Finite Group Databasebeta

← C₂×C₅×D₃₀₇ #20259596

Subgroups — C₂×C₅×D₃₀₇ #20259596

Order 6140.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃₀₇	C₂	1	2	yes	maximal, direct product factor
3	C₅×C₃₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₃₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃₀₇	C₂×C₅	1	1	yes	characteristic, complemented
6	D₃₀₇	C₂×C₅	1	2	yes	direct product factor
7	C₃₀₇	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₅	—	307	1	no	maximal, Hall
9	C₂×C₅	—	307	2	no	—
10	C₂×C₅	D₃₀₇	1	1	yes	characteristic, direct product factor
11	C₅	C₂×D₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²	—	307	1	no	Sylow
13	C₂	—	307	2	no	—
14	C₂	C₅×D₃₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₃₀₇
commutator, hypocenter	C₃₀₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₀₇	C₂
LCS	G ▷ C₃₀₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₃₀₇	C₂	semidirect
2. C₅×D₃₀₇	C₂	direct (N × H)
3. C₅×C₃₀₇	C₂²	semidirect
4. C₂×D₃₀₇	C₅	direct (N × H)
5. C₂×C₃₀₇	C₂×C₅	semidirect
6. D₃₀₇	C₂×C₅	direct (N × H)
7. C₃₀₇	C₂²×C₅	semidirect
10. C₂×C₅	D₃₀₇	direct (N × H)
11. C₅	C₂×D₃₀₇	direct (N × H)
14. C₂	C₅×D₃₀₇	direct (N × H)