Finite Group Databasebeta

← C₁₃×D₁₃×C₄₁ #28357331

Subgroups — C₁₃×D₁₃×C₄₁ #28357331

Order 13858.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃×C₄₁	—	13	1	no	maximal
3	D₁₃×C₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor
4	C₁₃×C₄₁	—	2	6	no	—
5	C₁₃×C₄₁	D₁₃	1	1	yes	characteristic, direct product factor
6	C₁₃×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃²	C₂×C₄₁	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₄₁	—	13	1	no	Hall
10	C₄₁	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₃	—	13	1	no	—
12	D₁₃	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor
13	C₁₃	—	2	6	no	—
14	C₁₃	D₁₃×C₄₁	1	1	yes	characteristic, direct product factor
15	C₁₃	C₂×C₁₃×C₄₁	1	1	yes	characteristic, complemented
16	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₄₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₃²×C₄₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₃²×C₄₁	C₂	semidirect
3. D₁₃×C₄₁	C₁₃	direct (N × H)
5. C₁₃×C₄₁	D₁₃	direct (N × H)
6. C₁₃×C₄₁	C₂×C₁₃	semidirect
7. C₁₃×D₁₃	C₄₁	direct (N × H)
8. C₁₃²	C₂×C₄₁	semidirect
10. C₄₁	C₁₃×D₁₃	direct (N × H)
12. D₁₃	C₁₃×C₄₁	direct (N × H)
14. C₁₃	D₁₃×C₄₁	direct (N × H)
15. C₁₃	C₂×C₁₃×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃²×C₄₁	2
C₂×C₁₃×C₄₁	13
D₁₃×C₄₁	13
C₁₃×D₁₃	41