Finite Group Databasebeta

← C₂×C₁₃⋊C₃×C₂₃₃ #31827872

Subgroups — C₂×C₁₃⋊C₃×C₂₃₃ #31827872

Order 18174.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×C₂₃₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₂₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₂₃₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₃₃	—	13	1	no	maximal, Hall
5	C₃×C₂₃₃	—	13	1	no	Hall
6	C₂×C₂₃₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂₃₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₁₃⋊C₃	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃⋊C₃	C₂×C₂₃₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	C₃×C₂₃₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃	C₂×C₃×C₂₃₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	13	1	no	Hall
13	C₃	—	13	1	no	Sylow
14	C₂	C₁₃⋊C₃×C₂₃₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₂₃₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₂₃₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₂₃₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₂₃₃

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×C₂₃₃	C₂	direct (N × H)
2. C₂×C₁₃×C₂₃₃	C₃	semidirect
3. C₁₃×C₂₃₃	C₂×C₃	semidirect
6. C₂×C₂₃₃	C₁₃⋊C₃	direct (N × H)
7. C₂₃₃	C₂×C₁₃⋊C₃	direct (N × H)
8. C₂×C₁₃⋊C₃	C₂₃₃	direct (N × H)
9. C₁₃⋊C₃	C₂×C₂₃₃	direct (N × H)
10. C₂×C₁₃	C₃×C₂₃₃	semidirect
11. C₁₃	C₂×C₃×C₂₃₃	semidirect
14. C₂	C₁₃⋊C₃×C₂₃₃	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⋊C₃×C₂₃₃	2
C₂×C₁₃×C₂₃₃	3
C₂×C₃×C₂₃₃	13
C₂×C₁₃⋊C₃	233