Finite Group Databasebeta

← C₂×C₇×C₁₃×C₅₉ #24924380

Subgroups — C₂×C₇×C₁₃×C₅₉ #24924380

Order 10738.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₇×C₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₅₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
5	C₇×C₅₉	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₇×C₁₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₃	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Hall
9	C₅₉	C₂×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₃	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇	C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃	C₂×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₂×C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₇×C₁₃×C₅₉	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. C₇×C₁₃×C₅₉	C₂	direct (N × H)
2. C₂×C₁₃×C₅₉	C₇	direct (N × H)
3. C₂×C₇×C₅₉	C₁₃	direct (N × H)
4. C₁₃×C₅₉	C₂×C₇	direct (N × H)
5. C₇×C₅₉	C₂×C₁₃	direct (N × H)
6. C₂×C₇×C₁₃	C₅₉	direct (N × H)
7. C₂×C₅₉	C₇×C₁₃	direct (N × H)
8. C₇×C₁₃	C₂×C₅₉	direct (N × H)
9. C₅₉	C₂×C₇×C₁₃	direct (N × H)
10. C₂×C₁₃	C₇×C₅₉	direct (N × H)
11. C₂×C₇	C₁₃×C₅₉	direct (N × H)
12. C₁₃	C₂×C₇×C₅₉	direct (N × H)
13. C₇	C₂×C₁₃×C₅₉	direct (N × H)
14. C₂	C₇×C₁₃×C₅₉	direct (N × H)