Finite Group Databasebeta

← C₃×C₁₃×C₁₁₃⋊C₇ #44524745

Subgroups — C₃×C₁₃×C₁₁₃⋊C₇ #44524745

Order 30849.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₁₃⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₃×C₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×C₁₁₃⋊C₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₁₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
5	C₁₁₃⋊C₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₁₃	C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₁₃	—	113	1	no	maximal, Hall
8	C₁₁₃	C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₇×C₁₃	—	113	1	no	Hall
10	C₃×C₁₃	C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇	—	113	1	no	Hall
12	C₁₃	C₃×C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	—	113	1	no	Sylow
14	C₃	C₁₃×C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₁₃⋊C₇	C₃	direct (N × H)
2. C₃×C₁₃×C₁₁₃	C₇	semidirect
3. C₃×C₁₁₃⋊C₇	C₁₃	direct (N × H)
4. C₁₃×C₁₁₃	C₃×C₇	semidirect
5. C₁₁₃⋊C₇	C₃×C₁₃	direct (N × H)
6. C₃×C₁₁₃	C₇×C₁₃	semidirect
8. C₁₁₃	C₃×C₇×C₁₃	semidirect
10. C₃×C₁₃	C₁₁₃⋊C₇	direct (N × H)
12. C₁₃	C₃×C₁₁₃⋊C₇	direct (N × H)
14. C₃	C₁₃×C₁₁₃⋊C₇	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×C₁₁₃⋊C₇	3
C₃×C₁₃×C₁₁₃	7
C₃×C₁₁₃⋊C₇	13
C₃×C₇×C₁₃	113