Subgroups — C₃×#4133 #91979

Order 480.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#713	C₂	1	1	yes	maximal, characteristic
2	C₃×#700	C₂	1	3	yes	maximal, complemented
3	C₃×D₅⋊C₈	C₂	1	3	yes	maximal, complemented
4	#4133	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	C₄	1	1	yes	characteristic
6	C₃×D₂₀	C₄	1	3	yes	—
7	C₃×C₄×D₅	C₂²	1	3	yes	—
8	C₃×#170	C₂²	1	1	yes	characteristic
9	C₃×#170	C₂²	1	3	yes	—
10	C₃×#131	—	5	1	no	maximal, Hall
11	#713	C₂×C₃	1	1	yes	characteristic
12	#700	C₂×C₃	1	3	yes	complemented
13	D₅⋊C₈	C₂×C₃	1	3	yes	complemented
14	C₂×C₃×D₅	C₂×C₄	1	3	yes	—
15	C₃×C₄×C₅	C₂×C₄	1	3	yes	—
16	C₃×Dic₅	C₂³	1	1	yes	characteristic
17	C₃×#41	—	5	1	no	—
18	C₃×M₁₆	—	5	3	no	—
19	C₂×C₃×C₈	—	5	3	no	—
20	C₅×Q₈	C₃×C₄	1	1	yes	characteristic
21	D₂₀	C₃×C₄	1	3	yes	—
22	C₄×D₅	C₂²×C₃	1	3	yes	—
23	#170	C₂²×C₃	1	1	yes	characteristic
24	#170	C₂²×C₃	1	3	yes	—
25	#131	—	5	1	no	Sylow
26	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
27	C₃×D₅	—	2	3	no	—
28	C₃×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₃×D₄	—	5	3	no	—
30	C₂×C₃×C₄	—	5	3	no	—
31	C₃×C₈	—	5	1	no	—
32	C₃×C₈	—	5	3	no	—
33	C₂×D₅	C₂×C₃×C₄	1	3	yes	—
34	C₄×C₅	C₂×C₃×C₄	1	3	yes	—
35	Dic₅	C₂³×C₃	1	1	yes	characteristic
36	#41	—	5	1	no	—
37	M₁₆	—	5	3	no	—
38	C₂×C₈	—	5	3	no	—
39	C₃×C₅	#131	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₃	—	5	3	no	—
41	C₃×C₄	—	5	1	no	—
42	C₃×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
43	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
44	D₅	—	2	3	no	—
45	Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
46	D₄	—	5	3	no	—
47	C₂×C₄	—	5	3	no	—
48	C₈	—	5	1	no	—
49	C₈	—	5	3	no	—
50	C₂×C₃	—	10	3	no	—
51	C₂×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₅	C₃×#131	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	5	3	no	—
54	C₄	—	5	1	no	—
55	C₄	C₂×C₃×AGL(1,𝔽₅)	1	3	yes	—
56	C₃	#4133	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	10	3	no	—
58	C₂	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×Q₈	C₄
socle	C₂×C₃×C₅	C₂²×C₄
prime radical	C₃×#713	C₂
cosocle	Dic₅	C₂³×C₃
hypercenter	C₃×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×#700	C₂	semidirect
3. C₃×D₅⋊C₈	C₂	semidirect
4. #4133	C₃	direct (N × H)
12. #700	C₂×C₃	semidirect
13. D₅⋊C₈	C₂×C₃	semidirect
39. C₃×C₅	#131	semidirect
52. C₅	C₃×#131	semidirect
56. C₃	#4133	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×#713	2
C₃×#700	2
C₃×D₅⋊C₈	2
#4133	3
C₃×#131	5

Subgroups — C3×#4133 #91979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4133 #91979