Subgroups — C₃×C₅×C₆₄ #11745809

Order 960.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₅×C₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₆	C₄	1	1	yes	characteristic
4	C₃×C₆₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₃₂	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×C₈	C₈	1	1	yes	characteristic
7	C₃×C₃₂	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₆	C₃×C₄	1	1	yes	characteristic
9	C₆₄	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₄×C₅	C₁₆	1	1	yes	characteristic
11	C₃×C₁₆	C₄×C₅	1	1	yes	characteristic
12	C₅×C₈	C₃×C₈	1	1	yes	characteristic
13	C₃₂	C₂×C₃×C₅	1	1	yes	characteristic
14	C₂×C₃×C₅	C₃₂	1	1	yes	characteristic
15	C₃×C₈	C₅×C₈	1	1	yes	characteristic
16	C₄×C₅	C₃×C₁₆	1	1	yes	characteristic
17	C₁₆	C₃×C₄×C₅	1	1	yes	characteristic
18	C₃×C₅	C₆₄	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄	C₅×C₁₆	1	1	yes	characteristic
20	C₂×C₅	C₃×C₃₂	1	1	yes	characteristic
21	C₈	C₃×C₅×C₈	1	1	yes	characteristic
22	C₂×C₃	C₅×C₃₂	1	1	yes	characteristic
23	C₅	C₃×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
24	C₄	C₃×C₅×C₁₆	1	1	yes	characteristic
25	C₃	C₅×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×C₅×C₃₂	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.