Subgroups — C₅×AGL(1,𝔽₅)×C₁₀₇ #24924149

Order 10700.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
3	AGL(1,𝔽₅)×C₁₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₄×C₅×C₁₀₇	—	5	1	no	maximal
5	C₂×C₅×C₁₀₇	—	5	1	no	—
6	D₅×C₁₀₇	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₀₇	—	4	1	no	—
8	C₅×C₁₀₇	C₄×C₅	1	1	yes	characteristic, complemented
9	C₅×C₁₀₇	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
10	C₄×C₁₀₇	—	5	1	no	Hall
11	C₂×C₁₀₇	—	5	1	no	—
12	C₁₀₇	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
13	C₅×AGL(1,𝔽₅)	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×D₅	C₂×C₁₀₇	1	1	yes	characteristic
15	C₅²	C₄×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
16	AGL(1,𝔽₅)	C₅×C₁₀₇	1	1	yes	characteristic, direct product factor
17	C₄×C₅	—	5	1	no	—
18	C₂×C₅	—	5	1	no	—
19	D₅	C₂×C₅×C₁₀₇	1	1	yes	characteristic
20	C₅	—	4	1	no	—
21	C₅	C₄×C₅×C₁₀₇	1	1	yes	characteristic, complemented
22	C₅	AGL(1,𝔽₅)×C₁₀₇	1	1	yes	characteristic, direct product factor
23	C₄	—	5	1	no	Sylow
24	C₂	—	5	1	no	—

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