Subgroups — C₁₃₇×Dic₃₅ #34062793

Order 19180.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇×C₁₃₇	—	5	1	no	maximal, Hall
4	Dic₅×C₁₃₇	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₃₇	D₅	1	1	yes	characteristic
6	C₂×C₅×C₁₃₇	D₇	1	1	yes	characteristic
7	C₇×C₁₃₇	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₃₇	—	35	1	no	Hall
10	C₂×C₁₃₇	D₃₅	1	1	yes	characteristic
11	Dic₃₅	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃₇	Dic₃₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₅×C₇	C₂×C₁₃₇	1	1	yes	characteristic
14	C₅×C₇	C₄×C₁₃₇	1	1	yes	characteristic, complemented, Hall
15	Dic₇	—	5	1	no	Hall
16	Dic₅	—	7	1	no	Hall
17	C₂×C₇	D₅×C₁₃₇	1	1	yes	characteristic
18	C₂×C₅	D₇×C₁₃₇	1	1	yes	characteristic
19	C₇	Dic₅×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
20	C₅	Dic₇×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	35	1	no	Sylow
22	C₂	D₃₅×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.