Subgroups — C₁₃×AGL(1,𝔽₅)×C₄₇ #27132017

Order 12220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₃×C₄₇	—	5	1	no	maximal, Hall
4	C₂×C₁₃×C₄₇	—	5	1	no	—
5	AGL(1,𝔽₅)×C₄₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₇	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
7	D₅×C₄₇	C₂×C₁₃	1	1	yes	characteristic
8	C₁₃×AGL(1,𝔽₅)	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₄×C₄₇	—	5	1	no	Hall
11	D₅×C₁₃	C₂×C₄₇	1	1	yes	characteristic
12	C₂×C₄₇	—	5	1	no	—
13	C₅×C₁₃	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₃	—	5	1	no	Hall
15	C₄₇	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₃	—	5	1	no	—
17	AGL(1,𝔽₅)	C₁₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃	AGL(1,𝔽₅)×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	C₂×C₁₃×C₄₇	1	1	yes	characteristic
20	C₅	C₄×C₁₃×C₄₇	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.