Subgroups — C₅×#986 #91945

Order 480.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×GL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
3	C₅×AGL(1,ℤ/8)	—	3	1	no	maximal, Hall
4	C₅×D₁₂	—	4	1	no	maximal
5	C₅×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
6	#986	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×#41	D₃	1	1	yes	characteristic, complemented
8	C₂×C₅×D₄	—	3	1	no	—
9	C₅×SD₁₆	—	3	2	no	—
10	C₅×D₈	—	3	2	no	—
11	C₅×M₁₆	—	3	1	no	—
12	C₂×C₅×D₃	—	4	2	no	—
13	C₃×C₄×C₅	—	4	1	no	—
14	#41⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
15	GL(2,𝔽₃)	C₂×C₅	1	2	yes	complemented
16	C₂³×C₅	—	6	1	no	—
17	C₅×Q₈	C₂×D₃	1	1	yes	characteristic
18	C₅×D₄	—	3	1	no	—
19	C₅×D₄	—	3	2	no	—
20	C₅×D₄	—	6	1	no	—
21	C₂×C₄×C₅	—	3	1	no	—
22	C₅×C₈	—	3	2	no	—
23	AGL(1,ℤ/8)	—	3	1	no	Sylow
24	C₂×C₃×C₅	—	4	1	no	—
25	C₅×D₃	—	8	2	no	—
26	D₁₂	—	4	1	no	—
27	SL(2,𝔽₃)	C₂²×C₅	1	1	yes	characteristic, complemented
28	C₂²×C₅	—	3	1	no	—
29	C₂²×C₅	—	6	2	no	—
30	C₂²×C₅	—	12	2	no	—
31	C₄×C₅	—	3	1	no	—
32	C₄×C₅	S₄	1	1	yes	characteristic
33	#41	C₅×D₃	1	1	yes	characteristic, complemented
34	C₂×D₄	—	3	1	no	—
35	SD₁₆	—	3	2	no	—
36	D₈	—	3	2	no	—
37	M₁₆	—	3	1	no	—
38	C₃×C₅	—	4	1	no	Hall
39	C₂×D₃	—	4	2	no	—
40	C₃×C₄	—	4	1	no	—
41	C₂×C₅	—	6	1	no	—
42	C₂×C₅	—	12	2	no	—
43	C₂×C₅	C₂×S₄	1	1	yes	characteristic
44	C₂³	—	6	1	no	—
45	Q₈	C₂×C₅×D₃	1	1	yes	characteristic
46	D₄	—	3	1	no	—
47	D₄	—	3	2	no	—
48	D₄	—	6	1	no	—
49	C₂×C₄	—	3	1	no	—
50	C₈	—	3	2	no	—
51	C₂×C₃	—	4	1	no	—
52	D₃	—	8	2	no	—
53	C₅	#986	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	3	1	no	—
55	C₂²	—	6	2	no	—
56	C₂²	—	12	2	no	—
57	C₄	—	3	1	no	—
58	C₄	C₅×S₄	1	1	yes	characteristic
59	C₃	—	4	1	no	Sylow
60	C₂	—	6	1	no	—
61	C₂	—	12	2	no	—
62	C₂	C₂×C₅×S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₅
Frattini	C₂	C₂×C₅×S₄
Fitting	C₅×#41	D₃
hypercenter	C₄×C₅	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#41⋊C₃	C₂	semidirect
2. C₅×GL(2,𝔽₃)	C₂	semidirect
5. C₅×SL(2,𝔽₃)	C₂²	semidirect
6. #986	C₅	direct (N × H)
7. C₅×#41	D₃	semidirect
14. #41⋊C₃	C₂×C₅	semidirect
15. GL(2,𝔽₃)	C₂×C₅	semidirect
27. SL(2,𝔽₃)	C₂²×C₅	semidirect
33. #41	C₅×D₃	semidirect
53. C₅	#986	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#41⋊C₃	2
C₅×GL(2,𝔽₃)	2
C₅×AGL(1,ℤ/8)	3
C₅×D₁₂	4
#986	5

Subgroups — C5×#986 #91945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#986 #91945