Group #11993074 — subgroups

Subgroups — #11993074

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	#10600557	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×#3949	—	2	4	no	—
7	#65224	C₂²	1	4	yes	—
8	C₅×C₈²	C₄	1	4	yes	complemented
9	#64771	—	2	8	no	—
10	#8815	—	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	#3949	—	4	8	no	—
21	#1844	—	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	SD₁₆	1	8	yes	—
31	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
33	C₄²×C₅	C₂×Q₈	1	2	yes	—
34	C₄⋊Dic₅	—	4	8	no	—
35	C₄⋊Dic₅	—	4	16	no	—
36	C₂×#106	—	10	4	no	—
37	C₂×C₄×C₈	C₂×D₅	1	2	yes	—
38	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
39	#384	—	5	4	no	—
40	#340	—	10	8	no	—
41	C₈²	Dic₅	1	4	yes	complemented
42	C₂³×C₅	#127	1	1	yes	characteristic
43	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
47	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
48	C₂×C₄×C₅	#135	1	8	yes	—
49	C₂×Dic₅	—	8	4	no	—
50	C₂×Dic₅	—	8	8	no	—
51	C₅×C₈	—	2	8	no	—
52	C₅×C₈	#106	1	8	yes	—
53	C₂²×C₈	D₂₀	1	4	yes	—
54	C₂²×C₈	D₂₀	1	2	yes	—
55	C₂×C₄⋊C₄	—	10	8	no	—
56	C₂×C₄⋊C₄	—	10	4	no	—
57	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
58	#106	—	20	8	no	—
59	C₄×C₈	Dic₁₀	1	4	yes	—
60	C₄×C₈	Dic₁₀	1	2	yes	—
61	C₄×C₈	C₂×Dic₅	1	4	yes	—
62	C₄×C₈	C₂×Dic₅	1	2	yes	—
63	C₂²×C₅	#384	1	1	yes	characteristic
64	C₂²×C₅	#492	1	2	yes	—
65	C₂²×C₅	#495	1	4	yes	—
66	C₄×C₅	C₂×#106	1	2	yes	—
67	C₄×C₅	#427	1	4	yes	—
68	C₄×C₅	#498	1	2	yes	—
69	C₄×C₅	#499	1	4	yes	—
70	Dic₅	—	16	4	no	—
71	C₂²×C₄	—	20	4	no	—
72	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
73	C₂²×C₄	C₂×D₂₀	1	2	yes	—
74	C₂×C₈	—	2	8	no	—
75	C₂×C₈	#677	1	8	yes	—
76	C₂×C₈	C₄⋊Dic₅	1	8	yes	—
77	C₂×C₈	C₄⋊Dic₅	1	4	yes	—
78	C₄⋊C₄	—	20	8	no	—
79	C₄⋊C₄	—	20	16	no	—
80	C₄²	C₂×Dic₁₀	1	2	yes	—
81	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
82	C₄²	C₂²×Dic₅	1	1	yes	characteristic
83	C₂×C₅	#1708	1	4	yes	—
84	C₂×C₅	#1844	1	1	yes	characteristic
85	C₂×C₅	#1846	1	2	yes	—
86	C₂³	#4020	1	1	yes	characteristic
87	C₂×C₄	—	40	4	no	—
88	C₂×C₄	—	40	8	no	—
89	C₂×C₄	#4015	1	1	yes	characteristic
90	C₂×C₄	#4015	1	2	yes	—
91	C₂×C₄	C₂×#677	1	4	yes	—
92	C₂×C₄	#4050	1	8	yes	—
93	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
94	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	#3949	1	8	yes	—
97	C₅	#8815	1	1	yes	characteristic, complemented, Sylow
98	C₂²	#64982	1	2	yes	—
99	C₂²	#64985	1	4	yes	—
100	C₂²	#65224	1	1	yes	characteristic
101	C₄	—	80	4	no	—
102	C₄	#64969	1	2	yes	—
103	C₄	#64972	1	4	yes	—
104	C₄	C₂×#3949	1	2	yes	—
105	C₄	#65395	1	4	yes	—
106	C₂	#10598852	1	4	yes	—
107	C₂	#10600557	1	1	yes	characteristic
108	C₂	#10600559	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₈²

C₂

yes

maximal, characteristic

#10600557

C₂

yes

maximal

#10600555

C₂

yes

maximal

C₂×C₄×C₅×C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₂×#3949

—

#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

—

#3949

—

#1844

—

#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

SD₁₆

yes

—

C₄²×C₅

C₂²×C₄

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₂×#106

—

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

characteristic

C₂×C₄×C₅

C₄⋊Q₈

yes

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

#135

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₅×C₈

—

C₅×C₈

#106

yes

—

C₂²×C₈

D₂₀

yes

—

C₂²×C₈

D₂₀

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₅

yes

characteristic

#106

—

C₄×C₈

Dic₁₀

yes

—

C₄×C₈

Dic₁₀

yes

—

C₄×C₈

C₂×Dic₅

yes

—

C₄×C₈

C₂×Dic₅

yes

—

C₂²×C₅

#384

yes

characteristic

C₂²×C₅

#492

yes

—

C₂²×C₅

#495

yes

—

C₄×C₅

C₂×#106

yes

—

C₄×C₅

#427

yes

—

C₄×C₅

#498

yes

—

C₄×C₅

#499

yes

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₀

yes

characteristic

C₂²×C₄

C₂×D₂₀

yes

—

C₂×C₈

—

C₂×C₈

#677

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

#1708

yes

—

C₂×C₅

#1844

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×#677

yes

—

C₂×C₄

#4050

yes

—

C₂×C₄

C₂×C₄⋊Dic₅

yes

characteristic

C₂×C₄

C₂×C₄⋊Dic₅

yes

—

C₈

—

C₈

#3949

yes

—

C₅

#8815

yes

characteristic, complemented, Sylow

C₂²

#64982

yes

—

C₂²

#64985

yes

—

100

C₂²

#65224

yes

characteristic

101

C₄

—

102

C₄

#64969

yes

—

103

C₄

#64972

yes

—

104

C₄

C₂×#3949

yes

—

105

C₄

#65395

yes

—

106

C₂

#10598852

yes

—

107

C₂

#10600557

yes

characteristic

108

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	#8815
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

#8815

LCS

G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
8. C₅×C₈²	C₄	semidirect
41. C₈²	Dic₅	semidirect
97. C₅	#8815	semidirect

H ≅ G/N

type

8. C₅×C₈²

C₄

semidirect

41. C₈²

Dic₅

semidirect

97. C₅

#8815

semidirect

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

subgroup	index
C₂×C₅×C₈²	2
#10600557	2
#10600555	2
#8815	5

subgroup

index

C₂×C₅×C₈²

#10600557

#10600555

#8815

Subgroups — #11993074

Conjugacy classes of subgroups

Complements

Maximal subgroups