Subgroups — C₅×C₁₁×Dic₁₅₇ #46828754

Order 34540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₁₅₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₁₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₁×C₁₅₇	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₁₅₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₅₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₁₅₇	C₂×C₁₁	1	1	yes	characteristic
8	C₅×C₁₅₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₁₅₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₅₇	C₂×C₅×C₁₁	1	1	yes	characteristic
11	C₄×C₅×C₁₁	—	157	1	no	maximal, Hall
12	C₁₅₇	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₅×C₁₁	D₁₅₇	1	1	yes	characteristic
14	C₅×C₁₁	Dic₁₅₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	—	157	1	no	Hall
16	C₂×C₁₁	C₅×D₁₅₇	1	1	yes	characteristic
17	C₄×C₅	—	157	1	no	Hall
18	C₁₁	C₅×Dic₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₁₁×D₁₅₇	1	1	yes	characteristic
20	C₅	C₁₁×Dic₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	157	1	no	Sylow
22	C₂	C₅×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.