Subgroups — C₅×D₃×D₅ #64494

Order 300.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	—	3	1	no	maximal, Hall
5	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×D₃	—	5	1	no	maximal
7	D₃×D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₅²	—	3	1	no	—
9	C₅×D₅	—	3	1	no	—
10	C₅×D₅	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₅	—	5	1	no	—
12	D₁₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×D₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₃	—	2	2	no	—
15	C₅×D₃	—	5	1	no	—
16	C₅×D₃	D₅	1	1	yes	characteristic, direct product factor
17	C₅×D₃	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	15	1	no	—
20	C₂×D₅	—	3	1	no	—
21	C₃×C₅	—	2	2	no	—
22	C₃×C₅	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
24	C₂×D₃	—	5	1	no	Hall
25	C₂×C₅	—	3	1	no	—
26	C₂×C₅	—	3	1	no	—
27	C₂×C₅	—	5	1	no	—
28	C₂×C₅	—	6	2	no	—
29	C₂×C₅	—	15	1	no	—
30	D₅	—	3	1	no	—
31	D₅	C₅×D₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	5	1	no	—
33	D₃	—	5	1	no	—
34	D₃	C₅×D₅	1	1	yes	characteristic, direct product factor
35	C₅	—	2	2	no	—
36	C₅	D₃×D₅	1	1	yes	characteristic, direct product factor
37	C₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
38	C₂²	—	15	1	no	Sylow
39	C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	3	1	no	—
41	C₂	—	5	1	no	—
42	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅	C₂	semidirect
2. C₅²×D₃	C₂	semidirect
3. C₃×C₅×D₅	C₂	semidirect
5. C₃×C₅²	C₂²	semidirect
7. D₃×D₅	C₅	direct (N × H)
10. C₅×D₅	D₃	direct (N × H)
12. D₁₅	C₂×C₅	semidirect
13. C₃×D₅	C₂×C₅	semidirect
16. C₅×D₃	D₅	direct (N × H)
17. C₅×D₃	C₂×C₅	semidirect
18. C₅²	C₂×D₃	semidirect
22. C₃×C₅	C₂×D₅	semidirect
23. C₃×C₅	C₂²×C₅	semidirect
31. D₅	C₅×D₃	direct (N × H)
34. D₃	C₅×D₅	direct (N × H)
36. C₅	D₃×D₅	direct (N × H)
37. C₅	C₂×C₅×D₃	semidirect
39. C₃	C₂×C₅×D₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×D₁₅	2
C₅²×D₃	2
C₃×C₅×D₅	2
C₂×C₅×D₅	3
C₂×C₅×D₃	5
D₃×D₅	5

Subgroups — C5×D3×D5 #64494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₅ #64494