Finite Group Databasebeta

← C₅²×C₄₃⋊C₇ #21419081

Subgroups — C₅²×C₄₃⋊C₇ #21419081

Order 7525.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₃⋊C₇	C₅	1	6	yes	maximal, direct product factor
2	C₅²×C₄₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃⋊C₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
4	C₅×C₄₃	C₅×C₇	1	6	yes	complemented
5	C₅²×C₇	—	43	1	no	maximal, Hall
6	C₄₃	C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
7	C₅×C₇	—	43	6	no	—
8	C₅²	C₄₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₇	—	43	1	no	Sylow
10	C₅	C₅×C₄₃⋊C₇	1	6	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₅²	C₄₃⋊C₇
commutator, hypocenter	C₄₃	C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₄₃	C₇
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₃⋊C₇	C₅	direct (N × H)
2. C₅²×C₄₃	C₇	semidirect
3. C₄₃⋊C₇	C₅²	direct (N × H)
4. C₅×C₄₃	C₅×C₇	semidirect
6. C₄₃	C₅²×C₇	semidirect
8. C₅²	C₄₃⋊C₇	direct (N × H)
10. C₅	C₅×C₄₃⋊C₇	direct (N × H)