Subgroups — C₅×D₆₃₇ #20264010

Order 6370.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₉₁	—	7	1	no	maximal
4	C₁₃×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×D₄₉	—	13	1	no	maximal, Hall
6	C₅×C₇×C₁₃	D₇	1	1	yes	characteristic
7	C₅×C₄₉	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₉₁	—	7	1	no	—
9	C₅×D₁₃	—	49	1	no	Hall
10	D₄₉	—	13	1	no	Hall
11	C₇×C₁₃	C₅×D₇	1	1	yes	characteristic
12	C₅×D₇	—	91	1	no	—
13	C₅×C₁₃	D₄₉	1	1	yes	characteristic, complemented, Hall
14	C₄₉	C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
15	C₅×C₇	D₉₁	1	1	yes	characteristic
16	D₁₃	—	49	1	no	Hall
17	D₇	—	91	1	no	—
18	C₁₃	C₅×D₄₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	637	1	no	Hall
20	C₇	C₅×D₉₁	1	1	yes	characteristic
21	C₅	D₆₃₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	637	1	no	Sylow

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