Subgroups — C₃×#3932 #91002

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#3932	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×D₂₀	—	2	1	no	—
6	C₃×Dic₁₀	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₃×SD₃₂	—	5	1	no	maximal, Hall
9	Dic₂₀	C₂×C₃	1	1	yes	characteristic, complemented
10	D₄₀	C₂×C₃	1	1	yes	characteristic
11	C₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×D₅	—	4	1	no	—
13	C₃×C₄×C₅	D₄	1	1	yes	characteristic
14	C₃×Dic₅	—	4	1	no	—
15	C₃×Q₁₆	—	5	1	no	—
16	C₃×D₈	—	5	1	no	—
17	C₃×C₁₆	D₅	1	1	yes	characteristic, complemented
18	D₂₀	—	2	1	no	—
19	Dic₁₀	—	2	1	no	—
20	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
21	SD₃₂	—	5	1	no	Sylow
22	C₂×C₃×C₅	D₈	1	1	yes	characteristic
23	C₃×D₅	—	8	1	no	—
24	C₃×Q₈	—	10	1	no	—
25	C₃×D₄	—	10	1	no	—
26	C₃×C₈	C₂×D₅	1	1	yes	characteristic
27	C₂×D₅	—	4	1	no	—
28	C₄×C₅	C₃×D₄	1	1	yes	characteristic
29	Dic₅	—	4	1	no	—
30	Q₁₆	—	5	1	no	—
31	D₈	—	5	1	no	—
32	C₁₆	C₃×D₅	1	1	yes	characteristic, complemented
33	C₃×C₅	SD₃₂	1	1	yes	characteristic, complemented, Hall
34	C₂²×C₃	—	20	1	no	—
35	C₃×C₄	—	20	1	no	—
36	C₃×C₄	D₂₀	1	1	yes	characteristic
37	C₂×C₅	C₃×D₈	1	1	yes	characteristic
38	D₅	—	8	1	no	—
39	Q₈	—	10	1	no	—
40	D₄	—	10	1	no	—
41	C₈	C₂×C₃×D₅	1	1	yes	characteristic
42	C₂×C₃	—	40	1	no	—
43	C₂×C₃	D₄₀	1	1	yes	characteristic
44	C₅	C₃×SD₃₂	1	1	yes	characteristic, complemented, Sylow
45	C₂²	—	20	1	no	—
46	C₄	—	20	1	no	—
47	C₄	C₃×D₂₀	1	1	yes	characteristic
48	C₃	#3932	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	40	1	no	—
50	C₂	C₃×D₄₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄₀
commutator, cosocle	C₅×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×D₅
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	D₈
prime radical	C₃×D₄₀	C₂
hypercenter	C₃×C₁₆	D₅
hypocenter	C₅	C₃×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×Dic₂₀	C₂	semidirect
3. C₃×C₅×C₁₆	C₂	semidirect
4. #3932	C₃	direct (N × H)
9. Dic₂₀	C₂×C₃	semidirect
11. C₅×C₁₆	C₂×C₃	semidirect
17. C₃×C₁₆	D₅	semidirect
32. C₁₆	C₃×D₅	semidirect
33. C₃×C₅	SD₃₂	semidirect
44. C₅	C₃×SD₃₂	semidirect
48. C₃	#3932	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Dic₂₀	2
C₃×D₄₀	2
C₃×C₅×C₁₆	2
#3932	3
C₃×SD₃₂	5

Subgroups — C3×#3932 #91002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3932 #91002