Subgroups — C₂×C₅×C₄₇×D₃₇ #46852011

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₇×D₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₇×D₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃₇×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented
6	C₄₇×D₃₇	C₂×C₅	1	2	yes	direct product factor
7	C₃₇×C₄₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₄₇	—	37	1	no	maximal, Hall
9	C₂×C₅×D₃₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₄₇	—	37	2	no	—
11	C₂×C₅×C₄₇	D₃₇	1	1	yes	characteristic, direct product factor
12	C₂×C₅×C₃₇	C₂×C₄₇	1	1	yes	characteristic, complemented
13	C₅×D₃₇	C₂×C₄₇	1	2	yes	direct product factor
14	C₅×C₄₇	C₂×D₃₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₄₇	—	37	1	no	Hall
16	C₅×C₃₇	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃₇	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₄₇	—	37	2	no	—
19	C₂×C₄₇	C₅×D₃₇	1	1	yes	characteristic, direct product factor
20	C₂×C₃₇	C₂×C₅×C₄₇	1	1	yes	characteristic, complemented
21	D₃₇	C₂×C₅×C₄₇	1	2	yes	direct product factor
22	C₄₇	C₂×C₅×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₇	C₂²×C₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₅	—	37	1	no	Hall
25	C₂×C₅	—	37	2	no	—
26	C₂×C₅	C₄₇×D₃₇	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₄₇×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	37	1	no	Sylow
29	C₂	—	37	2	no	—
30	C₂	C₅×C₄₇×D₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₄₇	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂²×C₅×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₇×C₄₇	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₅×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₇×D₃₇	C₂	direct (N × H)
2. C₂×C₅×C₃₇×C₄₇	C₂	semidirect
3. C₅×C₃₇×C₄₇	C₂²	semidirect
4. C₂×C₄₇×D₃₇	C₅	direct (N × H)
5. C₂×C₃₇×C₄₇	C₂×C₅	semidirect
6. C₄₇×D₃₇	C₂×C₅	direct (N × H)
7. C₃₇×C₄₇	C₂²×C₅	semidirect
9. C₂×C₅×D₃₇	C₄₇	direct (N × H)
11. C₂×C₅×C₄₇	D₃₇	direct (N × H)
12. C₂×C₅×C₃₇	C₂×C₄₇	semidirect
13. C₅×D₃₇	C₂×C₄₇	direct (N × H)
14. C₅×C₄₇	C₂×D₃₇	direct (N × H)
16. C₅×C₃₇	C₂²×C₄₇	semidirect
17. C₂×D₃₇	C₅×C₄₇	direct (N × H)
19. C₂×C₄₇	C₅×D₃₇	direct (N × H)
20. C₂×C₃₇	C₂×C₅×C₄₇	semidirect
21. D₃₇	C₂×C₅×C₄₇	direct (N × H)
22. C₄₇	C₂×C₅×D₃₇	direct (N × H)
23. C₃₇	C₂²×C₅×C₄₇	semidirect
26. C₂×C₅	C₄₇×D₃₇	direct (N × H)
27. C₅	C₂×C₄₇×D₃₇	direct (N × H)
30. C₂	C₅×C₄₇×D₃₇	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×C₄₇×D₃₇	2
C₂×C₅×C₃₇×C₄₇	2
C₂×C₄₇×D₃₇	5
C₂²×C₅×C₄₇	37
C₂×C₅×D₃₇	47

Subgroups — C2×C5×C47×D37 #46852011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₄₇×D₃₇ #46852011