Finite Group Databasebeta

← C₅×C₁₃×D₇₁ #22604367

Subgroups — C₅×C₁₃×D₇₁ #22604367

Order 9230.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₇₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₇₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₁₃	—	71	1	no	maximal, Hall
8	C₇₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₃	D₇₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	71	1	no	Hall
11	C₁₃	C₅×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	71	1	no	Hall
13	C₅	C₁₃×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₇₁
commutator, hypocenter	C₇₁	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₇₁	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₇₁	C₂	semidirect
2. C₁₃×D₇₁	C₅	direct (N × H)
3. C₁₃×C₇₁	C₂×C₅	semidirect
4. C₅×D₇₁	C₁₃	direct (N × H)
5. C₅×C₇₁	C₂×C₁₃	semidirect
6. D₇₁	C₅×C₁₃	direct (N × H)
8. C₇₁	C₂×C₅×C₁₃	semidirect
9. C₅×C₁₃	D₇₁	direct (N × H)
11. C₁₃	C₅×D₇₁	direct (N × H)
13. C₅	C₁₃×D₇₁	direct (N × H)