Subgroups — C₃×C₅×D₅×C₁₆₃ #37587366

Order 24450.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₁₆₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅×C₁₆₃	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅×C₁₆₃	—	5	1	no	maximal
5	C₅²×C₁₆₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₆₃	—	2	2	no	—
7	C₃×C₅×C₁₆₃	D₅	1	1	yes	characteristic, direct product factor
8	C₃×C₅×C₁₆₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×C₁₆₃	—	5	1	no	—
10	D₅×C₁₆₃	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₁₆₃	—	5	1	no	Hall
12	C₅×C₁₆₃	—	2	2	no	—
13	C₅×C₁₆₃	C₃×D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₁₆₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	C₃×C₁₆₃	C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₆₃	—	5	1	no	Hall
17	C₁₆₃	C₃×C₅×D₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₅×D₅	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃×C₅²	C₂×C₁₆₃	1	1	yes	characteristic, complemented, Hall
20	C₅×D₅	C₃×C₁₆₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅	—	5	1	no	—
22	C₃×D₅	C₅×C₁₆₃	1	1	yes	characteristic, direct product factor
23	C₅²	C₂×C₃×C₁₆₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₅	—	2	2	no	—
25	C₃×C₅	D₅×C₁₆₃	1	1	yes	characteristic, direct product factor
26	C₃×C₅	C₂×C₅×C₁₆₃	1	1	yes	characteristic, complemented
27	C₂×C₅	—	5	1	no	—
28	D₅	C₃×C₅×C₁₆₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃	—	5	1	no	Hall
30	C₅	—	2	2	no	—
31	C₅	C₂×C₃×C₅×C₁₆₃	1	1	yes	characteristic, complemented
32	C₅	C₃×D₅×C₁₆₃	1	1	yes	characteristic, direct product factor
33	C₃	C₅×D₅×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₆₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₅×C₁₆₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₆₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₅×C₁₆₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₆₃	C₂	semidirect
2. C₅×D₅×C₁₆₃	C₃	direct (N × H)
3. C₃×D₅×C₁₆₃	C₅	direct (N × H)
5. C₅²×C₁₆₃	C₂×C₃	semidirect
7. C₃×C₅×C₁₆₃	D₅	direct (N × H)
8. C₃×C₅×C₁₆₃	C₂×C₅	semidirect
10. D₅×C₁₆₃	C₃×C₅	direct (N × H)
13. C₅×C₁₆₃	C₃×D₅	direct (N × H)
14. C₅×C₁₆₃	C₂×C₃×C₅	semidirect
15. C₃×C₁₆₃	C₅×D₅	direct (N × H)
17. C₁₆₃	C₃×C₅×D₅	direct (N × H)
18. C₃×C₅×D₅	C₁₆₃	direct (N × H)
19. C₃×C₅²	C₂×C₁₆₃	semidirect
20. C₅×D₅	C₃×C₁₆₃	direct (N × H)
22. C₃×D₅	C₅×C₁₆₃	direct (N × H)
23. C₅²	C₂×C₃×C₁₆₃	semidirect
25. C₃×C₅	D₅×C₁₆₃	direct (N × H)
26. C₃×C₅	C₂×C₅×C₁₆₃	semidirect
28. D₅	C₃×C₅×C₁₆₃	direct (N × H)
31. C₅	C₂×C₃×C₅×C₁₆₃	semidirect
32. C₅	C₃×D₅×C₁₆₃	direct (N × H)
33. C₃	C₅×D₅×C₁₆₃	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×C₅²×C₁₆₃	2
C₅×D₅×C₁₆₃	3
C₃×D₅×C₁₆₃	5
C₂×C₃×C₅×C₁₆₃	5
C₃×C₅×D₅	163

Subgroups — C3×C5×D5×C163 #37587366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₅×C₁₆₃ #37587366