Finite Group Databasebeta

← C₂×C₅²⋊C₃×C₁₀₃ #29508994

Subgroups — C₂×C₅²⋊C₃×C₁₀₃ #29508994

Order 15450.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₀₃	—	3	2	no	—
5	C₂×C₃×C₁₀₃	—	25	1	no	maximal, Hall
6	C₅×C₁₀₃	—	3	2	no	—
7	C₃×C₁₀₃	—	25	1	no	Hall
8	C₂×C₁₀₃	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅²⋊C₃	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₀₃	C₂×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₅²⋊C₃	C₂×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅²	C₃×C₁₀₃	1	1	yes	characteristic, complemented, Hall
13	C₅²	C₂×C₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅	—	3	2	no	—
15	C₂×C₃	—	25	1	no	Hall
16	C₅	—	3	2	no	—
17	C₃	—	25	1	no	Sylow
18	C₂	C₅²⋊C₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₀₃	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₀₃	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₅²⋊C₃×C₁₀₃	C₂	direct (N × H)
2. C₂×C₅²×C₁₀₃	C₃	semidirect
3. C₅²×C₁₀₃	C₂×C₃	semidirect
8. C₂×C₁₀₃	C₅²⋊C₃	direct (N × H)
9. C₂×C₅²⋊C₃	C₁₀₃	direct (N × H)
10. C₁₀₃	C₂×C₅²⋊C₃	direct (N × H)
11. C₅²⋊C₃	C₂×C₁₀₃	direct (N × H)
12. C₂×C₅²	C₃×C₁₀₃	semidirect
13. C₅²	C₂×C₃×C₁₀₃	semidirect
18. C₂	C₅²⋊C₃×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
C₅²⋊C₃×C₁₀₃	2
C₂×C₅²×C₁₀₃	3
C₂×C₃×C₁₀₃	25
C₂×C₅²⋊C₃	103