Finite Group Databasebeta

← C₁₃×C₂₃×D₁₇ #23779092

Subgroups — C₁₃×C₂₃×D₁₇ #23779092

Order 10166.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₃×C₂₃	—	17	1	no	maximal, Hall
4	C₁₃×D₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₂₃	D₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₁₃×C₁₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₂₃	—	17	1	no	Hall
9	D₁₇	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	17	1	no	Hall
11	C₂₃	C₁₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₇	C₂×C₁₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	C₂₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₂₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₁₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₂₃	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₂₃	C₂	semidirect
2. C₂₃×D₁₇	C₁₃	direct (N × H)
4. C₁₃×D₁₇	C₂₃	direct (N × H)
5. C₁₇×C₂₃	C₂×C₁₃	semidirect
6. C₁₃×C₂₃	D₁₇	direct (N × H)
7. C₁₃×C₁₇	C₂×C₂₃	semidirect
9. D₁₇	C₁₃×C₂₃	direct (N × H)
11. C₂₃	C₁₃×D₁₇	direct (N × H)
12. C₁₇	C₂×C₁₃×C₂₃	semidirect
13. C₁₃	C₂₃×D₁₇	direct (N × H)