Subgroups — C₃×C₅×C₁₇×D₄₇ #37561784

Order 23970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₇×D₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×D₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₄₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×D₄₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅×C₁₇	—	47	1	no	maximal, Hall
11	C₅×D₄₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×D₄₇	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₁₇	D₄₇	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₄₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₇	—	47	1	no	Hall
16	C₃×C₄₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₇	—	47	1	no	Hall
18	D₄₇	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₇	C₃×D₄₇	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₇	C₅×D₄₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄₇	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₇	—	47	1	no	Hall
23	C₂×C₃×C₅	—	47	1	no	Hall
24	C₁₇	C₃×C₅×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₁₇×D₄₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅	—	47	1	no	Hall
27	C₂×C₃	—	47	1	no	Hall
28	C₅	C₃×C₁₇×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₁₇×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	47	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₄₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₄₇	C₂	semidirect
2. C₅×C₁₇×D₄₇	C₃	direct (N × H)
3. C₃×C₁₇×D₄₇	C₅	direct (N × H)
4. C₅×C₁₇×C₄₇	C₂×C₃	semidirect
5. C₃×C₁₇×C₄₇	C₂×C₅	semidirect
6. C₁₇×D₄₇	C₃×C₅	direct (N × H)
7. C₃×C₅×D₄₇	C₁₇	direct (N × H)
8. C₁₇×C₄₇	C₂×C₃×C₅	semidirect
9. C₃×C₅×C₄₇	C₂×C₁₇	semidirect
11. C₅×D₄₇	C₃×C₁₇	direct (N × H)
12. C₃×D₄₇	C₅×C₁₇	direct (N × H)
13. C₃×C₅×C₁₇	D₄₇	direct (N × H)
14. C₅×C₄₇	C₂×C₃×C₁₇	semidirect
16. C₃×C₄₇	C₂×C₅×C₁₇	semidirect
18. D₄₇	C₃×C₅×C₁₇	direct (N × H)
19. C₅×C₁₇	C₃×D₄₇	direct (N × H)
20. C₃×C₁₇	C₅×D₄₇	direct (N × H)
21. C₄₇	C₂×C₃×C₅×C₁₇	semidirect
24. C₁₇	C₃×C₅×D₄₇	direct (N × H)
25. C₃×C₅	C₁₇×D₄₇	direct (N × H)
28. C₅	C₃×C₁₇×D₄₇	direct (N × H)
29. C₃	C₅×C₁₇×D₄₇	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×C₁₇×C₄₇	2
C₅×C₁₇×D₄₇	3
C₃×C₁₇×D₄₇	5
C₃×C₅×D₄₇	17
C₂×C₃×C₅×C₁₇	47

Subgroups — C3×C5×C17×D47 #37561784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₇×D₄₇ #37561784