Finite Group Databasebeta

← D₁₇×C₅₃⋊C₁₃ #37552838

Subgroups — D₁₇×C₅₃⋊C₁₃ #37552838

Order 23426.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅₃⋊C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇×C₅₃	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅₃⋊C₁₃	—	17	1	no	maximal, Hall
4	C₁₇×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₅₃⋊C₁₃	D₁₇	1	1	yes	characteristic, direct product factor, Hall
6	C₁₃×D₁₇	—	53	1	no	maximal, Hall
7	C₁₃×C₁₇	—	53	1	no	Hall
8	C₂×C₅₃	—	17	1	no	Hall
9	C₅₃	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
10	D₁₇	C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₃	—	901	1	no	Hall
12	C₁₇	C₂×C₅₃⋊C₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	—	53	1	no	Sylow
14	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₅₃	C₂×C₁₃
LCS	G ▷ C₁₇×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅₃⋊C₁₃	C₂	semidirect
2. D₁₇×C₅₃	C₁₃	semidirect
4. C₁₇×C₅₃	C₂×C₁₃	semidirect
5. C₅₃⋊C₁₃	D₁₇	direct (N × H)
9. C₅₃	C₁₃×D₁₇	semidirect
10. D₁₇	C₅₃⋊C₁₃	direct (N × H)
12. C₁₇	C₂×C₅₃⋊C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₅₃⋊C₁₃	2
D₁₇×C₅₃	13
C₂×C₅₃⋊C₁₃	17
C₁₃×D₁₇	53