Subgroups — C₉×C₁₉×C₁₃₇ #37552840

Order 23427.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₁₃₇	C₃	1	1	yes	maximal, characteristic
2	C₁₉×C₁₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₉×C₁₃₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃₇	C₃×C₁₉	1	1	yes	characteristic
5	C₉×C₁₉	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃₇	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₁₉	C₃×C₁₃₇	1	1	yes	characteristic
8	C₁₉	C₉×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	C₁₉×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₁₉×C₁₃₇	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.