Subgroups — C₁₇×Dic₅×C₃₁ #24902016

Order 10540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₇×C₃₁	—	5	1	no	maximal, Hall
4	C₂×C₁₇×C₃₁	D₅	1	1	yes	characteristic
5	Dic₅×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₃₁	Dic₅	1	1	yes	characteristic, direct product factor, Hall
7	C₁₇×Dic₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₃₁	C₂×C₁₇	1	1	yes	characteristic
9	C₂×C₅×C₁₇	C₂×C₃₁	1	1	yes	characteristic
10	C₅×C₃₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₄×C₃₁	—	5	1	no	Hall
12	C₅×C₁₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
13	C₄×C₁₇	—	5	1	no	Hall
14	C₂×C₃₁	D₅×C₁₇	1	1	yes	characteristic
15	C₂×C₁₇	D₅×C₃₁	1	1	yes	characteristic
16	C₃₁	C₁₇×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
17	Dic₅	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	Dic₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₇×C₃₁	1	1	yes	characteristic
20	C₅	C₄×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	D₅×C₁₇×C₃₁	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.