Subgroups — C₂²×C₅×C₉×C₁₅₁ #41030002

Order 27180.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₅₁	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₁₅₁	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₁₅₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₉×C₁₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₅₁	C₂×C₃	1	3	yes	—
6	C₂²×C₅×C₁₅₁	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₅₁	C₂×C₅	1	3	yes	direct product factor
8	C₃×C₅×C₁₅₁	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₃×C₁₅₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₅×C₁₅₁	C₂×C₉	1	3	yes	direct product factor
11	C₉×C₁₅₁	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₁₅₁	C₂×C₃×C₅	1	3	yes	—
13	C₅×C₁₅₁	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₁₅₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₅₁	C₂²×C₃×C₅	1	1	yes	characteristic
16	C₂×C₁₅₁	C₂×C₅×C₉	1	3	yes	direct product factor
17	C₂²×C₅×C₉	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₅₁	C₂²×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅×C₉	C₂×C₁₅₁	1	3	yes	direct product factor
20	C₂²×C₃×C₅	C₃×C₁₅₁	1	1	yes	characteristic
21	C₅×C₉	C₂²×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₉	C₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	C₂×C₃×C₁₅₁	1	3	yes	—
24	C₂²×C₅	C₉×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₉	C₂×C₅×C₁₅₁	1	3	yes	direct product factor
26	C₃×C₅	C₂²×C₃×C₁₅₁	1	1	yes	characteristic
27	C₂²×C₃	C₃×C₅×C₁₅₁	1	1	yes	characteristic
28	C₂×C₅	C₂×C₉×C₁₅₁	1	3	yes	direct product factor
29	C₉	C₂²×C₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₃×C₅×C₁₅₁	1	3	yes	—
31	C₅	C₂²×C₉×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²	C₅×C₉×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₅×C₁₅₁	1	1	yes	characteristic
34	C₂	C₂×C₅×C₉×C₁₅₁	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₅×C₁₅₁
socle, prime radical	C₂²×C₃×C₅×C₁₅₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₉×C₁₅₁	C₂	direct (N × H)
3. C₅×C₉×C₁₅₁	C₂²	direct (N × H)
4. C₂²×C₉×C₁₅₁	C₅	direct (N × H)
6. C₂²×C₅×C₁₅₁	C₉	direct (N × H)
7. C₂×C₉×C₁₅₁	C₂×C₅	direct (N × H)
10. C₂×C₅×C₁₅₁	C₂×C₉	direct (N × H)
11. C₉×C₁₅₁	C₂²×C₅	direct (N × H)
13. C₅×C₁₅₁	C₂²×C₉	direct (N × H)
14. C₂²×C₁₅₁	C₅×C₉	direct (N × H)
16. C₂×C₁₅₁	C₂×C₅×C₉	direct (N × H)
17. C₂²×C₅×C₉	C₁₅₁	direct (N × H)
18. C₁₅₁	C₂²×C₅×C₉	direct (N × H)
19. C₂×C₅×C₉	C₂×C₁₅₁	direct (N × H)
21. C₅×C₉	C₂²×C₁₅₁	direct (N × H)
22. C₂²×C₉	C₅×C₁₅₁	direct (N × H)
24. C₂²×C₅	C₉×C₁₅₁	direct (N × H)
25. C₂×C₉	C₂×C₅×C₁₅₁	direct (N × H)
28. C₂×C₅	C₂×C₉×C₁₅₁	direct (N × H)
29. C₉	C₂²×C₅×C₁₅₁	direct (N × H)
31. C₅	C₂²×C₉×C₁₅₁	direct (N × H)
32. C₂²	C₅×C₉×C₁₅₁	direct (N × H)
34. C₂	C₂×C₅×C₉×C₁₅₁	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×C₁₅₁	2
C₂²×C₃×C₅×C₁₅₁	3
C₂²×C₉×C₁₅₁	5
C₂²×C₅×C₉	151

Subgroups — C22×C5×C9×C151 #41030002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₉×C₁₅₁ #41030002