Finite Group Databasebeta

← C₂×C₅×C₂₃×C₁₀₁ #37551189

Subgroups — C₂×C₅×C₂₃×C₁₀₁ #37551189

Order 23230.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₁₀₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₃×C₁₀₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₁₀₁	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅×C₁₀₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₀₁	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₂₃	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₀₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₃	C₂×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₀₁	C₂×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₂₃	C₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂₃	C₂×C₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	C₂₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₂₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₂₃×C₁₀₁	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. C₅×C₂₃×C₁₀₁	C₂	direct (N × H)
2. C₂×C₂₃×C₁₀₁	C₅	direct (N × H)
3. C₂₃×C₁₀₁	C₂×C₅	direct (N × H)
4. C₂×C₅×C₁₀₁	C₂₃	direct (N × H)
5. C₅×C₁₀₁	C₂×C₂₃	direct (N × H)
6. C₂×C₅×C₂₃	C₁₀₁	direct (N × H)
7. C₂×C₁₀₁	C₅×C₂₃	direct (N × H)
8. C₅×C₂₃	C₂×C₁₀₁	direct (N × H)
9. C₁₀₁	C₂×C₅×C₂₃	direct (N × H)
10. C₂×C₂₃	C₅×C₁₀₁	direct (N × H)
11. C₂₃	C₂×C₅×C₁₀₁	direct (N × H)
12. C₂×C₅	C₂₃×C₁₀₁	direct (N × H)
13. C₅	C₂×C₂₃×C₁₀₁	direct (N × H)
14. C₂	C₅×C₂₃×C₁₀₁	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×C₂₃×C₁₀₁	2
C₂×C₂₃×C₁₀₁	5
C₂×C₅×C₁₀₁	23
C₂×C₅×C₂₃	101