Finite Group Databasebeta

← C₂×C₃×C₅×C₇ #6153

Subgroups — C₂×C₃×C₅×C₇ #6153

Order 210.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇	C₂×C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₅	C₂×C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₃	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₅×C₇	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	C₂	direct (N × H)
2. C₂×C₅×C₇	C₃	direct (N × H)
3. C₂×C₃×C₇	C₅	direct (N × H)
4. C₅×C₇	C₂×C₃	direct (N × H)
5. C₂×C₃×C₅	C₇	direct (N × H)
6. C₃×C₇	C₂×C₅	direct (N × H)
7. C₃×C₅	C₂×C₇	direct (N × H)
8. C₂×C₇	C₃×C₅	direct (N × H)
9. C₂×C₅	C₃×C₇	direct (N × H)
10. C₇	C₂×C₃×C₅	direct (N × H)
11. C₂×C₃	C₅×C₇	direct (N × H)
12. C₅	C₂×C₃×C₇	direct (N × H)
13. C₃	C₂×C₅×C₇	direct (N × H)
14. C₂	C₃×C₅×C₇	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	2
C₂×C₅×C₇	3
C₂×C₃×C₇	5
C₂×C₃×C₅	7