Finite Group Databasebeta

← C₇×C₁₃⋊C₃×C₁₁₃ #44524746

Subgroups — C₇×C₁₃⋊C₃×C₁₁₃ #44524746

Order 30849.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₁₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×C₁₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₁₃	—	13	1	no	maximal, Hall
4	C₁₃×C₁₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₁₃	—	13	1	no	Hall
7	C₇×C₁₃⋊C₃	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁₃	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₇×C₁₃	C₃×C₁₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃⋊C₃	C₇×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇	—	13	1	no	Hall
12	C₁₃	C₃×C₇×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₇	C₁₃⋊C₃×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₇×C₁₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇×C₁₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₁₁₃	C₃	semidirect
2. C₁₃⋊C₃×C₁₁₃	C₇	direct (N × H)
4. C₁₃×C₁₁₃	C₃×C₇	semidirect
5. C₇×C₁₁₃	C₁₃⋊C₃	direct (N × H)
7. C₇×C₁₃⋊C₃	C₁₁₃	direct (N × H)
8. C₁₁₃	C₇×C₁₃⋊C₃	direct (N × H)
9. C₇×C₁₃	C₃×C₁₁₃	semidirect
10. C₁₃⋊C₃	C₇×C₁₁₃	direct (N × H)
12. C₁₃	C₃×C₇×C₁₁₃	semidirect
13. C₇	C₁₃⋊C₃×C₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₁₁₃	3
C₁₃⋊C₃×C₁₁₃	7
C₃×C₇×C₁₁₃	13
C₇×C₁₃⋊C₃	113