Subgroups — C₅×C₄₁×Dic₁₇ #28358269

Order 13940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₁×Dic₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₇×C₄₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅×C₄₁	—	17	1	no	maximal, Hall
6	C₁₇×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₄₁	D₁₇	1	1	yes	characteristic
8	C₅×Dic₁₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄₁	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₇	C₂×C₄₁	1	1	yes	characteristic
11	C₄×C₄₁	—	17	1	no	Hall
12	C₅×C₁₇	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₁	C₅×D₁₇	1	1	yes	characteristic
14	Dic₁₇	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
15	C₄₁	C₅×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₇	C₂×C₅×C₄₁	1	1	yes	characteristic
17	C₄×C₅	—	17	1	no	Hall
18	C₁₇	C₄×C₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	D₁₇×C₄₁	1	1	yes	characteristic
20	C₅	C₄₁×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	17	1	no	Sylow
22	C₂	C₅×D₁₇×C₄₁	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.