Finite Group Databasebeta

← C₃₁×#10625202 #37525852

Subgroups — C₃₁×#10625202 #37525852

Order 22971.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×C₁₉⋊C₃	—	13	1	no	maximal, Hall
3	C₃₁×C₁₃⋊C₃	—	19	1	no	maximal, Hall
4	#10625202	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₃₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₁₉	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
8	C₃×C₃₁	—	247	1	no	Hall
9	C₁₉⋊C₃	—	13	1	no	Hall
10	C₁₃⋊C₃	—	19	1	no	Hall
11	C₃₁	#10625202	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₉	C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	C₃₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₃	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	#10625202
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉×C₃₁	C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₃₁	C₃	semidirect
4. #10625202	C₃₁	direct (N × H)
5. C₁₉×C₃₁	C₁₃⋊C₃	semidirect
6. C₁₃×C₃₁	C₁₉⋊C₃	semidirect
7. C₁₃×C₁₉	C₃×C₃₁	semidirect
11. C₃₁	#10625202	direct (N × H)
12. C₁₉	C₃₁×C₁₃⋊C₃	semidirect
13. C₁₃	C₃₁×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₃₁	3
C₃₁×C₁₉⋊C₃	13
C₃₁×C₁₃⋊C₃	19
#10625202	31