Subgroups — C₂²×C₅×C₃₇×C₄₇ #46851990

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₇×C₄₇	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₃₇×C₄₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₃₇×C₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃₇×C₄₇	C₂×C₅	1	3	yes	direct product factor
5	C₃₇×C₄₇	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₅×C₄₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₃₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₄₇	C₂×C₃₇	1	3	yes	direct product factor
9	C₂×C₅×C₃₇	C₂×C₄₇	1	3	yes	direct product factor
10	C₅×C₄₇	C₂²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₄₇	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₃₇	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃₇	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₄₇	C₂×C₅×C₃₇	1	3	yes	direct product factor
15	C₂×C₃₇	C₂×C₅×C₄₇	1	3	yes	direct product factor
16	C₄₇	C₂²×C₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₂²×C₅×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₅	C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₂×C₃₇×C₄₇	1	3	yes	direct product factor
20	C₅	C₂²×C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₅×C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₃₇×C₄₇	1	3	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. C₂×C₅×C₃₇×C₄₇	C₂	direct (N × H)
2. C₅×C₃₇×C₄₇	C₂²	direct (N × H)
3. C₂²×C₃₇×C₄₇	C₅	direct (N × H)
4. C₂×C₃₇×C₄₇	C₂×C₅	direct (N × H)
5. C₃₇×C₄₇	C₂²×C₅	direct (N × H)
6. C₂²×C₅×C₄₇	C₃₇	direct (N × H)
7. C₂²×C₅×C₃₇	C₄₇	direct (N × H)
8. C₂×C₅×C₄₇	C₂×C₃₇	direct (N × H)
9. C₂×C₅×C₃₇	C₂×C₄₇	direct (N × H)
10. C₅×C₄₇	C₂²×C₃₇	direct (N × H)
11. C₂²×C₄₇	C₅×C₃₇	direct (N × H)
12. C₅×C₃₇	C₂²×C₄₇	direct (N × H)
13. C₂²×C₃₇	C₅×C₄₇	direct (N × H)
14. C₂×C₄₇	C₂×C₅×C₃₇	direct (N × H)
15. C₂×C₃₇	C₂×C₅×C₄₇	direct (N × H)
16. C₄₇	C₂²×C₅×C₃₇	direct (N × H)
17. C₃₇	C₂²×C₅×C₄₇	direct (N × H)
18. C₂²×C₅	C₃₇×C₄₇	direct (N × H)
19. C₂×C₅	C₂×C₃₇×C₄₇	direct (N × H)
20. C₅	C₂²×C₃₇×C₄₇	direct (N × H)
21. C₂²	C₅×C₃₇×C₄₇	direct (N × H)
22. C₂	C₂×C₅×C₃₇×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₃₇×C₄₇	2
C₂²×C₃₇×C₄₇	5
C₂²×C₅×C₄₇	37
C₂²×C₅×C₃₇	47

Subgroups — C22×C5×C37×C47 #46851990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₃₇×C₄₇ #46851990