Subgroups — C₂×C₃×C₅×C₁₇×C₃₁ #30629020

Order 15810.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₇×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₇×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₇×C₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₅×C₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×C₃₁	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₃₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅×C₁₇	C₂×C₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₃₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₇	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₁₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₃₁	C₂×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₁₇	C₂×C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₇	C₂×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₇	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₃×C₅	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
24	C₁₇	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅	C₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅	C₂×C₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow

	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×C₃₁	C₂	direct (N × H)
2. C₂×C₅×C₁₇×C₃₁	C₃	direct (N × H)
3. C₂×C₃×C₁₇×C₃₁	C₅	direct (N × H)
4. C₅×C₁₇×C₃₁	C₂×C₃	direct (N × H)
5. C₃×C₁₇×C₃₁	C₂×C₅	direct (N × H)
6. C₂×C₁₇×C₃₁	C₃×C₅	direct (N × H)
7. C₂×C₃×C₅×C₃₁	C₁₇	direct (N × H)
8. C₁₇×C₃₁	C₂×C₃×C₅	direct (N × H)
9. C₂×C₃×C₅×C₁₇	C₃₁	direct (N × H)
10. C₃×C₅×C₃₁	C₂×C₁₇	direct (N × H)
11. C₂×C₅×C₃₁	C₃×C₁₇	direct (N × H)
12. C₃×C₅×C₁₇	C₂×C₃₁	direct (N × H)
13. C₂×C₃×C₃₁	C₅×C₁₇	direct (N × H)
14. C₂×C₅×C₁₇	C₃×C₃₁	direct (N × H)
15. C₅×C₃₁	C₂×C₃×C₁₇	direct (N × H)
16. C₂×C₃×C₁₇	C₅×C₃₁	direct (N × H)
17. C₃×C₃₁	C₂×C₅×C₁₇	direct (N × H)
18. C₅×C₁₇	C₂×C₃×C₃₁	direct (N × H)
19. C₂×C₃₁	C₃×C₅×C₁₇	direct (N × H)
20. C₃×C₁₇	C₂×C₅×C₃₁	direct (N × H)
21. C₂×C₁₇	C₃×C₅×C₃₁	direct (N × H)
22. C₃₁	C₂×C₃×C₅×C₁₇	direct (N × H)
23. C₂×C₃×C₅	C₁₇×C₃₁	direct (N × H)
24. C₁₇	C₂×C₃×C₅×C₃₁	direct (N × H)
25. C₃×C₅	C₂×C₁₇×C₃₁	direct (N × H)
26. C₂×C₅	C₃×C₁₇×C₃₁	direct (N × H)
27. C₂×C₃	C₅×C₁₇×C₃₁	direct (N × H)
28. C₅	C₂×C₃×C₁₇×C₃₁	direct (N × H)
29. C₃	C₂×C₅×C₁₇×C₃₁	direct (N × H)
30. C₂	C₃×C₅×C₁₇×C₃₁	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×C₃₁	2
C₂×C₅×C₁₇×C₃₁	3
C₂×C₃×C₁₇×C₃₁	5
C₂×C₃×C₅×C₃₁	17
C₂×C₃×C₅×C₁₇	31

Subgroups — C2×C3×C5×C17×C31 #30629020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₇×C₃₁ #30629020