Subgroups — C₄×C₂₇×C₁₀₁ #72189448

Order 10908.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₉×C₁₀₁	C₃	1	1	yes	maximal, characteristic
3	C₂₇×C₁₀₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₉×C₁₀₁	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₀₁	C₉	1	1	yes	characteristic
6	C₉×C₁₀₁	C₃×C₄	1	1	yes	characteristic
7	C₂×C₃×C₁₀₁	C₂×C₉	1	1	yes	characteristic
8	C₄×C₁₀₁	C₂₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₀₁	C₄×C₉	1	1	yes	characteristic
10	C₂×C₁₀₁	C₂×C₂₇	1	1	yes	characteristic
11	C₄×C₂₇	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₀₁	C₄×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₂₇	C₂×C₁₀₁	1	1	yes	characteristic
14	C₄×C₉	C₃×C₁₀₁	1	1	yes	characteristic
15	C₂₇	C₄×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₉	C₂×C₃×C₁₀₁	1	1	yes	characteristic
17	C₃×C₄	C₉×C₁₀₁	1	1	yes	characteristic
18	C₉	C₃×C₄×C₁₀₁	1	1	yes	characteristic
19	C₂×C₃	C₂×C₉×C₁₀₁	1	1	yes	characteristic
20	C₄	C₂₇×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₉×C₁₀₁	1	1	yes	characteristic
22	C₂	C₂×C₂₇×C₁₀₁	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.