Subgroups — C₁₁×AGL(1,𝔽₅)×C₁₀₇ #37555331

Order 23540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₁×C₁₀₇	—	5	1	no	maximal, Hall
4	C₂×C₁₁×C₁₀₇	—	5	1	no	—
5	AGL(1,𝔽₅)×C₁₀₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₀₇	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
7	D₅×C₁₀₇	C₂×C₁₁	1	1	yes	characteristic
8	C₅×C₁₀₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₀₇	—	5	1	no	Hall
10	C₁₁×AGL(1,𝔽₅)	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₀₇	—	5	1	no	—
12	D₅×C₁₁	C₂×C₁₀₇	1	1	yes	characteristic
13	C₁₀₇	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
14	C₅×C₁₁	C₄×C₁₀₇	1	1	yes	characteristic, complemented, Hall
15	C₄×C₁₁	—	5	1	no	Hall
16	C₂×C₁₁	—	5	1	no	—
17	AGL(1,𝔽₅)	C₁₁×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	AGL(1,𝔽₅)×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	C₂×C₁₁×C₁₀₇	1	1	yes	characteristic
20	C₅	C₄×C₁₁×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	—	5	1	no	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.