Subgroups — C₂×C₉×C₁₅₁⋊C₅ #28331128

Order 13590.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₅₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₅₁⋊C₅	C₂×C₃	1	1	yes	characteristic
5	C₂×C₁₅₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₅₁	C₃×C₅	1	1	yes	characteristic
8	C₁₅₁⋊C₅	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic
10	C₂×C₁₅₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
11	C₁₅₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅×C₉	—	151	1	no	maximal, Hall
13	C₅×C₉	—	151	1	no	Hall
14	C₂×C₃×C₅	—	151	1	no	—
15	C₂×C₉	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅	—	151	1	no	—
17	C₂×C₅	—	151	1	no	Hall
18	C₉	C₂×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₃×C₁₅₁⋊C₅	1	1	yes	characteristic
20	C₅	—	151	1	no	Sylow
21	C₃	C₂×C₃×C₁₅₁⋊C₅	1	1	yes	characteristic
22	C₂	C₉×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

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.