Subgroups — C₃₁×C₁₁⋊AGL(1,𝔽₅) #20291920

Order 6820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₁₁	—	5	1	no	maximal, Hall
4	C₂×C₁₁×C₃₁	—	5	1	no	—
5	AGL(1,𝔽₅)×C₃₁	—	11	1	no	maximal, Hall
6	C₁₁×C₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₃₁	D₁₁	1	1	yes	characteristic
8	C₁₁⋊AGL(1,𝔽₅)	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₃₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	C₄×C₃₁	—	55	1	no	Hall
11	D₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic
12	C₂×C₃₁	—	5	1	no	—
13	C₅×C₁₁	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
14	Dic₁₁	—	5	1	no	Hall
15	C₃₁	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₁	—	5	1	no	—
17	AGL(1,𝔽₅)	—	11	1	no	Hall
18	C₁₁	AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented, Sylow
19	D₅	D₁₁×C₃₁	1	1	yes	characteristic
20	C₅	C₃₁×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	55	1	no	Sylow
22	C₂	—	5	1	no	—

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