Finite Group Databasebeta

← C₂×C₅×C₁₇×C₆₁ #23780489

Subgroups — C₂×C₅×C₁₇×C₆₁ #23780489

Order 10370.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₆₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇×C₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₆₁	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅×C₆₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₆₁	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₁₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₆₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₇	C₂×C₆₁	1	1	yes	characteristic, direct product factor, Hall
9	C₆₁	C₂×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₇	C₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
11	C₁₇	C₂×C₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₁₇×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×C₁₇×C₆₁	C₂	direct (N × H)
2. C₂×C₁₇×C₆₁	C₅	direct (N × H)
3. C₁₇×C₆₁	C₂×C₅	direct (N × H)
4. C₂×C₅×C₆₁	C₁₇	direct (N × H)
5. C₅×C₆₁	C₂×C₁₇	direct (N × H)
6. C₂×C₅×C₁₇	C₆₁	direct (N × H)
7. C₂×C₆₁	C₅×C₁₇	direct (N × H)
8. C₅×C₁₇	C₂×C₆₁	direct (N × H)
9. C₆₁	C₂×C₅×C₁₇	direct (N × H)
10. C₂×C₁₇	C₅×C₆₁	direct (N × H)
11. C₁₇	C₂×C₅×C₆₁	direct (N × H)
12. C₂×C₅	C₁₇×C₆₁	direct (N × H)
13. C₅	C₂×C₁₇×C₆₁	direct (N × H)
14. C₂	C₅×C₁₇×C₆₁	direct (N × H)