Subgroups — C₃×#4022 #91593

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#685	C₂	1	3	yes	maximal
3	C₃×#683	C₂	1	3	yes	maximal, complemented
4	#4022	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₃×Dic₅	C₂²	1	3	yes	—
8	C₃×#126	—	5	1	no	maximal, Hall
9	C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
10	#685	C₂×C₃	1	3	yes	—
11	#683	C₂×C₃	1	3	yes	complemented
12	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
13	C₂×C₃×D₅	—	2	3	no	—
14	C₃×C₄×C₅	—	2	3	no	—
15	C₃×Dic₅	—	2	3	no	—
16	C₃×C₄⋊C₄	—	5	3	no	—
17	C₃×C₂²⋊C₄	—	5	3	no	—
18	C₃×C₄²	D₅	1	1	yes	characteristic, complemented
19	C₂²×D₅	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
21	C₂×Dic₅	C₂²×C₃	1	3	yes	—
22	#126	—	5	1	no	Sylow
23	C₂×C₃×C₅	#41	1	3	yes	—
24	C₃×D₅	—	4	1	no	—
25	C₂³×C₃	—	5	1	no	—
26	C₂×C₃×C₄	—	5	3	no	—
27	C₂×C₃×C₄	C₂×D₅	1	3	yes	—
28	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
29	C₂×D₅	—	2	3	no	—
30	C₄×C₅	—	2	3	no	—
31	Dic₅	—	2	3	no	—
32	C₄⋊C₄	—	5	3	no	—
33	C₂²⋊C₄	—	5	3	no	—
34	C₄²	C₃×D₅	1	1	yes	characteristic, complemented
35	C₃×C₅	#126	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃	—	10	3	no	—
37	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
38	C₃×C₄	—	2	3	no	—
39	C₃×C₄	—	10	3	no	—
40	C₂×C₅	C₃×#41	1	3	yes	—
41	D₅	—	4	1	no	—
42	C₂³	—	5	1	no	—
43	C₂×C₄	—	5	3	no	—
44	C₂×C₄	C₂×C₃×D₅	1	3	yes	—
45	C₂×C₃	—	20	1	no	—
46	C₂×C₃	#709	1	3	yes	—
47	C₅	C₃×#126	1	1	yes	characteristic, complemented, Sylow
48	C₂²	—	10	3	no	—
49	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	10	3	no	—
52	C₃	#4022	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	—	20	1	no	—
54	C₂	C₃×#709	1	3	yes	—

	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	C₂²×C₃×C₅	C₂³
prime radical	C₂²×C₃×D₅	C₂²
hypercenter	C₃×C₄²	D₅
hypocenter	C₅	C₃×#126
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
1. C₃×C₄²×C₅	C₂	semidirect
3. C₃×#683	C₂	semidirect
4. #4022	C₃	direct (N × H)
9. C₄²×C₅	C₂×C₃	semidirect
11. #683	C₂×C₃	semidirect
18. C₃×C₄²	D₅	semidirect
34. C₄²	C₃×D₅	semidirect
35. C₃×C₅	#126	semidirect
47. C₅	C₃×#126	semidirect
52. C₃	#4022	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×C₄²×C₅	2
C₃×#685	2
C₃×#683	2
#4022	3
C₃×#126	5

Subgroups — C3×#4022 #91593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4022 #91593