Subgroups — C₃×#4005 #91209

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₃×#704	C₂	1	2	yes	maximal
3	#4005	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₅	C₄	1	1	yes	characteristic
6	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
7	C₃×Dic₁₀	—	2	2	no	—
8	C₃×#170	—	2	2	no	—
9	C₃×#101	—	5	1	no	maximal, Hall
10	C₂×Dic₁₀	C₂×C₃	1	1	yes	characteristic
11	#704	C₂×C₃	1	2	yes	—
12	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₅	—	2	1	no	—
14	C₃×Dic₅	—	2	1	no	—
15	C₃×Dic₅	D₄	1	2	yes	—
16	C₂×C₃×Q₈	—	5	1	no	—
17	C₃×M₁₆	—	5	2	no	—
18	C₂×C₄×C₅	C₃×C₄	1	1	yes	characteristic
19	C₂×Dic₅	C₃×C₄	1	1	yes	characteristic
20	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
21	Dic₁₀	—	2	2	no	—
22	#170	—	2	2	no	—
23	#101	—	5	1	no	Sylow
24	C₂×C₃×C₅	—	2	1	no	—
25	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
26	C₃×Q₈	—	10	2	no	—
27	C₂×C₃×C₄	—	5	1	no	—
28	C₂×C₃×C₄	—	5	1	no	—
29	C₂×C₃×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₃×C₈	—	10	2	no	—
31	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
32	C₄×C₅	—	2	1	no	—
33	Dic₅	—	2	1	no	—
34	Dic₅	C₃×D₄	1	2	yes	—
35	C₂×Q₈	—	5	1	no	—
36	M₁₆	—	5	2	no	—
37	C₃×C₅	#101	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	5	2	no	—
41	C₃×C₄	—	10	1	no	—
42	C₂×C₅	—	2	1	no	—
43	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
44	Q₈	—	10	2	no	—
45	C₂×C₄	—	5	1	no	—
46	C₂×C₄	—	5	1	no	—
47	C₂×C₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
48	C₈	—	10	2	no	—
49	C₂×C₃	—	2	1	no	—
50	C₂×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
51	C₅	C₃×#101	1	1	yes	characteristic, complemented, Sylow
52	C₂²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	5	2	no	—
55	C₄	—	10	1	no	—
56	C₃	#4005	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	2	1	no	—
58	C₂	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²⋊AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂×C₃×C₄
Frattini	C₂²	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄×C₅	C₄
socle	C₂×C₃×C₅	C₂²⋊C₄
prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×Dic₅	C₂²×C₃
hypercenter	C₂×C₃×C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #4005	C₃	direct (N × H)
37. C₃×C₅	#101	semidirect
51. C₅	C₃×#101	semidirect
56. C₃	#4005	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×#704	2
#4005	3
C₃×#101	5

Subgroups — C3×#4005 #91209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4005 #91209