Finite Group Databasebeta

← C₅²×C₁₃×C₈₃ #41008661

Subgroups — C₅²×C₁₃×C₈₃ #41008661

Order 26975.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₈₃	C₅	1	6	yes	maximal, direct product factor
2	C₅²×C₈₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₈₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
4	C₅×C₈₃	C₅×C₁₃	1	6	yes	direct product factor
5	C₅²×C₁₃	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₈₃	C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₅×C₁₃	C₅×C₈₃	1	6	yes	direct product factor
8	C₅²	C₁₃×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₁₃	C₅²×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₅	C₅×C₁₃×C₈₃	1	6	yes	direct product factor

	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. C₅×C₁₃×C₈₃	C₅	direct (N × H)
2. C₅²×C₈₃	C₁₃	direct (N × H)
3. C₁₃×C₈₃	C₅²	direct (N × H)
4. C₅×C₈₃	C₅×C₁₃	direct (N × H)
5. C₅²×C₁₃	C₈₃	direct (N × H)
6. C₈₃	C₅²×C₁₃	direct (N × H)
7. C₅×C₁₃	C₅×C₈₃	direct (N × H)
8. C₅²	C₁₃×C₈₃	direct (N × H)
9. C₁₃	C₅²×C₈₃	direct (N × H)
10. C₅	C₅×C₁₃×C₈₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₈₃	5
C₅²×C₈₃	13
C₅²×C₁₃	83