Subgroups — C₁₁×C₉⋊AGL(1,𝔽₅) #14520396

Order 1980.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×ΓL(1,𝔽₁₆)	—	3	1	no	maximal
3	C₅×C₉×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₉	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₁	D₃	1	1	yes	characteristic
6	C₁₁×AGL(1,𝔽₅)	—	9	1	no	Hall
7	C₂×C₉×C₁₁	—	5	1	no	—
8	C₉⋊AGL(1,𝔽₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁	Dic₃	1	1	yes	characteristic
10	C₁₁×Dic₃	—	15	1	no	—
11	D₅×C₁₁	D₉	1	1	yes	characteristic
12	C₉×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
13	C₉×D₅	C₂×C₁₁	1	1	yes	characteristic
14	C₂×C₃×C₁₁	—	5	1	no	—
15	ΓL(1,𝔽₁₆)	—	3	1	no	—
16	C₅×C₁₁	Dic₉	1	1	yes	characteristic, complemented, Hall
17	C₅×C₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₄×C₁₁	—	45	1	no	Hall
19	Dic₉	—	5	1	no	Hall
20	C₃×C₁₁	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
21	C₃×D₅	D₃×C₁₁	1	1	yes	characteristic
22	C₂×C₁₁	—	5	1	no	—
23	AGL(1,𝔽₅)	—	9	1	no	Hall
24	C₂×C₉	—	5	1	no	—
25	C₃×C₅	C₁₁×Dic₃	1	1	yes	characteristic
26	Dic₃	—	15	1	no	—
27	C₁₁	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
28	D₅	C₁₁×D₉	1	1	yes	characteristic
29	C₉	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	1	no	—
31	C₅	C₁₁×Dic₉	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	45	1	no	Sylow
33	C₃	C₁₁×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
34	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.