Finite Group Databasebeta

← C₃×C₅×D₃₄₇ #23780980

Subgroups — C₃×C₅×D₃₄₇ #23780980

Order 10410.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₃₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₃₄₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₃₄₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₅	—	347	1	no	maximal, Hall
9	C₃×C₅	D₃₄₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅	—	347	1	no	Hall
11	C₂×C₃	—	347	1	no	Hall
12	C₅	C₃×D₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₃	C₅×D₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	347	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₃₄₇
commutator, cosocle, hypocenter	C₃₄₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₄₇	C₂
LCS	G ▷ C₃₄₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₃₄₇	C₂	semidirect
2. C₅×D₃₄₇	C₃	direct (N × H)
3. C₃×D₃₄₇	C₅	direct (N × H)
4. C₅×C₃₄₇	C₂×C₃	semidirect
5. C₃×C₃₄₇	C₂×C₅	semidirect
6. D₃₄₇	C₃×C₅	direct (N × H)
7. C₃₄₇	C₂×C₃×C₅	semidirect
9. C₃×C₅	D₃₄₇	direct (N × H)
12. C₅	C₃×D₃₄₇	direct (N × H)
13. C₃	C₅×D₃₄₇	direct (N × H)