Finite Group Databasebeta

← C₁₇×C₁₃⋊C₃×C₄₃ #43250013

Subgroups — C₁₇×C₁₃⋊C₃×C₄₃ #43250013

Order 28509.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₇×C₄₃	—	13	1	no	maximal, Hall
3	C₁₃⋊C₃×C₄₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₄₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₁₇×C₁₃⋊C₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₁₇	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₃	—	13	1	no	Hall
9	C₃×C₁₇	—	13	1	no	Hall
10	C₄₃	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₁₃⋊C₃	C₁₇×C₄₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₇	C₁₃⋊C₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	C₃×C₁₇×C₄₃	1	1	yes	characteristic, complemented, Sylow
14	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₄₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₁₇×C₄₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₄₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₇×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₄₃	C₃	semidirect
3. C₁₃⋊C₃×C₄₃	C₁₇	direct (N × H)
4. C₁₇×C₄₃	C₁₃⋊C₃	direct (N × H)
5. C₁₇×C₁₃⋊C₃	C₄₃	direct (N × H)
6. C₁₃×C₄₃	C₃×C₁₇	semidirect
7. C₁₃×C₁₇	C₃×C₄₃	semidirect
10. C₄₃	C₁₇×C₁₃⋊C₃	direct (N × H)
11. C₁₃⋊C₃	C₁₇×C₄₃	direct (N × H)
12. C₁₇	C₁₃⋊C₃×C₄₃	direct (N × H)
13. C₁₃	C₃×C₁₇×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₇×C₄₃	3
C₃×C₁₇×C₄₃	13
C₁₃⋊C₃×C₄₃	17
C₁₇×C₁₃⋊C₃	43