Subgroups — C₄×C₅×C₉×C₁₀₁ #32911368

Order 18180.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₁₀₁	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₁₀₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₉×C₁₀₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₀₁	C₂×C₃	1	1	yes	characteristic
6	C₄×C₅×C₁₀₁	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₀₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₀₁	C₃×C₄	1	1	yes	characteristic
9	C₃×C₄×C₁₀₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₅×C₁₀₁	C₂×C₉	1	1	yes	characteristic
11	C₉×C₁₀₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₁₀₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×C₁₀₁	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₀₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₀₁	C₃×C₄×C₅	1	1	yes	characteristic
16	C₂×C₁₀₁	C₂×C₅×C₉	1	1	yes	characteristic
17	C₄×C₅×C₉	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₀₁	C₄×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅×C₉	C₂×C₁₀₁	1	1	yes	characteristic
20	C₃×C₄×C₅	C₃×C₁₀₁	1	1	yes	characteristic
21	C₅×C₉	C₄×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
22	C₄×C₉	C₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	C₂×C₃×C₁₀₁	1	1	yes	characteristic
24	C₄×C₅	C₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₉	C₂×C₅×C₁₀₁	1	1	yes	characteristic
26	C₃×C₅	C₃×C₄×C₁₀₁	1	1	yes	characteristic
27	C₃×C₄	C₃×C₅×C₁₀₁	1	1	yes	characteristic
28	C₂×C₅	C₂×C₉×C₁₀₁	1	1	yes	characteristic
29	C₉	C₄×C₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₃×C₅×C₁₀₁	1	1	yes	characteristic
31	C₅	C₄×C₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	C₅×C₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₅×C₁₀₁	1	1	yes	characteristic
34	C₂	C₂×C₅×C₉×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₅×C₁₀₁
socle, prime radical	C₂×C₃×C₅×C₁₀₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅×C₉×C₁₀₁	C₄	direct (N × H)
4. C₄×C₉×C₁₀₁	C₅	direct (N × H)
6. C₄×C₅×C₁₀₁	C₉	direct (N × H)
11. C₉×C₁₀₁	C₄×C₅	direct (N × H)
13. C₅×C₁₀₁	C₄×C₉	direct (N × H)
14. C₄×C₁₀₁	C₅×C₉	direct (N × H)
17. C₄×C₅×C₉	C₁₀₁	direct (N × H)
18. C₁₀₁	C₄×C₅×C₉	direct (N × H)
21. C₅×C₉	C₄×C₁₀₁	direct (N × H)
22. C₄×C₉	C₅×C₁₀₁	direct (N × H)
24. C₄×C₅	C₉×C₁₀₁	direct (N × H)
29. C₉	C₄×C₅×C₁₀₁	direct (N × H)
31. C₅	C₄×C₉×C₁₀₁	direct (N × H)
32. C₄	C₅×C₉×C₁₀₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×C₉×C₁₀₁	2
C₃×C₄×C₅×C₁₀₁	3
C₄×C₉×C₁₀₁	5
C₄×C₅×C₉	101

Subgroups — C4×C5×C9×C101 #32911368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₉×C₁₀₁ #32911368