Subgroups — C₃×#4015 #91586

Order 480.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₀	C₂	1	2	yes	maximal
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₅	C₂	1	4	yes	maximal
4	#4015	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
7	C₂×C₃×Dic₅	C₂²	1	4	yes	—
8	C₃×Dic₁₀	—	2	4	no	—
9	C₃×C₄⋊Q₈	—	5	1	no	maximal, Hall
10	C₂×Dic₁₀	C₂×C₃	1	2	yes	—
11	C₄²×C₅	C₂×C₃	1	1	yes	characteristic
12	C₄⋊Dic₅	C₂×C₃	1	4	yes	—
13	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
14	C₃×C₄×C₅	D₄	1	2	yes	—
15	C₃×C₄×C₅	Q₈	1	4	yes	complemented
16	C₃×Dic₅	—	2	4	no	—
17	C₂×C₃×Q₈	—	5	2	no	—
18	C₃×C₄⋊C₄	—	5	4	no	—
19	C₃×C₄²	D₅	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
21	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
22	C₂×Dic₅	C₂²×C₃	1	4	yes	—
23	Dic₁₀	—	2	4	no	—
24	C₄⋊Q₈	—	5	1	no	Sylow
25	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
26	C₂×C₃×C₅	C₂×Q₈	1	2	yes	—
27	C₃×Q₈	—	10	4	no	—
28	C₂×C₃×C₄	—	5	4	no	—
29	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
30	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
31	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
32	C₄×C₅	C₃×D₄	1	2	yes	—
33	C₄×C₅	C₃×Q₈	1	4	yes	complemented
34	Dic₅	—	2	4	no	—
35	C₂×Q₈	—	5	2	no	—
36	C₄⋊C₄	—	5	4	no	—
37	C₄²	C₃×D₅	1	1	yes	characteristic
38	C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
40	C₃×C₄	—	10	4	no	—
41	C₃×C₄	Dic₁₀	1	4	yes	complemented
42	C₃×C₄	D₂₀	1	2	yes	—
43	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
44	C₂×C₅	C₂×C₃×Q₈	1	2	yes	—
45	Q₈	—	10	4	no	—
46	C₂×C₄	—	5	4	no	—
47	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
48	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
49	C₂×C₃	C₂×Dic₁₀	1	2	yes	—
50	C₂×C₃	C₂×D₂₀	1	1	yes	characteristic
51	C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
53	C₄	—	10	4	no	—
54	C₄	C₃×Dic₁₀	1	4	yes	complemented
55	C₄	C₃×D₂₀	1	2	yes	—
56	C₃	#4015	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	C₂×C₃×Dic₁₀	1	2	yes	—
58	C₂	C₂×C₃×D₂₀	1	1	yes	characteristic

	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, prime radical	C₂²×C₃×C₅	C₂³
hypercenter	C₃×C₄²	D₅
hypocenter	C₅	C₃×C₄⋊Q₈
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
4. #4015	C₃	direct (N × H)
15. C₃×C₄×C₅	Q₈	semidirect
33. C₄×C₅	C₃×Q₈	semidirect
38. C₃×C₅	C₄⋊Q₈	semidirect
41. C₃×C₄	Dic₁₀	semidirect
51. C₅	C₃×C₄⋊Q₈	semidirect
54. C₄	C₃×Dic₁₀	semidirect
56. C₃	#4015	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×Dic₁₀	2
C₃×C₄²×C₅	2
C₃×C₄⋊Dic₅	2
#4015	3
C₃×C₄⋊Q₈	5

Subgroups — C3×#4015 #91586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4015 #91586