Finite Group Databasebeta

← C₂×C₁₃²×C₈₃ #43242575

Subgroups — C₂×C₁₃²×C₈₃ #43242575

Order 28054.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₈₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₈₃	C₁₃	1	14	yes	maximal, direct product factor
3	C₁₃×C₈₃	C₂×C₁₃	1	14	yes	direct product factor
4	C₂×C₁₃²	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃²	C₂×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₈₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₈₃	C₂×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₁₃	C₁₃×C₈₃	1	14	yes	direct product factor
9	C₁₃	C₂×C₁₃×C₈₃	1	14	yes	direct product factor
10	C₂	C₁₃²×C₈₃	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. C₁₃²×C₈₃	C₂	direct (N × H)
2. C₂×C₁₃×C₈₃	C₁₃	direct (N × H)
3. C₁₃×C₈₃	C₂×C₁₃	direct (N × H)
4. C₂×C₁₃²	C₈₃	direct (N × H)
5. C₁₃²	C₂×C₈₃	direct (N × H)
6. C₂×C₈₃	C₁₃²	direct (N × H)
7. C₈₃	C₂×C₁₃²	direct (N × H)
8. C₂×C₁₃	C₁₃×C₈₃	direct (N × H)
9. C₁₃	C₂×C₁₃×C₈₃	direct (N × H)
10. C₂	C₁₃²×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
C₁₃²×C₈₃	2
C₂×C₁₃×C₈₃	13
C₂×C₁₃²	83