Finite Group Databasebeta

← C₂×C₃×C₁₇₈₉ #24924376

Subgroups — C₂×C₃×C₁₇₈₉ #24924376

Order 10734.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇₈₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇₈₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇₈₉	C₂×C₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₃	C₁₇₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃	C₂×C₁₇₈₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	C₃×C₁₇₈₉	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. C₃×C₁₇₈₉	C₂	direct (N × H)
2. C₂×C₁₇₈₉	C₃	direct (N × H)
3. C₁₇₈₉	C₂×C₃	direct (N × H)
4. C₂×C₃	C₁₇₈₉	direct (N × H)
5. C₃	C₂×C₁₇₈₉	direct (N × H)
6. C₂	C₃×C₁₇₈₉	direct (N × H)