Finite Group Databasebeta

← C₅×C₁₃×D₇₃ #23748751

Subgroups — C₅×C₁₃×D₇₃ #23748751

Order 9490.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₇₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₁₃	—	73	1	no	maximal, Hall
8	C₇₃	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₃	D₇₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	73	1	no	Hall
11	C₁₃	C₅×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	73	1	no	Hall
13	C₅	C₁₃×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	73	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₇₃	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₇₃	C₂	semidirect
2. C₁₃×D₇₃	C₅	direct (N × H)
3. C₁₃×C₇₃	C₂×C₅	semidirect
4. C₅×D₇₃	C₁₃	direct (N × H)
5. C₅×C₇₃	C₂×C₁₃	semidirect
6. D₇₃	C₅×C₁₃	direct (N × H)
8. C₇₃	C₂×C₅×C₁₃	semidirect
9. C₅×C₁₃	D₇₃	direct (N × H)
11. C₁₃	C₅×D₇₃	direct (N × H)
13. C₅	C₁₃×D₇₃	direct (N × H)