	—
89	C₂×C₅	#1845	1	1	yes	characteristic
90	C₂×C₅	#1846	1	2	yes	—
91	C₂³	#4020	1	1	yes	characteristic
92	C₂×C₄	—	40	4	no	—
93	C₂×C₄	—	40	8	no	—
94	C₂×C₄	#4015	1	1	yes	characteristic
95	C₂×C₄	#4015	1	2	yes	—
96	C₂×C₄	C₂×D₄₀	1	2	yes	—
97	C₂×C₄	#4050	1	8	yes	—
98	C₂×C₄	C₂×Dic₂₀	1	2	yes	—
99	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
100	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
101	C₈	—	2	8	no	—
102	C₈	#3950	1	8	yes	—
103	C₅	#8816	1	1	yes	characteristic, complemented, Sylow
104	C₂²	#64984	1	1	yes	characteristic
105	C₂²	#64985	1	4	yes	—
106	C₂²	#64988	1	1	yes	characteristic
107	C₂²	#65224	1	1	yes	characteristic
108	C₄	—	80	4	no	—
109	C₄	#64971	1	2	yes	—
110	C₄	#64972	1	4	yes	—
111	C₄	C₂×#3950	1	2	yes	—
112	C₄	#65395	1	4	yes	—
113	C₂	#10598853	1	2	yes	—
114	C₂	#10598857	1	2	yes	—
115	C₂	#10600558	1	1	yes	characteristic
116	C₂	#10600559	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₈²

C₂

yes

maximal, characteristic

#10600558

C₂

yes

maximal

#10600555

C₂

yes

maximal

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₂×#3950

—

#65224

C₂²

yes

—

C₅×C₈²

C₄

yes

—

—

C₂²×C₅×C₈

D₄

yes

—

C₂²×C₅×C₈

D₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₂×C₄⋊Dic₅

—

C₂×C₄⋊Dic₅

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

C₂×C₄

yes

—

C₄×C₅×C₈

Q₈

yes

—

C₄×C₅×C₈

Q₈

yes

—

#3950

—

#1845

—

#1834

—

C₂×C₈²

D₅

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂²×Dic₅

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

C₄⋊C₄

yes

—

C₂×C₅×C₈

D₈

yes

—

C₂×C₅×C₈

Q₁₆

yes

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₂×#107

—

C₂×C₄×C₈

C₂×D₅

yes

—

C₂×C₄×C₈

C₂×D₅

yes

characteristic

#384

—

#340

—

C₈²

Dic₅

yes

complemented

C₂³×C₅

#127

yes

characteristic

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₅

C₂×D₈

yes

—

C₂×C₄×C₅

C₂×Q₁₆

yes

—

C₂×C₄×C₅

#135

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₅×C₈

—

C₅×C₈

#107

yes

—

C₂²×C₈

D₂₀

yes

—

C₂²×C₈

D₂₀

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₅

yes

characteristic

#107

—

C₄×C₈

Dic₁₀

yes

—

C₄×C₈

Dic₁₀

yes

—

C₄×C₈

C₂×Dic₅

yes

—

C₄×C₈

C₂×Dic₅

yes

—

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

—

C₄×C₅

C₂×#107

yes

—

C₄×C₅

#427

yes

—

C₄×C₅

#499

yes

—

C₄×C₅

#500

yes

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₀

yes

characteristic

C₂²×C₄

C₂×D₂₀

yes

—

C₂×C₈

—

C₂×C₈

D₄₀

yes

—

C₂×C₈

Dic₂₀

yes

—

C₂×C₈

C₄⋊Dic₅

yes

—

C₂×C₈

C₄⋊Dic₅

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Dic₁₀

yes

—

C₄²

C₂×Dic₁₀

yes

characteristic

C₄²

C₂²×Dic₅

yes

characteristic

C₂×C₅

#1709

yes

—

C₂×C₅

#1710

yes

—

C₂×C₅

#1845

yes

characteristic

C₂×C₅

#1846

yes

—

C₂³

#4020

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#4015

yes

characteristic

C₂×C₄

#4015

yes

—

C₂×C₄

C₂×D₄₀

yes

—

C₂×C₄

#4050

yes

—

C₂×C₄

C₂×Dic₂₀

yes

—

C₂×C₄

C₂×C₄⋊Dic₅

yes

characteristic

100

C₂×C₄

C₂×C₄⋊Dic₅

yes

—

101

C₈

—

102

C₈

#3950

yes

—

103

C₅

#8816

yes

characteristic, complemented, Sylow

104

C₂²

#64984

yes

characteristic

105

C₂²

#64985

yes

—

106

C₂²

#64988

yes

characteristic

107

C₂²

#65224

yes

characteristic

108

C₄

—

109

C₄

#64971

yes

—

110

C₄

#64972

yes

—

111

C₄

C₂×#3950

yes

—

112

C₄

#65395

yes

—

113

C₂

#10598853

yes

—

114

C₂

#10598857

yes

—

115

C₂

#10600558

yes

characteristic

116

C₂

#10600559

yes

—

	subgroup	G/H
center	C₂³	#4020
commutator	C₄²×C₅	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×C₈²	C₂
socle, prime radical	C₂³×C₅	#127
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×C₈²	D₅
hypocenter	C₅	#8816
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center

C₂³

#4020

commutator

C₄²×C₅

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅

Fitting

C₂×C₅×C₈²

C₂

socle, prime radical

C₂³×C₅

#127

cosocle

C₂×C₄²×C₅

C₂³

hypercenter

C₂×C₈²

D₅

hypocenter

C₅

#8816

LCS

G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
8. C₅×C₈²	C₄	semidirect
42. C₈²	Dic₅	semidirect
103. C₅	#8816	semidirect

H ≅ G/N

type

8. C₅×C₈²

C₄

semidirect

42. C₈²

Dic₅

semidirect

103. C₅

#8816

semidirect

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

subgroup	index
C₂×C₅×C₈²	2
#10600558	2
#10600555	2
#8816	5

subgroup

index

C₂×C₅×C₈²

#10600558

#10600555

#8816

Subgroups — #11993077

Conjugacy classes of subgroups

Complements

Maximal subgroups