Subgroups — C₁₁×C₃⋊#170 #13050339

Order 1320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#170	—	3	1	no	maximal, Hall
3	C₂×C₃×C₅×C₁₁	C₄	1	1	yes	characteristic
4	C₁₁×C₃⋊C₈	—	5	1	no	maximal, Hall
5	C₁₁×Dic₅	D₃	1	1	yes	characteristic
6	C₃×C₅×C₁₁	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₁	—	5	1	no	—
8	C₃⋊#170	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₁₁	Dic₃	1	1	yes	characteristic
10	C₈×C₁₁	—	15	1	no	Hall
11	C₂×C₃×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic
12	C₃×Dic₅	C₂×C₁₁	1	1	yes	characteristic
13	C₅×C₁₁	C₃⋊C₈	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₁	—	5	1	no	—
15	#170	—	3	1	no	Hall
16	C₃×C₁₁	#170	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅	C₄×C₁₁	1	1	yes	characteristic
18	C₃⋊C₈	—	5	1	no	Hall
19	C₂×C₁₁	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
20	Dic₅	D₃×C₁₁	1	1	yes	characteristic
21	C₃×C₅	C₈×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₄	—	5	1	no	—
23	C₁₁	C₃⋊#170	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₅	C₁₁×Dic₃	1	1	yes	characteristic
25	C₈	—	15	1	no	Sylow
26	C₂×C₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₅	C₁₁×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	5	1	no	—
29	C₃	C₁₁×#170	1	1	yes	characteristic, complemented, Sylow
30	C₂	C₁₁×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

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.