Subgroups — C₅×C₇×C₁₀₃⋊C₉ #44570064

Order 32445.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₀₃	C₃	1	1	yes	maximal, characteristic
2	C₇×C₁₀₃⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₀₃⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₀₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₀₃	C₃×C₅	1	1	yes	characteristic
6	C₃×C₅×C₁₀₃	C₃×C₇	1	1	yes	characteristic
7	C₁₀₃⋊C₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₀₃	C₅×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₀₃	C₇×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₇×C₉	—	103	1	no	maximal, Hall
11	C₃×C₁₀₃	C₃×C₅×C₇	1	1	yes	characteristic
12	C₃×C₅×C₇	C₁₀₃⋊C₃	1	1	yes	characteristic
13	C₁₀₃	C₅×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₉	—	103	1	no	Hall
15	C₅×C₉	—	103	1	no	Hall
16	C₅×C₇	C₁₀₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇	C₅×C₁₀₃⋊C₃	1	1	yes	characteristic
18	C₃×C₅	C₇×C₁₀₃⋊C₃	1	1	yes	characteristic
19	C₉	—	103	1	no	Sylow
20	C₇	C₅×C₁₀₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×C₁₀₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₅×C₇×C₁₀₃⋊C₃	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.