Finite Group Databasebeta

← C₅×C₁₇×C₄₃⋊C₃ #24926608

Subgroups — C₅×C₁₇×C₄₃⋊C₃ #24926608

Order 10965.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₄₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₄₃⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₇	—	43	1	no	maximal, Hall
6	C₅×C₄₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₄₃⋊C₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₇	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₇	—	43	1	no	Hall
10	C₄₃	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
11	C₁₇	C₅×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	—	43	1	no	Hall
13	C₅	C₁₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₄₃	C₃	semidirect
2. C₁₇×C₄₃⋊C₃	C₅	direct (N × H)
3. C₁₇×C₄₃	C₃×C₅	semidirect
4. C₅×C₄₃⋊C₃	C₁₇	direct (N × H)
6. C₅×C₄₃	C₃×C₁₇	semidirect
7. C₄₃⋊C₃	C₅×C₁₇	direct (N × H)
8. C₅×C₁₇	C₄₃⋊C₃	direct (N × H)
10. C₄₃	C₃×C₅×C₁₇	semidirect
11. C₁₇	C₅×C₄₃⋊C₃	direct (N × H)
13. C₅	C₁₇×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₁₇×C₄₃	3
C₁₇×C₄₃⋊C₃	5
C₅×C₄₃⋊C₃	17
C₃×C₅×C₁₇	43