Finite Group Databasebeta

← C₁₃×C₁₇×D₆₁ #41004044

Subgroups — C₁₃×C₁₇×D₆₁ #41004044

Order 26962.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₆₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×D₆₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₆₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₆₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₇	—	61	1	no	maximal, Hall
7	C₁₃×C₁₇	D₆₁	1	1	yes	characteristic, direct product factor, Hall
8	D₆₁	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₆₁	C₂×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₇	—	61	1	no	Hall
11	C₂×C₁₃	—	61	1	no	Hall
12	C₁₇	C₁₃×D₆₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	C₁₇×D₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	61	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₇	D₆₁
commutator, cosocle, hypocenter	C₆₁	C₂×C₁₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₆₁	C₂
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₁₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₆₁	C₂	semidirect
2. C₁₇×D₆₁	C₁₃	direct (N × H)
3. C₁₃×D₆₁	C₁₇	direct (N × H)
4. C₁₇×C₆₁	C₂×C₁₃	semidirect
5. C₁₃×C₆₁	C₂×C₁₇	semidirect
7. C₁₃×C₁₇	D₆₁	direct (N × H)
8. D₆₁	C₁₃×C₁₇	direct (N × H)
9. C₆₁	C₂×C₁₃×C₁₇	semidirect
12. C₁₇	C₁₃×D₆₁	direct (N × H)
13. C₁₃	C₁₇×D₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₇×C₆₁	2
C₁₇×D₆₁	13
C₁₃×D₆₁	17
C₂×C₁₃×C₁₇	61