Finite Group Databasebeta

← C₇×C₂₉×C₅₃ #24924459

Subgroups — C₇×C₂₉×C₅₃ #24924459

Order 10759.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₇×C₅₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₂₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅₃	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
5	C₂₉	C₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₇	C₂₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₅₃	C₇	direct (N × H)
2. C₇×C₅₃	C₂₉	direct (N × H)
3. C₇×C₂₉	C₅₃	direct (N × H)
4. C₅₃	C₇×C₂₉	direct (N × H)
5. C₂₉	C₇×C₅₃	direct (N × H)
6. C₇	C₂₉×C₅₃	direct (N × H)