Finite Group Databasebeta

← C₁₃×D₁₃×C₁₀₁ #46802457

Subgroups — C₁₃×D₁₃×C₁₀₁ #46802457

Order 34138.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃×C₁₀₁	—	13	1	no	maximal
3	D₁₃×C₁₀₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor
4	C₁₃×C₁₀₁	—	2	6	no	—
5	C₁₃×C₁₀₁	D₁₃	1	1	yes	characteristic, direct product factor
6	C₁₃×C₁₀₁	C₂×C₁₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₃	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₀₁	—	13	1	no	Hall
9	C₁₃²	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
10	C₁₀₁	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₃	—	13	1	no	—
12	D₁₃	C₁₃×C₁₀₁	1	1	yes	characteristic, direct product factor
13	C₁₃	—	2	6	no	—
14	C₁₃	D₁₃×C₁₀₁	1	1	yes	characteristic, direct product factor
15	C₁₃	C₂×C₁₃×C₁₀₁	1	1	yes	characteristic, complemented
16	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₀₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₃×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₁₃²×C₁₀₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₃×C₁₀₁

Complements

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

N	H ≅ G/N	type
1. C₁₃²×C₁₀₁	C₂	semidirect
3. D₁₃×C₁₀₁	C₁₃	direct (N × H)
5. C₁₃×C₁₀₁	D₁₃	direct (N × H)
6. C₁₃×C₁₀₁	C₂×C₁₃	semidirect
7. C₁₃×D₁₃	C₁₀₁	direct (N × H)
9. C₁₃²	C₂×C₁₀₁	semidirect
10. C₁₀₁	C₁₃×D₁₃	direct (N × H)
12. D₁₃	C₁₃×C₁₀₁	direct (N × H)
14. C₁₃	D₁₃×C₁₀₁	direct (N × H)
15. C₁₃	C₂×C₁₃×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃²×C₁₀₁	2
C₂×C₁₃×C₁₀₁	13
D₁₃×C₁₀₁	13
C₁₃×D₁₃	101