Subgroups — C₃×C₁₁×Dic₁₅₇ #35208552

Order 20724.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₁₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×C₁₅₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₁₅₇	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₁₅₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₅₇	C₂×C₁₁	1	1	yes	characteristic
8	Dic₁₅₇	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₅₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₅₇	C₂×C₃×C₁₁	1	1	yes	characteristic
11	C₁₅₇	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₁₁	—	157	1	no	maximal, Hall
13	C₂×C₃×C₁₁	D₁₅₇	1	1	yes	characteristic
14	C₄×C₁₁	—	157	1	no	Hall
15	C₃×C₁₁	Dic₁₅₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₁	C₃×D₁₅₇	1	1	yes	characteristic
17	C₃×C₄	—	157	1	no	Hall
18	C₁₁	C₃×Dic₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₁₁×D₁₅₇	1	1	yes	characteristic
20	C₄	—	157	1	no	Sylow
21	C₃	C₁₁×Dic₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₁₁×D₁₅₇	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.