Finite Group Databasebeta

← C₃×C₅×C₃₇×C₆₁ #46799650

Subgroups — C₃×C₅×C₃₇×C₆₁ #46799650

Order 33855.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₃₇×C₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₇×C₆₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅×C₆₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₃₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₆₁	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₃₇	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₆₁	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₃₇	C₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
10	C₆₁	C₃×C₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₇	C₃×C₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	C₃₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₃×C₃₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₅×C₃₇×C₆₁	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. C₅×C₃₇×C₆₁	C₃	direct (N × H)
2. C₃×C₃₇×C₆₁	C₅	direct (N × H)
3. C₃₇×C₆₁	C₃×C₅	direct (N × H)
4. C₃×C₅×C₆₁	C₃₇	direct (N × H)
5. C₃×C₅×C₃₇	C₆₁	direct (N × H)
6. C₅×C₆₁	C₃×C₃₇	direct (N × H)
7. C₅×C₃₇	C₃×C₆₁	direct (N × H)
8. C₃×C₆₁	C₅×C₃₇	direct (N × H)
9. C₃×C₃₇	C₅×C₆₁	direct (N × H)
10. C₆₁	C₃×C₅×C₃₇	direct (N × H)
11. C₃₇	C₃×C₅×C₆₁	direct (N × H)
12. C₃×C₅	C₃₇×C₆₁	direct (N × H)
13. C₅	C₃×C₃₇×C₆₁	direct (N × H)
14. C₃	C₅×C₃₇×C₆₁	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×C₃₇×C₆₁	3
C₃×C₃₇×C₆₁	5
C₃×C₅×C₆₁	37
C₃×C₅×C₃₇	61