Subgroups — C₉×C₂₃×D₆₅ #41002081

Order 26910.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₃×D₆₅	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₃×D₁₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₂₃×D₆₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₃×C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₉×D₅×C₂₃	—	13	1	no	maximal, Hall
8	C₃×C₂₃×D₁₃	—	5	1	no	—
9	C₅×C₁₃×C₂₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₉×D₆₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₉×C₂₃	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₂₃	C₃×D₅	1	1	yes	characteristic
13	C₃×D₅×C₂₃	—	13	1	no	—
14	C₂₃×D₁₃	—	5	1	no	Hall
15	C₅×C₉×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₉×C₂₃	—	65	1	no	Hall
17	C₃×D₆₅	C₃×C₂₃	1	1	yes	characteristic
18	C₃×C₅×C₂₃	C₃×D₁₃	1	1	yes	characteristic
19	C₁₃×C₂₃	C₉×D₅	1	1	yes	characteristic, complemented, Hall
20	C₉×D₁₃	—	5	1	no	Hall
21	D₅×C₂₃	—	13	1	no	Hall
22	C₉×C₂₃	D₆₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic
24	C₂×C₃×C₂₃	—	65	1	no	—
25	D₆₅	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₉×C₁₃	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
27	C₅×C₂₃	C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
28	C₉×D₅	—	13	1	no	Hall
29	C₃×D₁₃	—	5	1	no	—
30	C₃×C₂₃	C₃×D₆₅	1	1	yes	characteristic
31	C₅×C₁₃	C₂×C₉×C₂₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₃	—	65	1	no	Hall
33	C₅×C₉	C₂₃×D₁₃	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₃	C₃×D₅×C₂₃	1	1	yes	characteristic
35	C₃×D₅	—	13	1	no	—
36	D₁₃	—	5	1	no	Hall
37	C₂₃	C₉×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₉	—	65	1	no	Hall
39	C₃×C₅	C₃×C₂₃×D₁₃	1	1	yes	characteristic
40	C₁₃	C₉×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	13	1	no	Hall
42	C₉	C₂₃×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	65	1	no	—
44	C₅	C₉×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×C₂₃×D₆₅	1	1	yes	characteristic
46	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₂₃	D₆₅
commutator, hypocenter	C₅×C₁₃	C₂×C₉×C₂₃
Frattini	C₃	C₃×C₂₃×D₆₅
Fitting	C₅×C₉×C₁₃×C₂₃	C₂
socle	C₃×C₅×C₁₃×C₂₃	C₂×C₃
prime radical	C₃×C₂₃×D₆₅	C₃
cosocle	C₃×C₅×C₁₃	C₂×C₃×C₂₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₉×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₃×C₂₃	C₂	semidirect
5. C₂₃×D₆₅	C₉	direct (N × H)
6. C₉×C₁₃×C₂₃	D₅	semidirect
9. C₅×C₁₃×C₂₃	C₂×C₉	semidirect
10. C₉×D₆₅	C₂₃	direct (N × H)
11. C₅×C₉×C₂₃	D₁₃	semidirect
15. C₅×C₉×C₁₃	C₂×C₂₃	semidirect
19. C₁₃×C₂₃	C₉×D₅	semidirect
22. C₉×C₂₃	D₆₅	direct (N × H)
25. D₆₅	C₉×C₂₃	direct (N × H)
26. C₉×C₁₃	D₅×C₂₃	semidirect
27. C₅×C₂₃	C₉×D₁₃	semidirect
31. C₅×C₁₃	C₂×C₉×C₂₃	semidirect
33. C₅×C₉	C₂₃×D₁₃	semidirect
37. C₂₃	C₉×D₆₅	direct (N × H)
40. C₁₃	C₉×D₅×C₂₃	semidirect
42. C₉	C₂₃×D₆₅	direct (N × H)
44. C₅	C₉×C₂₃×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₃×C₂₃	2
C₃×C₂₃×D₆₅	3
C₉×C₂₃×D₁₃	5
C₉×D₅×C₂₃	13
C₉×D₆₅	23

Subgroups — C9×C23×D65 #41002081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂₃×D₆₅ #41002081