Subgroups — C₅×C₉×C₁₀₁⋊C₅ #36384367

Order 22725.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₀₁⋊C₅	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₀₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
3	C₅×C₉×C₁₀₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₀₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₁₀₁	C₃×C₅	1	1	yes	characteristic
6	C₃×C₁₀₁⋊C₅	C₃×C₅	1	5	yes	—
7	C₉×C₁₀₁	C₅²	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₀₁	C₅×C₉	1	1	yes	characteristic, complemented
9	C₁₀₁⋊C₅	C₅×C₉	1	5	yes	direct product factor
10	C₃×C₁₀₁	C₃×C₅²	1	1	yes	characteristic
11	C₅²×C₉	—	101	1	no	maximal, Hall
12	C₁₀₁	C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₅²	—	101	1	no	—
14	C₅×C₉	—	101	5	no	—
15	C₅×C₉	C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor
16	C₅²	—	101	1	no	Sylow
17	C₃×C₅	—	101	5	no	—
18	C₃×C₅	C₃×C₁₀₁⋊C₅	1	1	yes	characteristic
19	C₉	C₅×C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	—	101	5	no	—
21	C₅	C₉×C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor
22	C₃	C₃×C₅×C₁₀₁⋊C₅	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.