Subgroups — C₅⋊D₅×D₁₀₇ #24924158

Order 10700.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₁₀₇	—	5	6	no	maximal
6	D₅₃₅	—	5	6	no	—
7	C₅×D₁₀₇	D₅	1	6	yes	complemented
8	D₅×C₁₀₇	—	5	6	no	—
9	C₅×C₁₀₇	C₂×D₅	1	6	yes	complemented
10	C₂×D₁₀₇	—	25	1	no	Hall
11	C₂×C₁₀₇	—	25	1	no	—
12	D₁₀₇	—	25	1	no	—
13	D₁₀₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor
14	C₁₀₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅⋊D₅	—	107	1	no	maximal, Hall
16	C₂×C₅²	—	107	1	no	—
17	C₅⋊D₅	—	107	1	no	—
18	C₅⋊D₅	D₁₀₇	1	1	yes	characteristic, direct product factor
19	C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₅	—	535	6	no	—
21	C₂×C₅	—	107	6	no	—
22	D₅	—	5	6	no	—
23	D₅	—	535	6	no	—
24	C₅	D₅×D₁₀₇	1	6	yes	complemented
25	C₂²	—	2675	1	no	Sylow
26	C₂	—	25	1	no	—
27	C₂	—	107	1	no	—
28	C₂	—	2675	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₀₇	C₂²
LCS	G ▷ C₅²×C₁₀₇
UCS	C₁

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