Subgroups — C₉×D₅×C₁₁×C₃₁ #44501651

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×C₁₁×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₁₁×C₃₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic
5	D₅×C₁₁×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁×C₃₁	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₉×D₅×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁×C₃₁	—	5	1	no	—
9	C₅×C₁₁×C₃₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₃×D₅	1	1	yes	characteristic
12	C₉×D₅×C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×C₃₁	C₃×C₁₁	1	1	yes	characteristic
14	C₂×C₁₁×C₃₁	—	5	1	no	Hall
15	C₂×C₉×C₃₁	—	5	1	no	Hall
16	C₅×C₉×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	C₂×C₃×C₁₁	1	1	yes	characteristic
18	C₁₁×C₃₁	C₉×D₅	1	1	yes	characteristic, direct product factor, Hall
19	C₃×D₅×C₁₁	C₃×C₃₁	1	1	yes	characteristic
20	D₅×C₃₁	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₉×C₃₁	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₉×C₁₁	—	5	1	no	Hall
23	C₂×C₃×C₃₁	—	5	1	no	—
24	C₃×C₅×C₁₁	C₂×C₃×C₃₁	1	1	yes	characteristic
25	C₅×C₃₁	C₂×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
26	D₅×C₁₁	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
27	C₉×C₁₁	D₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₃₁	C₃×D₅×C₁₁	1	1	yes	characteristic
29	C₉×D₅	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₁	—	5	1	no	—
31	C₂×C₃₁	—	5	1	no	Hall
32	C₅×C₁₁	C₂×C₉×C₃₁	1	1	yes	characteristic, complemented, Hall
33	C₅×C₉	C₂×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	C₃×D₅×C₃₁	1	1	yes	characteristic
35	C₃₁	C₉×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×D₅	C₃×C₁₁×C₃₁	1	1	yes	characteristic
37	C₂×C₁₁	—	5	1	no	Hall
38	C₂×C₉	—	5	1	no	Hall
39	C₃×C₅	C₂×C₃×C₁₁×C₃₁	1	1	yes	characteristic
40	C₁₁	C₉×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	C₉×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
42	C₉	D₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	5	1	no	—
44	C₅	C₂×C₉×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×D₅×C₁₁×C₃₁	1	1	yes	characteristic
46	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₁₁×C₃₁	D₅
commutator, hypocenter	C₅	C₂×C₉×C₁₁×C₃₁
Frattini	C₃	C₃×D₅×C₁₁×C₃₁
Fitting	C₅×C₉×C₁₁×C₃₁	C₂
socle	C₃×C₅×C₁₁×C₃₁	C₂×C₃
prime radical	C₃×D₅×C₁₁×C₃₁	C₃
cosocle	C₃×C₅	C₂×C₃×C₁₁×C₃₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₁₁×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₃₁	C₂	semidirect
5. D₅×C₁₁×C₃₁	C₉	direct (N × H)
6. C₉×C₁₁×C₃₁	D₅	direct (N × H)
7. C₉×D₅×C₃₁	C₁₁	direct (N × H)
9. C₅×C₁₁×C₃₁	C₂×C₉	semidirect
10. C₅×C₉×C₃₁	C₂×C₁₁	semidirect
12. C₉×D₅×C₁₁	C₃₁	direct (N × H)
16. C₅×C₉×C₁₁	C₂×C₃₁	semidirect
18. C₁₁×C₃₁	C₉×D₅	direct (N × H)
20. D₅×C₃₁	C₉×C₁₁	direct (N × H)
21. C₉×C₃₁	D₅×C₁₁	direct (N × H)
25. C₅×C₃₁	C₂×C₉×C₁₁	semidirect
26. D₅×C₁₁	C₉×C₃₁	direct (N × H)
27. C₉×C₁₁	D₅×C₃₁	direct (N × H)
29. C₉×D₅	C₁₁×C₃₁	direct (N × H)
32. C₅×C₁₁	C₂×C₉×C₃₁	semidirect
33. C₅×C₉	C₂×C₁₁×C₃₁	semidirect
35. C₃₁	C₉×D₅×C₁₁	direct (N × H)
40. C₁₁	C₉×D₅×C₃₁	direct (N × H)
41. D₅	C₉×C₁₁×C₃₁	direct (N × H)
42. C₉	D₅×C₁₁×C₃₁	direct (N × H)
44. C₅	C₂×C₉×C₁₁×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₁×C₃₁	2
C₃×D₅×C₁₁×C₃₁	3
C₂×C₉×C₁₁×C₃₁	5
C₉×D₅×C₃₁	11
C₉×D₅×C₁₁	31

Subgroups — C9×D5×C11×C31 #44501651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₅×C₁₁×C₃₁ #44501651