Finite Group Databasebeta

← C₂×C₃×C₁₃×C₁₃₇ #24922708

Subgroups — C₂×C₃×C₁₃×C₁₃₇ #24922708

Order 10686.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₁₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₁₃₇	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃₇	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₃₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₁₃₇	C₂×C₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₃×C₁₃	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₃	C₂×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	C₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃	C₂×C₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	C₁₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₁₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₁₃×C₁₃₇	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×C₁₃×C₁₃₇	C₂	direct (N × H)
2. C₂×C₁₃×C₁₃₇	C₃	direct (N × H)
3. C₁₃×C₁₃₇	C₂×C₃	direct (N × H)
4. C₂×C₃×C₁₃₇	C₁₃	direct (N × H)
5. C₃×C₁₃₇	C₂×C₁₃	direct (N × H)
6. C₂×C₁₃₇	C₃×C₁₃	direct (N × H)
7. C₁₃₇	C₂×C₃×C₁₃	direct (N × H)
8. C₂×C₃×C₁₃	C₁₃₇	direct (N × H)
9. C₃×C₁₃	C₂×C₁₃₇	direct (N × H)
10. C₂×C₁₃	C₃×C₁₃₇	direct (N × H)
11. C₁₃	C₂×C₃×C₁₃₇	direct (N × H)
12. C₂×C₃	C₁₃×C₁₃₇	direct (N × H)
13. C₃	C₂×C₁₃×C₁₃₇	direct (N × H)
14. C₂	C₃×C₁₃×C₁₃₇	direct (N × H)