Subgroups — C₂×C₅×C₇×C₃₇⋊C₃ #21441069

Order 7770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₇×C₃₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₃₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₃₇⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₃₇⋊C₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇×C₃₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₃₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₇⋊C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×C₇	—	37	1	no	maximal, Hall
13	C₅×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
14	C₃₇⋊C₃	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₇	—	37	1	no	Hall
16	C₂×C₃₇	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₇	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇	—	37	1	no	Hall
19	C₃₇	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅	—	37	1	no	Hall
22	C₃×C₇	—	37	1	no	Hall
23	C₃×C₅	—	37	1	no	Hall
24	C₂×C₇	C₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅	C₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
26	C₇	C₂×C₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	37	1	no	Hall
28	C₅	C₂×C₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	37	1	no	Sylow
30	C₂	C₅×C₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	C₃₇⋊C₃
commutator, hypocenter	C₃₇	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₃₇	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₃₇⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₃₇	C₃	semidirect
3. C₂×C₇×C₃₇⋊C₃	C₅	direct (N × H)
4. C₅×C₇×C₃₇	C₂×C₃	semidirect
5. C₂×C₅×C₃₇⋊C₃	C₇	direct (N × H)
6. C₇×C₃₇⋊C₃	C₂×C₅	direct (N × H)
7. C₅×C₃₇⋊C₃	C₂×C₇	direct (N × H)
8. C₂×C₇×C₃₇	C₃×C₅	semidirect
9. C₂×C₅×C₃₇	C₃×C₇	semidirect
10. C₇×C₃₇	C₂×C₃×C₅	semidirect
11. C₂×C₃₇⋊C₃	C₅×C₇	direct (N × H)
13. C₅×C₃₇	C₂×C₃×C₇	semidirect
14. C₃₇⋊C₃	C₂×C₅×C₇	direct (N × H)
16. C₂×C₃₇	C₃×C₅×C₇	semidirect
17. C₂×C₅×C₇	C₃₇⋊C₃	direct (N × H)
19. C₃₇	C₂×C₃×C₅×C₇	semidirect
20. C₅×C₇	C₂×C₃₇⋊C₃	direct (N × H)
24. C₂×C₇	C₅×C₃₇⋊C₃	direct (N × H)
25. C₂×C₅	C₇×C₃₇⋊C₃	direct (N × H)
26. C₇	C₂×C₅×C₃₇⋊C₃	direct (N × H)
28. C₅	C₂×C₇×C₃₇⋊C₃	direct (N × H)
30. C₂	C₅×C₇×C₃₇⋊C₃	direct (N × H)

Subgroups — C2×C5×C7×C37⋊C3 #21441069

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×C₃₇⋊C₃ #21441069