Subgroups — C₁₃×C₁₃₁⋊AGL(1,𝔽₅) #46801547

Order 34060.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×Dic₁₃₁	—	5	1	no	maximal, Hall
4	C₂×C₁₃×C₁₃₁	—	5	1	no	—
5	C₁₃₁⋊AGL(1,𝔽₅)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₁₃₁	C₂×C₁₃	1	1	yes	characteristic
8	C₅×C₁₃₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	Dic₁₃₁	—	5	1	no	Hall
10	C₂×C₁₃₁	—	5	1	no	—
11	C₁₃×AGL(1,𝔽₅)	—	131	1	no	maximal, Hall
12	C₁₃₁	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
13	D₅×C₁₃	D₁₃₁	1	1	yes	characteristic
14	C₅×C₁₃	Dic₁₃₁	1	1	yes	characteristic, complemented, Hall
15	C₄×C₁₃	—	655	1	no	Hall
16	C₂×C₁₃	—	5	1	no	—
17	AGL(1,𝔽₅)	—	131	1	no	Hall
18	C₁₃	C₁₃₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	C₁₃×D₁₃₁	1	1	yes	characteristic
20	C₅	C₁₃×Dic₁₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	655	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.