Finite Group Databasebeta

← D₅×C₁₃×C₁₃₁ #30684591

Subgroups — D₅×C₁₃×C₁₃₁ #30684591

Order 17030.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃×C₁₃₁	—	5	1	no	maximal, Hall
3	C₁₃×C₁₃₁	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃₁	—	5	1	no	Hall
7	C₁₃₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
8	D₅×C₁₃	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₃	C₂×C₁₃₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	—	5	1	no	Hall
11	C₁₃	D₅×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₁₃×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₁₃×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₃₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₃×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₃₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₃×C₁₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₁₃₁	C₂	semidirect
3. C₁₃×C₁₃₁	D₅	direct (N × H)
4. D₅×C₁₃₁	C₁₃	direct (N × H)
5. C₅×C₁₃₁	C₂×C₁₃	semidirect
7. C₁₃₁	D₅×C₁₃	direct (N × H)
8. D₅×C₁₃	C₁₃₁	direct (N × H)
9. C₅×C₁₃	C₂×C₁₃₁	semidirect
11. C₁₃	D₅×C₁₃₁	direct (N × H)
12. D₅	C₁₃×C₁₃₁	direct (N × H)
13. C₅	C₂×C₁₃×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₁₃₁	2
C₂×C₁₃×C₁₃₁	5
D₅×C₁₃₁	13
D₅×C₁₃	131