Subgroups — C₅×C₃₂×C₁₃₇ #72199392

Order 21920.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₁₃₇	C₄	1	1	yes	characteristic
3	C₃₂×C₁₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₅×C₁₃₇	C₈	1	1	yes	characteristic
5	C₁₆×C₁₃₇	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₁₃₇	C₁₆	1	1	yes	characteristic
7	C₈×C₁₃₇	C₄×C₅	1	1	yes	characteristic
8	C₅×C₁₃₇	C₃₂	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₁₃₇	C₅×C₈	1	1	yes	characteristic
10	C₂×C₁₃₇	C₅×C₁₆	1	1	yes	characteristic
11	C₅×C₃₂	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃₇	C₅×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
13	C₅×C₁₆	C₂×C₁₃₇	1	1	yes	characteristic
14	C₅×C₈	C₄×C₁₃₇	1	1	yes	characteristic
15	C₃₂	C₅×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₄×C₅	C₈×C₁₃₇	1	1	yes	characteristic
17	C₁₆	C₂×C₅×C₁₃₇	1	1	yes	characteristic
18	C₂×C₅	C₁₆×C₁₃₇	1	1	yes	characteristic
19	C₈	C₄×C₅×C₁₃₇	1	1	yes	characteristic
20	C₅	C₃₂×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₅×C₈×C₁₃₇	1	1	yes	characteristic
22	C₂	C₅×C₁₆×C₁₃₇	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.