Subgroups — C₃×Dic₁₁⋊C₅ #10620331

Order 660.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	Dic₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁	C₂×C₅	1	1	yes	characteristic
7	C₃×C₄×C₅	—	11	1	no	maximal, Hall
8	C₁₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	Dic₁₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅	—	11	1	no	—
12	C₂×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₄×C₅	—	11	1	no	Hall
14	C₃×C₅	—	11	1	no	Hall
15	C₃×C₄	—	11	1	no	Hall
16	C₁₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅	—	11	1	no	—
18	C₂×C₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic
19	C₅	—	11	1	no	Sylow
20	C₄	—	11	1	no	Sylow
21	C₃	Dic₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×AGL(1,𝔽₁₁)	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.