Subgroups — C₃×#4020 #91591

Order 480.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₀	C₂	1	6	yes	maximal, complemented
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#4020	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×D₅	C₂²	1	4	yes	—
5	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
6	C₃×D₂₀	—	2	12	no	—
7	C₃×#127	—	5	1	no	maximal, Hall
8	C₂×D₂₀	C₂×C₃	1	6	yes	complemented
9	C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
11	C₂×C₃×D₅	—	2	12	no	—
12	C₃×C₄×C₅	D₄	1	6	yes	complemented
13	C₂×C₃×D₄	—	5	6	no	—
14	C₃×C₄²	D₅	1	1	yes	characteristic, complemented
15	C₂²×D₅	C₂²×C₃	1	4	yes	—
16	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
17	D₂₀	—	2	12	no	—
18	#127	—	5	1	no	Sylow
19	C₂×C₃×C₅	C₂×D₄	1	3	yes	—
20	C₃×D₅	—	4	4	no	—
21	C₂³×C₃	—	5	4	no	—
22	C₃×D₄	—	10	12	no	—
23	C₂×C₃×C₄	C₂×D₅	1	3	yes	—
24	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
25	C₂×D₅	—	2	12	no	—
26	C₄×C₅	C₃×D₄	1	6	yes	complemented
27	C₂×D₄	—	5	6	no	—
28	C₄²	C₃×D₅	1	1	yes	characteristic, complemented
29	C₃×C₅	#127	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	—	10	12	no	—
31	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
32	C₃×C₄	D₂₀	1	6	yes	complemented
33	C₂×C₅	C₂×C₃×D₄	1	3	yes	—
34	D₅	—	4	4	no	—
35	C₂³	—	5	4	no	—
36	D₄	—	10	12	no	—
37	C₂×C₄	C₂×C₃×D₅	1	3	yes	—
38	C₂×C₃	—	20	4	no	—
39	C₂×C₃	C₂×D₂₀	1	3	yes	—
40	C₅	C₃×#127	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	10	12	no	—
42	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
43	C₄	C₃×D₂₀	1	6	yes	complemented
44	C₃	#4020	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	20	4	no	—
46	C₂	C₂×C₃×D₂₀	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂³
hypercenter	C₃×C₄²	D₅
hypocenter	C₅	C₃×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₂₀	C₂	semidirect
2. C₃×C₄²×C₅	C₂	semidirect
3. #4020	C₃	direct (N × H)
8. C₂×D₂₀	C₂×C₃	semidirect
9. C₄²×C₅	C₂×C₃	semidirect
12. C₃×C₄×C₅	D₄	semidirect
14. C₃×C₄²	D₅	semidirect
26. C₄×C₅	C₃×D₄	semidirect
28. C₄²	C₃×D₅	semidirect
29. C₃×C₅	#127	semidirect
32. C₃×C₄	D₂₀	semidirect
40. C₅	C₃×#127	semidirect
43. C₄	C₃×D₂₀	semidirect
44. C₃	#4020	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₂₀	2
C₃×C₄²×C₅	2
#4020	3
C₃×#127	5

Subgroups — C3×#4020 #91591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4020 #91591