Subgroups — C₅×C₁₉×C₆₄ #72185255

Order 6080.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₆×C₁₉	C₄	1	1	yes	characteristic
3	C₁₉×C₆₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₈×C₁₉	C₈	1	1	yes	characteristic
5	C₁₉×C₃₂	C₂×C₅	1	1	yes	characteristic
6	C₄×C₅×C₁₉	C₁₆	1	1	yes	characteristic
7	C₅×C₆₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₆×C₁₉	C₄×C₅	1	1	yes	characteristic
9	C₂×C₅×C₁₉	C₃₂	1	1	yes	characteristic
10	C₅×C₃₂	C₂×C₁₉	1	1	yes	characteristic
11	C₈×C₁₉	C₅×C₈	1	1	yes	characteristic
12	C₅×C₁₉	C₆₄	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₁₆	C₄×C₁₉	1	1	yes	characteristic
14	C₄×C₁₉	C₅×C₁₆	1	1	yes	characteristic
15	C₆₄	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₈	C₈×C₁₉	1	1	yes	characteristic
17	C₂×C₁₉	C₅×C₃₂	1	1	yes	characteristic
18	C₃₂	C₂×C₅×C₁₉	1	1	yes	characteristic
19	C₄×C₅	C₁₆×C₁₉	1	1	yes	characteristic
20	C₁₉	C₅×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₁₆	C₄×C₅×C₁₉	1	1	yes	characteristic
22	C₂×C₅	C₁₉×C₃₂	1	1	yes	characteristic
23	C₈	C₅×C₈×C₁₉	1	1	yes	characteristic
24	C₅	C₁₉×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
25	C₄	C₅×C₁₆×C₁₉	1	1	yes	characteristic
26	C₂	C₅×C₁₉×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.