Subgroups — C₂×C₅×C₇×C₁₃×C₃₇ #46797597

Order 33670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₃×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₁₃×C₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₃₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₅×C₇×C₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×C₃₇	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₇×C₃₇	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₃×C₃₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₇×C₁₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₃₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃×C₃₇	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₇×C₁₃	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₃₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₃₇	C₂×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₇	C₂×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₇×C₁₃	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₃	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₃	C₂×C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₇	C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₇	C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₁₃	C₂×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃₇	C₂×C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₅×C₇	C₂×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₁₃	C₅×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	C₅×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
26	C₁₃	C₂×C₅×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₅	C₇×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
28	C₇	C₂×C₅×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₂×C₇×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₅×C₇×C₁₃×C₃₇	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. C₅×C₇×C₁₃×C₃₇	C₂	direct (N × H)
2. C₂×C₇×C₁₃×C₃₇	C₅	direct (N × H)
3. C₂×C₅×C₁₃×C₃₇	C₇	direct (N × H)
4. C₇×C₁₃×C₃₇	C₂×C₅	direct (N × H)
5. C₂×C₅×C₇×C₃₇	C₁₃	direct (N × H)
6. C₅×C₁₃×C₃₇	C₂×C₇	direct (N × H)
7. C₅×C₇×C₃₇	C₂×C₁₃	direct (N × H)
8. C₂×C₁₃×C₃₇	C₅×C₇	direct (N × H)
9. C₂×C₅×C₇×C₁₃	C₃₇	direct (N × H)
10. C₂×C₇×C₃₇	C₅×C₁₃	direct (N × H)
11. C₁₃×C₃₇	C₂×C₅×C₇	direct (N × H)
12. C₅×C₇×C₁₃	C₂×C₃₇	direct (N × H)
13. C₂×C₅×C₃₇	C₇×C₁₃	direct (N × H)
14. C₇×C₃₇	C₂×C₅×C₁₃	direct (N × H)
15. C₅×C₃₇	C₂×C₇×C₁₃	direct (N × H)
16. C₂×C₇×C₁₃	C₅×C₃₇	direct (N × H)
17. C₂×C₅×C₁₃	C₇×C₃₇	direct (N × H)
18. C₇×C₁₃	C₂×C₅×C₃₇	direct (N × H)
19. C₂×C₃₇	C₅×C₇×C₁₃	direct (N × H)
20. C₂×C₅×C₇	C₁₃×C₃₇	direct (N × H)
21. C₅×C₁₃	C₂×C₇×C₃₇	direct (N × H)
22. C₃₇	C₂×C₅×C₇×C₁₃	direct (N × H)
23. C₅×C₇	C₂×C₁₃×C₃₇	direct (N × H)
24. C₂×C₁₃	C₅×C₇×C₃₇	direct (N × H)
25. C₂×C₇	C₅×C₁₃×C₃₇	direct (N × H)
26. C₁₃	C₂×C₅×C₇×C₃₇	direct (N × H)
27. C₂×C₅	C₇×C₁₃×C₃₇	direct (N × H)
28. C₇	C₂×C₅×C₁₃×C₃₇	direct (N × H)
29. C₅	C₂×C₇×C₁₃×C₃₇	direct (N × H)
30. C₂	C₅×C₇×C₁₃×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₃×C₃₇	2
C₂×C₇×C₁₃×C₃₇	5
C₂×C₅×C₁₃×C₃₇	7
C₂×C₅×C₇×C₃₇	13
C₂×C₅×C₇×C₁₃	37

Subgroups — C2×C5×C7×C13×C37 #46797597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₁₃×C₃₇ #46797597