Subgroups — C₂²×C₃×C₄₇×C₅₉ #45685409

Order 33276.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₇×C₅₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₄₇×C₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄₇×C₅₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₄₇×C₅₉	C₂×C₃	1	3	yes	direct product factor
5	C₄₇×C₅₉	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₃×C₅₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅₉	C₂×C₄₇	1	3	yes	direct product factor
9	C₂×C₃×C₄₇	C₂×C₅₉	1	3	yes	direct product factor
10	C₂²×C₅₉	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₄₇	C₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅₉	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₄₇	C₂²×C₅₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅₉	C₂×C₃×C₄₇	1	3	yes	direct product factor
15	C₂×C₄₇	C₂×C₃×C₅₉	1	3	yes	direct product factor
16	C₅₉	C₂²×C₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₇	C₂²×C₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	C₄₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₄₇×C₅₉	1	3	yes	direct product factor
20	C₂²	C₃×C₄₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₄₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₄₇×C₅₉	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×C₃×C₄₇×C₅₉	C₂	direct (N × H)
2. C₂²×C₄₇×C₅₉	C₃	direct (N × H)
3. C₃×C₄₇×C₅₉	C₂²	direct (N × H)
4. C₂×C₄₇×C₅₉	C₂×C₃	direct (N × H)
5. C₄₇×C₅₉	C₂²×C₃	direct (N × H)
6. C₂²×C₃×C₅₉	C₄₇	direct (N × H)
7. C₂²×C₃×C₄₇	C₅₉	direct (N × H)
8. C₂×C₃×C₅₉	C₂×C₄₇	direct (N × H)
9. C₂×C₃×C₄₇	C₂×C₅₉	direct (N × H)
10. C₂²×C₅₉	C₃×C₄₇	direct (N × H)
11. C₂²×C₄₇	C₃×C₅₉	direct (N × H)
12. C₃×C₅₉	C₂²×C₄₇	direct (N × H)
13. C₃×C₄₇	C₂²×C₅₉	direct (N × H)
14. C₂×C₅₉	C₂×C₃×C₄₇	direct (N × H)
15. C₂×C₄₇	C₂×C₃×C₅₉	direct (N × H)
16. C₅₉	C₂²×C₃×C₄₇	direct (N × H)
17. C₄₇	C₂²×C₃×C₅₉	direct (N × H)
18. C₂²×C₃	C₄₇×C₅₉	direct (N × H)
19. C₂×C₃	C₂×C₄₇×C₅₉	direct (N × H)
20. C₂²	C₃×C₄₇×C₅₉	direct (N × H)
21. C₃	C₂²×C₄₇×C₅₉	direct (N × H)
22. C₂	C₂×C₃×C₄₇×C₅₉	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×C₃×C₄₇×C₅₉	2
C₂²×C₄₇×C₅₉	3
C₂²×C₃×C₅₉	47
C₂²×C₃×C₄₇	59

Subgroups — C22×C3×C47×C59 #45685409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄₇×C₅₉ #45685409