Subgroups — C₈×C₂₅×C₁₅₁ #72206993

Order 30200.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₁₅₁	C₅	1	1	yes	maximal, characteristic
2	C₄×C₂₅×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₅×C₁₅₁	C₄	1	1	yes	characteristic
4	C₂₅×C₁₅₁	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₅×C₁₅₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₁₅₁	C₄×C₅	1	1	yes	characteristic
7	C₈×C₁₅₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₅₁	C₅×C₈	1	1	yes	characteristic
9	C₄×C₁₅₁	C₂×C₂₅	1	1	yes	characteristic
10	C₂×C₁₅₁	C₄×C₂₅	1	1	yes	characteristic
11	C₈×C₂₅	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₅₁	C₈×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₄×C₂₅	C₂×C₁₅₁	1	1	yes	characteristic
14	C₂×C₂₅	C₄×C₁₅₁	1	1	yes	characteristic
15	C₅×C₈	C₅×C₁₅₁	1	1	yes	characteristic
16	C₂₅	C₈×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₅	C₂×C₅×C₁₅₁	1	1	yes	characteristic
18	C₂×C₅	C₄×C₅×C₁₅₁	1	1	yes	characteristic
19	C₈	C₂₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₅×C₈×C₁₅₁	1	1	yes	characteristic
21	C₄	C₂×C₂₅×C₁₅₁	1	1	yes	characteristic
22	C₂	C₄×C₂₅×C₁₅₁	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.