Subgroups — C₃×#3961 #91031

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic
3	C₃×#672	C₂	1	1	yes	maximal, characteristic
4	#3961	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	—	2	1	no	—
6	C₃×Dic₁₀	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₃×Q₃₂	—	5	1	no	maximal, Hall
9	C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic
10	Dic₂₀	C₂×C₃	1	1	yes	characteristic
11	#672	C₂×C₃	1	1	yes	characteristic
12	C₃×C₄×C₅	—	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×Q₁₆	D₅	1	1	yes	characteristic
17	C₃×C₁₆	—	5	1	no	—
18	C₅×Q₈	—	2	1	no	—
19	Dic₁₀	—	2	1	no	—
20	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
21	Q₃₂	—	5	1	no	Sylow
22	C₂×C₃×C₅	D₈	1	1	yes	characteristic
23	C₃×Q₈	—	2	1	no	—
24	C₃×Q₈	—	10	1	no	—
25	C₃×C₈	C₂×D₅	1	1	yes	characteristic
26	C₄×C₅	—	4	1	no	—
27	C₄×C₅	C₃×D₄	1	1	yes	characteristic
28	Dic₅	—	4	1	no	—
29	Q₁₆	—	5	1	no	—
30	Q₁₆	C₃×D₅	1	1	yes	characteristic
31	C₁₆	—	5	1	no	—
32	C₃×C₅	Q₃₂	1	1	yes	characteristic, complemented, Hall
33	C₃×C₄	—	4	1	no	—
34	C₃×C₄	—	20	1	no	—
35	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
36	C₂×C₅	C₃×D₈	1	1	yes	characteristic
37	Q₈	—	2	1	no	—
38	Q₈	—	10	1	no	—
39	C₈	C₂×C₃×D₅	1	1	yes	characteristic
40	C₂×C₃	#686	1	1	yes	characteristic
41	C₅	C₃×Q₃₂	1	1	yes	characteristic, complemented, Sylow
42	C₄	—	4	1	no	—
43	C₄	—	20	1	no	—
44	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
45	C₃	#3961	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×#686	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#686
commutator, cosocle	C₅×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×D₅
Fitting	C₃×C₅×Q₁₆	C₂
socle, prime radical	C₂×C₃×C₅	D₈
hypercenter	C₃×Q₁₆	D₅
hypocenter	C₅	C₃×Q₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #3961	C₃	direct (N × H)
32. C₃×C₅	Q₃₂	semidirect
41. C₅	C₃×Q₃₂	semidirect
45. C₃	#3961	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×C₅×Q₁₆	2
C₃×Dic₂₀	2
C₃×#672	2
#3961	3
C₃×Q₃₂	5

Subgroups — C3×#3961 #91031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3961 #91031