Subgroups — C₂²×C₅×C₇×C₂₇₁ #49182005

Order 37940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₂₇₁	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₇×C₂₇₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₇×C₂₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₅×C₂₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₂₇₁	C₂×C₅	1	3	yes	direct product factor
6	C₂×C₅×C₂₇₁	C₂×C₇	1	3	yes	direct product factor
7	C₇×C₂₇₁	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₇₁	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂²×C₂₇₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₇₁	C₂×C₅×C₇	1	3	yes	direct product factor
11	C₂₇₁	C₂²×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₅×C₇	C₂₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₇	C₂×C₂₇₁	1	3	yes	direct product factor
14	C₅×C₇	C₂²×C₂₇₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₇	C₅×C₂₇₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₅	C₇×C₂₇₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₇	C₂×C₅×C₂₇₁	1	3	yes	direct product factor
18	C₂×C₅	C₂×C₇×C₂₇₁	1	3	yes	direct product factor
19	C₇	C₂²×C₅×C₂₇₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₂²×C₇×C₂₇₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₅×C₇×C₂₇₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₇×C₂₇₁	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×C₇×C₂₇₁	C₂	direct (N × H)
2. C₅×C₇×C₂₇₁	C₂²	direct (N × H)
3. C₂²×C₇×C₂₇₁	C₅	direct (N × H)
4. C₂²×C₅×C₂₇₁	C₇	direct (N × H)
5. C₂×C₇×C₂₇₁	C₂×C₅	direct (N × H)
6. C₂×C₅×C₂₇₁	C₂×C₇	direct (N × H)
7. C₇×C₂₇₁	C₂²×C₅	direct (N × H)
8. C₅×C₂₇₁	C₂²×C₇	direct (N × H)
9. C₂²×C₂₇₁	C₅×C₇	direct (N × H)
10. C₂×C₂₇₁	C₂×C₅×C₇	direct (N × H)
11. C₂₇₁	C₂²×C₅×C₇	direct (N × H)
12. C₂²×C₅×C₇	C₂₇₁	direct (N × H)
13. C₂×C₅×C₇	C₂×C₂₇₁	direct (N × H)
14. C₅×C₇	C₂²×C₂₇₁	direct (N × H)
15. C₂²×C₇	C₅×C₂₇₁	direct (N × H)
16. C₂²×C₅	C₇×C₂₇₁	direct (N × H)
17. C₂×C₇	C₂×C₅×C₂₇₁	direct (N × H)
18. C₂×C₅	C₂×C₇×C₂₇₁	direct (N × H)
19. C₇	C₂²×C₅×C₂₇₁	direct (N × H)
20. C₅	C₂²×C₇×C₂₇₁	direct (N × H)
21. C₂²	C₅×C₇×C₂₇₁	direct (N × H)
22. C₂	C₂×C₅×C₇×C₂₇₁	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×C₇×C₂₇₁	2
C₂²×C₇×C₂₇₁	5
C₂²×C₅×C₂₇₁	7
C₂²×C₅×C₇	271

Subgroups — C22×C5×C7×C271 #49182005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₇×C₂₇₁ #49182005