Finite Group Databasebeta

← C₂×C₅×C₂₉×C₃₇ #24924343

Subgroups — C₂×C₅×C₂₉×C₃₇ #24924343

Order 10730.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×C₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₉×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₃₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅×C₃₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₂₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₃₇	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₂₉	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃₇	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₂₉	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃₇	C₂×C₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₉	C₂×C₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	C₂₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₂₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₂₉×C₃₇	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×C₂₉×C₃₇	C₂	direct (N × H)
2. C₂×C₂₉×C₃₇	C₅	direct (N × H)
3. C₂₉×C₃₇	C₂×C₅	direct (N × H)
4. C₂×C₅×C₃₇	C₂₉	direct (N × H)
5. C₂×C₅×C₂₉	C₃₇	direct (N × H)
6. C₅×C₃₇	C₂×C₂₉	direct (N × H)
7. C₅×C₂₉	C₂×C₃₇	direct (N × H)
8. C₂×C₃₇	C₅×C₂₉	direct (N × H)
9. C₂×C₂₉	C₅×C₃₇	direct (N × H)
10. C₃₇	C₂×C₅×C₂₉	direct (N × H)
11. C₂₉	C₂×C₅×C₃₇	direct (N × H)
12. C₂×C₅	C₂₉×C₃₇	direct (N × H)
13. C₅	C₂×C₂₉×C₃₇	direct (N × H)
14. C₂	C₅×C₂₉×C₃₇	direct (N × H)