Subgroups — C₂×C₃×C₅×C₇×C₂₁₁ #56004607

Order 44310.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₂₁₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇×C₂₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₇×C₂₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₂₁₁	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₂₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×C₂₁₁	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₂₁₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇×C₂₁₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₂₁₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₂₁₁	C₂×C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₂₁₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₂₁₁	C₂×C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₂₁₁	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₁₁	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂₁₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₅×C₇	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₅×C₇	C₂×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₇	C₃×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₇	C₅×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₇	C₂×C₃×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅	C₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₇	C₂×C₅×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅	C₂×C₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₇	C₃×C₅×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅	C₃×C₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₇	C₂×C₃×C₅×C₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₅×C₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅	C₂×C₃×C₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₅×C₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₅×C₇×C₂₁₁	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. C₃×C₅×C₇×C₂₁₁	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₁₁	C₃	direct (N × H)
3. C₂×C₃×C₇×C₂₁₁	C₅	direct (N × H)
4. C₅×C₇×C₂₁₁	C₂×C₃	direct (N × H)
5. C₂×C₃×C₅×C₂₁₁	C₇	direct (N × H)
6. C₃×C₇×C₂₁₁	C₂×C₅	direct (N × H)
7. C₃×C₅×C₂₁₁	C₂×C₇	direct (N × H)
8. C₂×C₇×C₂₁₁	C₃×C₅	direct (N × H)
9. C₂×C₅×C₂₁₁	C₃×C₇	direct (N × H)
10. C₇×C₂₁₁	C₂×C₃×C₅	direct (N × H)
11. C₂×C₃×C₂₁₁	C₅×C₇	direct (N × H)
12. C₅×C₂₁₁	C₂×C₃×C₇	direct (N × H)
13. C₃×C₂₁₁	C₂×C₅×C₇	direct (N × H)
14. C₂×C₂₁₁	C₃×C₅×C₇	direct (N × H)
15. C₂₁₁	C₂×C₃×C₅×C₇	direct (N × H)
16. C₂×C₃×C₅×C₇	C₂₁₁	direct (N × H)
17. C₃×C₅×C₇	C₂×C₂₁₁	direct (N × H)
18. C₂×C₅×C₇	C₃×C₂₁₁	direct (N × H)
19. C₂×C₃×C₇	C₅×C₂₁₁	direct (N × H)
20. C₅×C₇	C₂×C₃×C₂₁₁	direct (N × H)
21. C₂×C₃×C₅	C₇×C₂₁₁	direct (N × H)
22. C₃×C₇	C₂×C₅×C₂₁₁	direct (N × H)
23. C₃×C₅	C₂×C₇×C₂₁₁	direct (N × H)
24. C₂×C₇	C₃×C₅×C₂₁₁	direct (N × H)
25. C₂×C₅	C₃×C₇×C₂₁₁	direct (N × H)
26. C₇	C₂×C₃×C₅×C₂₁₁	direct (N × H)
27. C₂×C₃	C₅×C₇×C₂₁₁	direct (N × H)
28. C₅	C₂×C₃×C₇×C₂₁₁	direct (N × H)
29. C₃	C₂×C₅×C₇×C₂₁₁	direct (N × H)
30. C₂	C₃×C₅×C₇×C₂₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₂₁₁	2
C₂×C₅×C₇×C₂₁₁	3
C₂×C₃×C₇×C₂₁₁	5
C₂×C₃×C₅×C₂₁₁	7
C₂×C₃×C₅×C₇	211

Subgroups — C2×C3×C5×C7×C211 #56004607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₇×C₂₁₁ #56004607