Finite Group Databasebeta

← C₃×C₅×C₇×C₆₇ #20296366

Subgroups — C₃×C₅×C₇×C₆₇ #20296366

Order 7035.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇×C₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₆₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₆₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₆₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₇	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₆₇	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₇	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₇	C₅×C₆₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅	C₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇	C₃×C₅×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₅	C₃×C₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₅×C₇×C₆₇	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×C₇×C₆₇	C₃	direct (N × H)
2. C₃×C₇×C₆₇	C₅	direct (N × H)
3. C₃×C₅×C₆₇	C₇	direct (N × H)
4. C₇×C₆₇	C₃×C₅	direct (N × H)
5. C₅×C₆₇	C₃×C₇	direct (N × H)
6. C₃×C₆₇	C₅×C₇	direct (N × H)
7. C₃×C₅×C₇	C₆₇	direct (N × H)
8. C₆₇	C₃×C₅×C₇	direct (N × H)
9. C₅×C₇	C₃×C₆₇	direct (N × H)
10. C₃×C₇	C₅×C₆₇	direct (N × H)
11. C₃×C₅	C₇×C₆₇	direct (N × H)
12. C₇	C₃×C₅×C₆₇	direct (N × H)
13. C₅	C₃×C₇×C₆₇	direct (N × H)
14. C₃	C₅×C₇×C₆₇	direct (N × H)