Subgroups — C₂×C₅×C₇×C₉×C₁₁ #20294114

Order 6930.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₁₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅×C₇×C₁₁	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₉×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₁	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₉×C₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₁	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₁₁	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₅×C₇×C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₉×C₁₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₁₁	C₃×C₅	1	1	yes	characteristic
11	C₅×C₇×C₁₁	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×C₁₁	C₃×C₇	1	1	yes	characteristic
13	C₅×C₇×C₉	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₂×C₃×C₅×C₇	C₃×C₁₁	1	1	yes	characteristic
16	C₂×C₉×C₁₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅×C₁₁	C₂×C₃×C₇	1	1	yes	characteristic
18	C₂×C₇×C₁₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇×C₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₁	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅×C₇	C₂×C₃×C₁₁	1	1	yes	characteristic
22	C₉×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₉	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₁₁	C₂×C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅×C₇	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃×C₁₁	C₃×C₅×C₇	1	1	yes	characteristic
27	C₇×C₉	C₂×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₁	C₂×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₉	C₂×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₇	C₃×C₅×C₁₁	1	1	yes	characteristic
31	C₅×C₇	C₂×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
33	C₂×C₃×C₅	C₃×C₇×C₁₁	1	1	yes	characteristic
34	C₂×C₁₁	C₅×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
36	C₂×C₉	C₅×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic
38	C₂×C₇	C₅×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
39	C₁₁	C₂×C₅×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₅	C₇×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
41	C₉	C₂×C₅×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₅×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃×C₅×C₇×C₁₁	1	1	yes	characteristic
44	C₅	C₂×C₇×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂×C₃×C₅×C₇×C₁₁	1	1	yes	characteristic
46	C₂	C₅×C₇×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₂×C₃×C₅×C₇×C₁₁
socle	C₂×C₃×C₅×C₇×C₁₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₁	C₂	direct (N × H)
3. C₂×C₇×C₉×C₁₁	C₅	direct (N × H)
5. C₂×C₅×C₉×C₁₁	C₇	direct (N × H)
6. C₂×C₅×C₇×C₁₁	C₉	direct (N × H)
7. C₇×C₉×C₁₁	C₂×C₅	direct (N × H)
8. C₂×C₅×C₇×C₉	C₁₁	direct (N × H)
9. C₅×C₉×C₁₁	C₂×C₇	direct (N × H)
11. C₅×C₇×C₁₁	C₂×C₉	direct (N × H)
13. C₅×C₇×C₉	C₂×C₁₁	direct (N × H)
16. C₂×C₉×C₁₁	C₅×C₇	direct (N × H)
18. C₂×C₇×C₁₁	C₅×C₉	direct (N × H)
19. C₂×C₇×C₉	C₅×C₁₁	direct (N × H)
20. C₂×C₅×C₁₁	C₇×C₉	direct (N × H)
22. C₉×C₁₁	C₂×C₅×C₇	direct (N × H)
23. C₂×C₅×C₉	C₇×C₁₁	direct (N × H)
24. C₇×C₁₁	C₂×C₅×C₉	direct (N × H)
25. C₂×C₅×C₇	C₉×C₁₁	direct (N × H)
27. C₇×C₉	C₂×C₅×C₁₁	direct (N × H)
28. C₅×C₁₁	C₂×C₇×C₉	direct (N × H)
29. C₅×C₉	C₂×C₇×C₁₁	direct (N × H)
31. C₅×C₇	C₂×C₉×C₁₁	direct (N × H)
34. C₂×C₁₁	C₅×C₇×C₉	direct (N × H)
36. C₂×C₉	C₅×C₇×C₁₁	direct (N × H)
38. C₂×C₇	C₅×C₉×C₁₁	direct (N × H)
39. C₁₁	C₂×C₅×C₇×C₉	direct (N × H)
40. C₂×C₅	C₇×C₉×C₁₁	direct (N × H)
41. C₉	C₂×C₅×C₇×C₁₁	direct (N × H)
42. C₇	C₂×C₅×C₉×C₁₁	direct (N × H)
44. C₅	C₂×C₇×C₉×C₁₁	direct (N × H)
46. C₂	C₅×C₇×C₉×C₁₁	direct (N × H)

Subgroups — C2×C5×C7×C9×C11 #20294114

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×C₉×C₁₁ #20294114