Group #13014146 — subgroups

Subgroups — #13014146

Order 1280.

124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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	#10602214	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#3928	C₂	1	2	yes	maximal
3	C₂×C₅×M₃₂	C₄	1	1	yes	characteristic
4	#65390	C₄	1	1	yes	characteristic
5	C₂²×#672	C₂²	1	1	yes	characteristic
6	C₂×#3928	—	2	2	no	—
7	#64721	—	2	2	no	—
8	#7363	—	5	1	no	maximal, Sylow
9	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
10	#4072	C₈	1	1	yes	characteristic
11	C₂×#681	C₈	1	1	yes	characteristic
12	C₅×M₃₂	—	4	1	no	—
13	C₂×C₅×C₁₆	—	2	1	no	—
14	#3947	—	2	1	no	—
15	C₈×Dic₅	—	2	1	no	—
16	C₂×#672	—	4	1	no	—
17	C₂×#672	D₄	1	2	yes	—
18	#3928	—	4	2	no	—
19	#2151	—	5	1	no	—
20	C₂²⋊C₃₂	—	5	2	no	—
21	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
22	C₂×C₅×C₈	—	2	1	no	—
23	C₂×C₅×C₈	—	2	1	no	—
24	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₅×C₈	M₁₆	1	1	yes	characteristic
26	C₂²⋊Dic₅	—	2	1	no	—
27	C₄⋊Dic₅	C₁₆	1	2	yes	—
28	C₄×Dic₅	—	2	1	no	—
29	#681	—	4	1	no	—
30	C₂×#168	—	2	1	no	—
31	C₅×C₁₆	—	4	1	no	—
32	#672	—	2	2	no	—
33	C₂×M₃₂	AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₂²×C₁₆	—	5	1	no	—
35	#405	—	5	1	no	—
36	C₂×C₃₂	—	10	2	no	—
37	C₄⋊C₁₆	—	10	2	no	—
38	C₂³×C₅	M₃₂	1	1	yes	characteristic
39	C₂×C₄×C₅	—	2	1	no	—
40	C₂×C₄×C₅	—	2	1	no	—
41	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
42	C₂×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
43	C₂×Dic₅	—	2	2	no	—
44	C₅×C₈	—	2	1	no	—
45	C₅×C₈	#99	1	1	yes	characteristic
46	C₅×C₈	#101	1	1	yes	characteristic
47	#168	—	4	1	no	—
48	C₂×M₁₆	—	5	1	no	—
49	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
50	#117	—	5	1	no	—
51	M₃₂	—	4	1	no	—
52	C₂×C₁₆	—	2	1	no	—
53	C₂×C₁₆	—	5	2	no	—
54	C₂×C₁₆	—	20	1	no	—
55	#97	—	10	1	no	—
56	C₄×C₈	—	10	1	no	—
57	C₃₂	—	20	2	no	—
58	C₂²×C₅	—	2	1	no	—
59	C₂²×C₅	—	2	2	no	—
60	C₂²×C₅	C₂²⋊C₁₆	1	1	yes	characteristic
61	C₄×C₅	—	2	1	no	—
62	C₄×C₅	#324	1	1	yes	characteristic
63	C₄×C₅	#349	1	1	yes	characteristic
64	Dic₅	—	4	2	no	—
65	C₂²×C₄	D₅⋊C₈	1	1	yes	characteristic
66	M₁₆	—	20	1	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	10	1	no	—
70	C₂×C₈	#700	1	1	yes	characteristic
71	C₂×C₈	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
72	C₄⋊C₄	—	5	2	no	—
73	C₂²⋊C₄	—	10	1	no	—
74	C₄²	—	10	1	no	—
75	C₁₆	—	4	1	no	—
76	C₁₆	—	10	2	no	—
77	C₂×C₅	—	4	1	no	—
78	C₂×C₅	#1322	1	1	yes	characteristic
79	C₂×C₅	#1401	1	2	yes	—
80	C₂³	#3990	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	10	2	no	—
84	C₂×C₄	D₅⋊C₁₆	1	1	yes	characteristic
85	C₂×C₄	#4003	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	20	1	no	—
88	C₈	#4005	1	1	yes	characteristic
89	C₈	#4011	1	1	yes	characteristic
90	C₅	#7363	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	2	2	no	—
92	C₂²	—	2	1	no	—
93	C₂²	#64887	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	20	2	no	—
96	C₄	#64891	1	1	yes	characteristic
97	C₄	#64914	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#10598669	1	2	yes	—
100	C₂	#10598761	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10602214

C₂

yes

maximal, characteristic

C₂²⋊#3928

C₂

yes

maximal

C₂×C₅×M₃₂

C₄

yes

characteristic

#65390

C₄

yes

characteristic

C₂²×#672

C₂²

yes

—

—

—

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

#4072

C₈

yes

characteristic

C₂×#681

C₈

yes

characteristic

C₅×M₃₂

—

C₂×C₅×C₁₆

—

#3947

—

C₈×Dic₅

—

C₂×#672

—

C₂×#672

D₄

yes

—

#3928

—

#2151

—

C₂²⋊C₃₂

—

C₂²×C₄×C₅

C₂×C₈

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅×C₈

M₁₆

yes

characteristic

C₂²⋊Dic₅

—

C₄⋊Dic₅

C₁₆

yes

—

C₄×Dic₅

—

#681

—

C₂×#168

—

C₅×C₁₆

—

#672

—

C₂×M₃₂

AGL(1,𝔽₅)

yes

characteristic

C₂²×C₁₆

—

#405

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₂³×C₅

M₃₂

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₅

C₂×C₁₆

yes

characteristic

C₂×Dic₅

—

C₅×C₈

—

C₅×C₈

yes

C₅×C₈

yes

—

C₂×M₁₆

—

C₂²×C₈

C₂×AGL(1,𝔽₅)

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₃₂

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

C₂²⋊C₁₆

yes

characteristic

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

Dic₅

—

C₂²×C₄

D₅⋊C₈

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#700

yes

characteristic

C₂×C₈

C₂²⋊AGL(1,𝔽₅)

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₂×C₅

—

C₂×C₅

#1322

yes

characteristic

C₂×C₅

#1401

yes

—

C₂³

#3990

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₅⋊C₁₆

yes

characteristic

C₂×C₄

#4003

yes

characteristic

C₈

—

C₈

—

C₈

yes

C₈

yes

C₅

yes

characteristic, complemented, Sylow

C₂²

—

C₂²

—

C₂²

#64887

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#10598669

yes

—

100

C₂

#10598761

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂×C₁₆
Frattini	C₂²×C₈	C₂×AGL(1,𝔽₅)
Fitting	C₂×C₅×M₃₂	C₄
socle	C₂²×C₅	C₂²⋊C₁₆
prime radical	C₂³×C₅	M₃₂
cosocle	C₂²×#672	C₂²
hypercenter	C₂×M₃₂	AGL(1,𝔽₅)
hypocenter	C₅	#7363
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²⋊AGL(1,𝔽₅)

commutator

C₂×C₄×C₅

C₂×C₁₆

Frattini

C₂²×C₈

C₂×AGL(1,𝔽₅)

Fitting

C₂×C₅×M₃₂

C₄

socle

C₂²×C₅

C₂²⋊C₁₆

prime radical

C₂³×C₅

M₃₂

cosocle

C₂²×#672

C₂²

C₂×M₃₂

C₅

G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
90. C₅	#7363	semidirect

H ≅ G/N

type

90. C₅

#7363

semidirect

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

subgroup	index
#10602214	2
C₂²⋊#3928	2
#7363	5

subgroup

index

#10602214

C₂²⋊#3928

#7363

Subgroups — #13014146

Conjugacy classes of subgroups

Complements

Maximal subgroups