Subgroups — C₅×Dic₅₂₇ #24902015

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	Dic₅₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₃₁	—	17	1	no	maximal, Hall
6	C₁₇×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×Dic₁₇	—	31	1	no	maximal, Hall
8	C₂×C₅×C₃₁	D₁₇	1	1	yes	characteristic
9	C₂×C₅×C₁₇	D₃₁	1	1	yes	characteristic
10	C₅×C₃₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
11	Dic₃₁	—	17	1	no	Hall
12	C₅×C₁₇	Dic₃₁	1	1	yes	characteristic, complemented, Hall
13	Dic₁₇	—	31	1	no	Hall
14	C₂×C₃₁	C₅×D₁₇	1	1	yes	characteristic
15	C₂×C₁₇	C₅×D₃₁	1	1	yes	characteristic
16	C₃₁	C₅×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₅	—	527	1	no	Hall
18	C₁₇	C₅×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	D₅₂₇	1	1	yes	characteristic
20	C₅	Dic₅₂₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	527	1	no	Sylow
22	C₂	C₅×D₅₂₇	1	1	yes	characteristic

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