Finite Group Databasebeta

← C₄×C₅²×C₁₀₇ #24924142

Subgroups — C₄×C₅²×C₁₀₇ #24924142

Order 10700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₀₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₅×C₁₀₇	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅×C₁₀₇	C₂×C₅	1	6	yes	—
5	C₅×C₁₀₇	C₄×C₅	1	6	yes	direct product factor
6	C₄×C₁₀₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₀₇	C₂×C₅²	1	1	yes	characteristic
8	C₁₀₇	C₄×C₅²	1	1	yes	characteristic, direct product factor, Sylow
9	C₄×C₅²	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅²	C₂×C₁₀₇	1	1	yes	characteristic
11	C₅²	C₄×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₅	C₅×C₁₀₇	1	6	yes	direct product factor
13	C₂×C₅	C₂×C₅×C₁₀₇	1	6	yes	—
14	C₅	C₄×C₅×C₁₀₇	1	6	yes	direct product factor
15	C₄	C₅²×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₅²×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅²×C₁₀₇
socle, prime radical	C₂×C₅²×C₁₀₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₀₇	C₄	direct (N × H)
3. C₄×C₅×C₁₀₇	C₅	direct (N × H)
5. C₅×C₁₀₇	C₄×C₅	direct (N × H)
6. C₄×C₁₀₇	C₅²	direct (N × H)
8. C₁₀₇	C₄×C₅²	direct (N × H)
9. C₄×C₅²	C₁₀₇	direct (N × H)
11. C₅²	C₄×C₁₀₇	direct (N × H)
12. C₄×C₅	C₅×C₁₀₇	direct (N × H)
14. C₅	C₄×C₅×C₁₀₇	direct (N × H)
15. C₄	C₅²×C₁₀₇	direct (N × H)