Subgroups — C₂×C₃×C₅×D₃ #4388

Order 180.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₃	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₃×C₅	—	3	1	no	maximal
4	C₂×C₅×D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅	—	2	1	no	—
8	C₂×C₃×C₅	—	3	2	no	—
9	C₂×C₃×C₅	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₅	C₂×C₃	1	1	yes	characteristic, complemented
11	C₅×D₃	C₂×C₃	1	2	yes	direct product factor
12	C₂²×C₅	—	3	1	no	Hall
13	C₂×C₃²	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×D₃	C₂×C₅	1	2	yes	direct product factor
15	C₃×C₅	—	2	1	no	—
16	C₃×C₅	C₂×D₃	1	1	yes	characteristic, direct product factor
17	C₃×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃	—	3	1	no	—
19	C₂×D₃	C₃×C₅	1	1	yes	characteristic, direct product factor
20	C₂×C₅	—	3	2	no	—
21	C₂×C₅	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃	—	2	1	no	—
24	C₂×C₃	—	3	2	no	—
25	C₂×C₃	C₅×D₃	1	1	yes	characteristic, direct product factor
26	C₂×C₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
27	D₃	C₂×C₃×C₅	1	2	yes	direct product factor
28	C₅	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	—	3	1	no	Sylow
30	C₃	—	2	1	no	—
31	C₃	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
33	C₂	—	3	2	no	—
34	C₂	C₃×C₅×D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₅	C₂	semidirect
2. C₃×C₅×D₃	C₂	direct (N × H)
4. C₂×C₅×D₃	C₃	direct (N × H)
5. C₃²×C₅	C₂²	semidirect
6. C₂×C₃×D₃	C₅	direct (N × H)
9. C₂×C₃×C₅	D₃	direct (N × H)
10. C₂×C₃×C₅	C₂×C₃	semidirect
11. C₅×D₃	C₂×C₃	direct (N × H)
13. C₂×C₃²	C₂×C₅	semidirect
14. C₃×D₃	C₂×C₅	direct (N × H)
16. C₃×C₅	C₂×D₃	direct (N × H)
17. C₃×C₅	C₂²×C₃	semidirect
19. C₂×D₃	C₃×C₅	direct (N × H)
21. C₂×C₅	C₃×D₃	direct (N × H)
22. C₃²	C₂²×C₅	semidirect
25. C₂×C₃	C₅×D₃	direct (N × H)
26. C₂×C₃	C₂×C₃×C₅	semidirect
27. D₃	C₂×C₃×C₅	direct (N × H)
28. C₅	C₂×C₃×D₃	direct (N × H)
31. C₃	C₂×C₅×D₃	direct (N × H)
32. C₃	C₂²×C₃×C₅	semidirect
34. C₂	C₃×C₅×D₃	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×C₃²×C₅	2
C₃×C₅×D₃	2
C₂²×C₃×C₅	3
C₂×C₅×D₃	3
C₂×C₃×D₃	5

Subgroups — C2×C3×C5×D3 #4388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×D₃ #4388