Subgroups — C₃×D₅×A₄ #67212

Order 360.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₅	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×A₄	C₃	1	3	yes	maximal, direct product factor
4	C₃²×D₅	—	4	1	no	maximal
5	C₂×C₃×A₄	—	5	1	no	maximal, Hall
6	C₂²×C₃×C₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₅	—	3	1	no	—
8	C₂×C₃×D₅	—	3	1	no	—
9	C₅×A₄	C₂×C₃	1	3	yes	complemented
10	C₃²×C₅	—	4	1	no	Hall
11	C₂²×D₅	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×A₄	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₃×C₅	—	3	1	no	—
14	C₃×D₅	—	3	1	no	—
15	C₃×D₅	—	4	3	no	—
16	C₃×D₅	A₄	1	1	yes	characteristic, direct product factor
17	C₂³×C₃	—	5	1	no	—
18	C₂×A₄	—	5	3	no	—
19	C₂²×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₂×D₅	—	3	1	no	—
21	C₂×D₅	—	3	1	no	—
22	C₂×C₃²	—	20	1	no	—
23	C₃×C₅	—	4	3	no	—
24	C₃×C₅	C₂×A₄	1	1	yes	characteristic, complemented
25	C₂²×C₃	—	15	1	no	—
26	C₂²×C₃	—	15	1	no	—
27	C₂²×C₃	C₃×D₅	1	1	yes	characteristic, complemented
28	A₄	C₃×D₅	1	3	yes	direct product factor
29	C₂×C₅	—	3	1	no	—
30	D₅	—	3	1	no	—
31	D₅	C₃×A₄	1	1	yes	characteristic, direct product factor
32	C₃²	—	4	1	no	Sylow
33	C₂³	—	5	1	no	Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂×C₃	—	5	1	no	—
36	C₂×C₃	—	15	1	no	—
37	C₂×C₃	—	20	3	no	—
38	C₅	C₂×C₃×A₄	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	15	1	no	—
40	C₂²	—	15	1	no	—
41	C₂²	C₃²×D₅	1	1	yes	characteristic, complemented
42	C₃	—	4	3	no	—
43	C₃	D₅×A₄	1	1	yes	characteristic, direct product factor
44	C₂	—	3	1	no	—
45	C₂	—	5	1	no	—
46	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×A₄
commutator, cosocle, hypocenter	C₂²×C₅	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅	C₂×C₃
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×A₄	C₂	semidirect
2. C₂²×C₃×D₅	C₃	semidirect
3. D₅×A₄	C₃	direct (N × H)
6. C₂²×C₃×C₅	C₂×C₃	semidirect
9. C₅×A₄	C₂×C₃	semidirect
11. C₂²×D₅	C₃²	semidirect
12. C₃×A₄	D₅	direct (N × H)
16. C₃×D₅	A₄	direct (N × H)
19. C₂²×C₅	C₂×C₃²	semidirect
24. C₃×C₅	C₂×A₄	semidirect
27. C₂²×C₃	C₃×D₅	semidirect
28. A₄	C₃×D₅	direct (N × H)
31. D₅	C₃×A₄	direct (N × H)
38. C₅	C₂×C₃×A₄	semidirect
41. C₂²	C₃²×D₅	semidirect
43. C₃	D₅×A₄	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×A₄	2
C₂²×C₃×D₅	3
D₅×A₄	3
C₃²×D₅	4
C₂×C₃×A₄	5

Subgroups — C3×D5×A4 #67212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×A₄ #67212