Finite Group Databasebeta

← C₅²×C₉×C₁₀₃ #37550751

Subgroups — C₅²×C₉×C₁₀₃ #37550751

Order 23175.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₀₃	C₃	1	1	yes	maximal, characteristic
2	C₅×C₉×C₁₀₃	C₅	1	6	yes	maximal, direct product factor
3	C₅²×C₁₀₃	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅×C₁₀₃	C₃×C₅	1	6	yes	—
5	C₉×C₁₀₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₁₀₃	C₅×C₉	1	6	yes	direct product factor
7	C₃×C₁₀₃	C₃×C₅²	1	1	yes	characteristic
8	C₅²×C₉	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₀₃	C₅²×C₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₅²	C₃×C₁₀₃	1	1	yes	characteristic
11	C₅×C₉	C₅×C₁₀₃	1	6	yes	direct product factor
12	C₅²	C₉×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₅	C₃×C₅×C₁₀₃	1	6	yes	—
14	C₉	C₅²×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₅	C₅×C₉×C₁₀₃	1	6	yes	direct product factor
16	C₃	C₃×C₅²×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅²×C₁₀₃
socle, prime radical	C₃×C₅²×C₁₀₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×C₉×C₁₀₃	C₅	direct (N × H)
3. C₅²×C₁₀₃	C₉	direct (N × H)
5. C₉×C₁₀₃	C₅²	direct (N × H)
6. C₅×C₁₀₃	C₅×C₉	direct (N × H)
8. C₅²×C₉	C₁₀₃	direct (N × H)
9. C₁₀₃	C₅²×C₉	direct (N × H)
11. C₅×C₉	C₅×C₁₀₃	direct (N × H)
12. C₅²	C₉×C₁₀₃	direct (N × H)
14. C₉	C₅²×C₁₀₃	direct (N × H)
15. C₅	C₅×C₉×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
C₃×C₅²×C₁₀₃	3
C₅×C₉×C₁₀₃	5
C₅²×C₉	103