Subgroups — C₅×C₆₄ #64664

Order 320.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₆	C₄	1	1	yes	characteristic
3	C₆₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₅×C₈	C₈	1	1	yes	characteristic
5	C₃₂	C₂×C₅	1	1	yes	characteristic
6	C₄×C₅	C₁₆	1	1	yes	characteristic
7	C₁₆	C₄×C₅	1	1	yes	characteristic
8	C₂×C₅	C₃₂	1	1	yes	characteristic
9	C₈	C₅×C₈	1	1	yes	characteristic
10	C₅	C₆₄	1	1	yes	characteristic, direct product factor, Sylow
11	C₄	C₅×C₁₆	1	1	yes	characteristic
12	C₂	C₅×C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₆₄	C₅	direct (N × H)
10. C₅	C₆₄	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₃₂	2
C₆₄	5