Finite Group Databasebeta

← C₅×C₁₁×C₁₇₉ #23754381

Subgroups — C₅×C₁₁×C₁₇₉ #23754381

Order 9845.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₁₇₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
4	C₅×C₁₁	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁	C₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	C₁₁×C₁₇₉	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. C₁₁×C₁₇₉	C₅	direct (N × H)
2. C₅×C₁₇₉	C₁₁	direct (N × H)
3. C₁₇₉	C₅×C₁₁	direct (N × H)
4. C₅×C₁₁	C₁₇₉	direct (N × H)
5. C₁₁	C₅×C₁₇₉	direct (N × H)
6. C₅	C₁₁×C₁₇₉	direct (N × H)