Finite Group Databasebeta

Subgroups — #24925708

Order 10842.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129429	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃₉⋊C₃	—	13	1	no	maximal, Hall
5	C₁₃₉⋊C₃	—	13	1	no	Hall
6	C₂×C₁₃₉	—	13	1	no	Hall
7	C₁₃₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
8	D₁₃⋊C₃	—	139	1	no	maximal, Hall
9	C₁₃⋊C₃	—	139	1	no	Hall
10	D₁₃	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃	C₂×C₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	1807	1	no	Hall
13	C₃	—	1807	1	no	Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₃₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₃₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #19129429	C₂	semidirect
2. D₁₃×C₁₃₉	C₃	semidirect
3. C₁₃×C₁₃₉	C₂×C₃	semidirect
7. C₁₃₉	D₁₃⋊C₃	semidirect
10. D₁₃	C₁₃₉⋊C₃	semidirect
11. C₁₃	C₂×C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#19129429	2
D₁₃×C₁₃₉	3
C₂×C₁₃₉⋊C₃	13
D₁₃⋊C₃	139