Subgroups — C₃×#261×C₁₃₁ #35205449

Order 20436.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#261×C₁₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₃₁	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₁₃₁	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₃₁	—	13	1	no	—
8	C₄×C₁₃₁	—	13	1	no	Hall
9	C₃×C₁₃₁	#261	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃₁	—	13	1	no	—
11	C₃×#261	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃₁	C₃×#261	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×D₁₃	C₂×C₁₃₁	1	1	yes	characteristic
14	#261	C₃×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃	C₄×C₁₃₁	1	1	yes	characteristic, complemented, Hall
16	D₁₃	C₂×C₃×C₁₃₁	1	1	yes	characteristic
17	C₁₃	C₃×C₄×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	13	1	no	Hall
19	C₂×C₃	—	13	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	#261×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	13	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.