Subgroups — C₁₃⋊C₉×C₁₇₃ #35202245

Order 20241.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₇₃	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇₃	C₉	1	1	yes	characteristic, complemented, Hall
3	C₉×C₁₇₃	—	13	1	no	maximal, Hall
4	C₃×C₁₇₃	C₁₃⋊C₃	1	1	yes	characteristic
5	C₁₇₃	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₁₃⋊C₉	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₃	C₃×C₁₇₃	1	1	yes	characteristic
8	C₁₃	C₉×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	13	1	no	Sylow
10	C₃	C₁₃⋊C₃×C₁₇₃	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.