Subgroups — C₃²×C₅×C₁₇×C₄₁ #44535852

Order 31365.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₄₁	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₁₇×C₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₇×C₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₁₇×C₄₁	C₃×C₅	1	4	yes	direct product factor
5	C₃²×C₅×C₄₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₅×C₁₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×C₄₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅×C₄₁	C₃×C₁₇	1	4	yes	direct product factor
9	C₃²×C₄₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₁₇	C₃×C₄₁	1	4	yes	direct product factor
11	C₅×C₄₁	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₁₇	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₄₁	C₃×C₅×C₁₇	1	4	yes	direct product factor
14	C₅×C₁₇	C₃²×C₄₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₇	C₃×C₅×C₄₁	1	4	yes	direct product factor
16	C₃²×C₅	C₁₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
17	C₄₁	C₃²×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₇	C₃²×C₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₃×C₁₇×C₄₁	1	4	yes	direct product factor
20	C₃²	C₅×C₁₇×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃²×C₁₇×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₅×C₁₇×C₄₁	1	4	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₄₁	C₃	direct (N × H)
2. C₃²×C₁₇×C₄₁	C₅	direct (N × H)
3. C₅×C₁₇×C₄₁	C₃²	direct (N × H)
4. C₃×C₁₇×C₄₁	C₃×C₅	direct (N × H)
5. C₃²×C₅×C₄₁	C₁₇	direct (N × H)
6. C₃²×C₅×C₁₇	C₄₁	direct (N × H)
7. C₁₇×C₄₁	C₃²×C₅	direct (N × H)
8. C₃×C₅×C₄₁	C₃×C₁₇	direct (N × H)
9. C₃²×C₄₁	C₅×C₁₇	direct (N × H)
10. C₃×C₅×C₁₇	C₃×C₄₁	direct (N × H)
11. C₅×C₄₁	C₃²×C₁₇	direct (N × H)
12. C₃²×C₁₇	C₅×C₄₁	direct (N × H)
13. C₃×C₄₁	C₃×C₅×C₁₇	direct (N × H)
14. C₅×C₁₇	C₃²×C₄₁	direct (N × H)
15. C₃×C₁₇	C₃×C₅×C₄₁	direct (N × H)
16. C₃²×C₅	C₁₇×C₄₁	direct (N × H)
17. C₄₁	C₃²×C₅×C₁₇	direct (N × H)
18. C₁₇	C₃²×C₅×C₄₁	direct (N × H)
19. C₃×C₅	C₃×C₁₇×C₄₁	direct (N × H)
20. C₃²	C₅×C₁₇×C₄₁	direct (N × H)
21. C₅	C₃²×C₁₇×C₄₁	direct (N × H)
22. C₃	C₃×C₅×C₁₇×C₄₁	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×C₄₁	3
C₃²×C₁₇×C₄₁	5
C₃²×C₅×C₄₁	17
C₃²×C₅×C₁₇	41

Subgroups — C32×C5×C17×C41 #44535852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₁₇×C₄₁ #44535852