Finite Group Databasebeta

← C₇×D₁₃×C₅₉ #24924382

Subgroups — C₇×D₁₃×C₅₉ #24924382

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, complemented, Hall
2	D₁₃×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₇×C₅₉	—	13	1	no	maximal, Hall
4	C₁₃×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₅₉	D₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₇×D₁₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅₉	—	13	1	no	Hall
8	C₇×C₁₃	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
9	C₅₉	C₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	D₁₃	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇	—	13	1	no	Hall
12	C₁₃	C₂×C₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
13	C₇	D₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₅₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₅₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇×C₅₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×C₁₃×C₅₉	C₂	semidirect
2. D₁₃×C₅₉	C₇	direct (N × H)
4. C₁₃×C₅₉	C₂×C₇	semidirect
5. C₇×C₅₉	D₁₃	direct (N × H)
6. C₇×D₁₃	C₅₉	direct (N × H)
8. C₇×C₁₃	C₂×C₅₉	semidirect
9. C₅₉	C₇×D₁₃	direct (N × H)
10. D₁₃	C₇×C₅₉	direct (N × H)
12. C₁₃	C₂×C₇×C₅₉	semidirect
13. C₇	D₁₃×C₅₉	direct (N × H)