Finite Group Databasebeta

← C₃³×C₅×C₁₀₃ #72192126

Subgroups — C₃³×C₅×C₁₀₃ #72192126

Order 13905.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₀₃	C₃	1	13	yes	maximal, direct product factor
2	C₃³×C₁₀₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₀₃	C₃²	1	13	yes	direct product factor
4	C₃²×C₁₀₃	C₃×C₅	1	13	yes	direct product factor
5	C₅×C₁₀₃	C₃³	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₀₃	C₃²×C₅	1	13	yes	direct product factor
7	C₃³×C₅	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₀₃	C₃³×C₅	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²×C₅	C₃×C₁₀₃	1	13	yes	direct product factor
10	C₃³	C₅×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×C₅	C₃²×C₁₀₃	1	13	yes	direct product factor
12	C₃²	C₃×C₅×C₁₀₃	1	13	yes	direct product factor
13	C₅	C₃³×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₃²×C₅×C₁₀₃	1	13	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. C₃²×C₅×C₁₀₃	C₃	direct (N × H)
2. C₃³×C₁₀₃	C₅	direct (N × H)
3. C₃×C₅×C₁₀₃	C₃²	direct (N × H)
4. C₃²×C₁₀₃	C₃×C₅	direct (N × H)
5. C₅×C₁₀₃	C₃³	direct (N × H)
6. C₃×C₁₀₃	C₃²×C₅	direct (N × H)
7. C₃³×C₅	C₁₀₃	direct (N × H)
8. C₁₀₃	C₃³×C₅	direct (N × H)
9. C₃²×C₅	C₃×C₁₀₃	direct (N × H)
10. C₃³	C₅×C₁₀₃	direct (N × H)
11. C₃×C₅	C₃²×C₁₀₃	direct (N × H)
12. C₃²	C₃×C₅×C₁₀₃	direct (N × H)
13. C₅	C₃³×C₁₀₃	direct (N × H)
14. C₃	C₃²×C₅×C₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₀₃	3
C₃³×C₁₀₃	5
C₃³×C₅	103