Finite Group Databasebeta

← C₅×C₆₇×C₃₁⋊C₃ #44528290

Subgroups — C₅×C₆₇×C₃₁⋊C₃ #44528290

Order 31155.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₇×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₆₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₆₇	—	31	1	no	maximal, Hall
5	C₅×C₃₁⋊C₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₆₇	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₆₇	—	31	1	no	Hall
8	C₅×C₃₁	C₃×C₆₇	1	1	yes	characteristic, complemented, Hall
9	C₃₁⋊C₃	C₅×C₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₆₇	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₃×C₅×C₆₇	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₅	—	31	1	no	Hall
13	C₅	C₆₇×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₆₇	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃×C₅×C₆₇
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₆₇	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₆₇	C₃	semidirect
2. C₆₇×C₃₁⋊C₃	C₅	direct (N × H)
3. C₃₁×C₆₇	C₃×C₅	semidirect
5. C₅×C₃₁⋊C₃	C₆₇	direct (N × H)
6. C₅×C₆₇	C₃₁⋊C₃	direct (N × H)
8. C₅×C₃₁	C₃×C₆₇	semidirect
9. C₃₁⋊C₃	C₅×C₆₇	direct (N × H)
10. C₆₇	C₅×C₃₁⋊C₃	direct (N × H)
11. C₃₁	C₃×C₅×C₆₇	semidirect
13. C₅	C₆₇×C₃₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₃₁×C₆₇	3
C₆₇×C₃₁⋊C₃	5
C₃×C₅×C₆₇	31
C₅×C₃₁⋊C₃	67