Subgroups — D₂₅×D₁₀₇ #24924138

Order 10700.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₅×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₅×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₁₀₇	—	5	1	no	maximal
6	D₅₃₅	—	5	1	no	—
7	C₅×D₁₀₇	D₅	1	1	yes	characteristic
8	D₅×C₁₀₇	—	5	1	no	—
9	C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic
10	C₂×D₁₀₇	—	25	1	no	Hall
11	C₂×C₁₀₇	—	25	1	no	—
12	D₁₀₇	—	25	1	no	—
13	D₁₀₇	D₂₅	1	1	yes	characteristic, direct product factor
14	C₁₀₇	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₂₅	—	107	1	no	maximal, Hall
16	C₂×C₂₅	—	107	1	no	—
17	D₂₅	—	107	1	no	—
18	D₂₅	D₁₀₇	1	1	yes	characteristic, direct product factor
19	C₂₅	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₅	—	535	1	no	—
21	C₂×C₅	—	107	1	no	—
22	D₅	—	5	1	no	—
23	D₅	—	535	1	no	—
24	C₅	D₅×D₁₀₇	1	1	yes	characteristic
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, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅×C₁₀₇	C₂²
Frattini	C₅	D₅×D₁₀₇
socle	C₅×C₁₀₇	C₂×D₅
LCS	G ▷ C₂₅×C₁₀₇
UCS	C₁

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