Finite Group Databasebeta

← D₅₇×C₃₀₇ #46854397

Subgroups — D₅₇×C₃₀₇ #46854397

Order 34998.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₃₀₇	—	3	1	no	maximal, Hall
3	C₁₉×C₃₀₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₃₀₇	—	19	1	no	maximal, Hall
5	C₃×C₃₀₇	D₁₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃₀₇	—	57	1	no	Hall
7	C₃₀₇	D₅₇	1	1	yes	characteristic, direct product factor, Sylow
8	D₅₇	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₉	C₂×C₃₀₇	1	1	yes	characteristic, complemented, Hall
10	D₁₉	—	3	1	no	Hall
11	C₁₉	D₃×C₃₀₇	1	1	yes	characteristic, complemented, Sylow
12	D₃	—	19	1	no	Hall
13	C₃	D₁₉×C₃₀₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₀₇	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃₀₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₃₀₇	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₃₀₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₃₀₇	C₂	semidirect
3. C₁₉×C₃₀₇	D₃	semidirect
5. C₃×C₃₀₇	D₁₉	semidirect
7. C₃₀₇	D₅₇	direct (N × H)
8. D₅₇	C₃₀₇	direct (N × H)
9. C₃×C₁₉	C₂×C₃₀₇	semidirect
11. C₁₉	D₃×C₃₀₇	semidirect
13. C₃	D₁₉×C₃₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×C₃₀₇	2
D₁₉×C₃₀₇	3
D₃×C₃₀₇	19
D₅₇	307