Group #14511536 — subgroups

Subgroups — #14511536

Order 1920.

110 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 19 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×#395⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#10598139	—	3	1	no	maximal, Hall
3	C₅×C₂²⋊SL(2,𝔽₃)	C₄	1	1	yes	characteristic
4	A₄⋊#168	—	4	1	no	maximal
5	#68002	—	5	1	no	maximal, Hall
6	C₅×#395	D₃	1	1	yes	characteristic
7	#64750	—	3	1	no	—
8	#64748	—	3	1	no	—
9	C₄×C₅×A₄	—	4	1	no	—
10	#395⋊C₃	D₅	1	1	yes	characteristic
11	C₂²×C₅×Q₈	Dic₃	1	1	yes	characteristic
12	C₂×C₅×C₄⋊C₄	—	3	1	no	—
13	C₂×#681	—	6	1	no	—
14	C₅×#95	—	3	1	no	—
15	C₂²⋊#168	—	6	1	no	—
16	#1354	—	15	1	no	Sylow
17	C₂×C₅×A₄	—	4	1	no	—
18	C₅×SL(2,𝔽₃)	—	16	1	no	—
19	C₃⋊#168	—	16	1	no	—
20	C₂²⋊SL(2,𝔽₃)	Dic₅	1	1	yes	characteristic
21	A₄⋊C₈	—	20	1	no	—
22	C₂×C₅×Q₈	—	12	1	no	—
23	C₂²×C₄×C₅	—	3	1	no	—
24	C₂²×C₄×C₅	—	3	1	no	—
25	C₂²×C₄×C₅	S₄	1	1	yes	characteristic
26	C₅×C₄⋊C₄	—	12	1	no	—
27	#681	—	6	2	no	—
28	#681	—	12	1	no	—
29	C₂×#168	—	12	1	no	—
30	C₂×#168	—	12	1	no	—
31	#395	D₁₅	1	1	yes	characteristic
32	#343	—	15	1	no	—
33	#324	—	15	1	no	—
34	C₅×A₄	—	4	1	no	—
35	C₃×C₄×C₅	—	16	1	no	—
36	C₄×A₄	—	4	1	no	—
37	C₂³×C₅	SL(2,ℤ/4)	1	1	yes	characteristic
38	C₅×Q₈	—	4	1	no	—
39	C₅×Q₈	—	12	1	no	—
40	C₂×C₄×C₅	—	3	1	no	—
41	C₂×C₄×C₅	—	3	1	no	—
42	C₂×C₄×C₅	—	6	1	no	—
43	C₂×C₄×C₅	—	6	1	no	—
44	C₂×C₄×C₅	—	6	1	no	—
45	C₂×C₄×C₅	—	6	1	no	—
46	C₂×C₄×C₅	—	12	1	no	—
47	#168	—	12	2	no	—
48	#168	—	24	1	no	—
49	C₂²×Q₈	Dic₁₅	1	1	yes	characteristic
50	C₂×M₁₆	—	30	1	no	—
51	C₂×C₄⋊C₄	—	3	1	no	—
52	C₂²⋊C₈	—	30	1	no	—
53	#95	—	3	1	no	—
54	C₂×C₃×C₅	—	16	1	no	—
55	C₂×A₄	—	4	1	no	—
56	SL(2,𝔽₃)	—	16	1	no	—
57	C₃⋊C₈	—	80	1	no	—
58	C₂²×C₅	—	3	1	no	—
59	C₂²×C₅	—	3	1	no	—
60	C₂²×C₅	GU(2,𝔽₃)	1	1	yes	characteristic
61	C₄×C₅	—	4	1	no	—
62	C₄×C₅	—	6	1	no	—
63	C₄×C₅	—	6	1	no	—
64	C₄×C₅	—	12	1	no	—
65	C₂×Q₈	—	12	1	no	—
66	C₂²×C₄	—	3	1	no	—
67	C₂²×C₄	—	3	1	no	—
68	C₂²×C₄	C₅⋊S₄	1	1	yes	characteristic
69	M₁₆	—	30	2	no	—
70	M₁₆	—	60	1	no	—
71	C₂×C₈	—	60	1	no	—
72	C₂×C₈	—	60	1	no	—
73	C₄⋊C₄	—	12	1	no	—
74	C₃×C₅	—	16	1	no	Hall
75	A₄	—	4	1	no	—
76	C₃×C₄	—	16	1	no	—
77	C₂×C₅	—	3	1	no	—
78	C₂×C₅	—	3	1	no	—
79	C₂×C₅	#4625	1	1	yes	characteristic
80	C₂³	A₄⋊Dic₅	1	1	yes	characteristic
81	Q₈	—	4	1	no	—
82	Q₈	—	12	1	no	—
83	C₂×C₄	—	3	1	no	—
84	C₂×C₄	—	3	1	no	—
85	C₂×C₄	—	6	1	no	—
86	C₂×C₄	—	6	1	no	—
87	C₂×C₄	—	6	1	no	—
88	C₂×C₄	—	6	1	no	—
89	C₂×C₄	—	12	1	no	—
90	C₈	—	60	2	no	—
91	C₈	—	120	1	no	—
92	C₂×C₃	—	16	1	no	—
93	C₅	#68002	1	1	yes	characteristic, complemented, Sylow
94	C₂²	—	3	1	no	—
95	C₂²	—	3	1	no	—
96	C₂²	#91185	1	1	yes	characteristic
97	C₄	—	4	1	no	—
98	C₄	—	6	1	no	—
99	C₄	—	6	1	no	—
100	C₄	—	12	1	no	—
101	C₃	—	16	1	no	Sylow
102	C₂	—	3	1	no	—
103	C₂	—	3	1	no	—
104	C₂	#11746597	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#395⋊C₃

C₂

yes

maximal, characteristic

#10598139

—

maximal, Hall

C₅×C₂²⋊SL(2,𝔽₃)

C₄

yes

—

—

D₃

yes

characteristic

#64750

—

#64748

—

C₄×C₅×A₄

—

#395⋊C₃

D₅

yes

characteristic

C₂²×C₅×Q₈

Dic₃

yes

characteristic

C₂×C₅×C₄⋊C₄

—

C₂×#681

—

C₅×#95

—

C₂²⋊#168

—

#1354

—

Sylow

C₂×C₅×A₄

—

C₅×SL(2,𝔽₃)

—

C₃⋊#168

—

C₂²⋊SL(2,𝔽₃)

Dic₅

yes

characteristic

A₄⋊C₈

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

S₄

yes

characteristic

C₅×C₄⋊C₄

—

—

—

—

—

D₁₅

yes

characteristic

#343

—

#324

—

C₅×A₄

—

C₃×C₄×C₅

—

C₄×A₄

—

C₂³×C₅

SL(2,ℤ/4)

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

#168

—

#168

—

C₂²×Q₈

Dic₁₅

yes

characteristic

C₂×M₁₆

—

C₂×C₄⋊C₄

—

C₂²⋊C₈

—

#95

—

C₂×C₃×C₅

—

C₂×A₄

—

SL(2,𝔽₃)

—

C₃⋊C₈

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

GU(2,𝔽₃)

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₅⋊S₄

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₃×C₅

—

Hall

A₄

—

C₃×C₄

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

#4625

yes

characteristic

C₂³

A₄⋊Dic₅

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₈

—

C₈

—

120

—

C₂×C₃

—

C₅

#68002

yes

characteristic, complemented, Sylow

C₂²

—

C₂²

—

C₂²

#91185

yes

characteristic

C₄

—

C₄

—

C₄

—

100

C₄

—

101

C₃

—

Sylow

102

C₂

—

103

C₂

—

104

C₂

#11746597

yes

characteristic

	subgroup	G/H
center, hypercenter	C₂	#11746597
commutator, prime radical, hypocenter	C₅×C₂²⋊SL(2,𝔽₃)	C₄
Frattini	C₂²×C₄	C₅⋊S₄
Fitting	C₅×#395	D₃
socle	C₂³×C₅	SL(2,ℤ/4)
cosocle	C₅×#395⋊C₃	C₂
LCS	G ▷ C₅×C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂

subgroup

G/H

center, hypercenter

C₂

#11746597

commutator, prime radical, hypocenter

C₅×C₂²⋊SL(2,𝔽₃)

C₄

Frattini

C₂²×C₄

C₅⋊S₄

D₃

C₂³×C₅

C₅×#395⋊C₃

C₂

LCS

G ▷ C₅×C₂²⋊SL(2,𝔽₃)

UCS

C₁ ◁ C₂

N	H ≅ G/N	type
93. C₅	#68002	semidirect

H ≅ G/N

type

93. C₅

#68002

semidirect

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

subgroup	index
C₅×#395⋊C₃	2
#10598139	3
A₄⋊#168	4
#68002	5

subgroup

index

C₅×#395⋊C₃

#10598139

A₄⋊#168

#68002

Subgroups — #14511536

Conjugacy classes of subgroups

Complements

Maximal subgroups