Subgroups — C₅×C₉×D₂₆₅ #37558701

Order 23850.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₂₆₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₂₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₉×D₅₃	—	5	1	no	maximal
5	C₃×C₅²×C₅₃	C₂×C₃	1	1	yes	characteristic
6	C₅×D₂₆₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₉×C₅₃	—	2	2	no	—
8	C₅×C₉×C₅₃	D₅	1	1	yes	characteristic, complemented
9	C₅×C₉×C₅₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×D₂₆₅	C₃×C₅	1	1	yes	characteristic
11	C₃×C₅×D₅₃	—	5	1	no	—
12	C₅²×C₅₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
13	C₉×D₅₃	—	5	1	no	Hall
14	C₃×C₅×C₅₃	—	2	2	no	—
15	C₃×C₅×C₅₃	C₃×D₅	1	1	yes	characteristic
16	C₃×C₅×C₅₃	C₂×C₃×C₅	1	1	yes	characteristic
17	D₂₆₅	C₅×C₉	1	1	yes	characteristic, direct product factor
18	C₅×D₅₃	—	5	1	no	—
19	C₉×C₅₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₉×D₅	—	53	1	no	maximal, Hall
21	C₃×D₅₃	—	5	1	no	—
22	C₅×C₅₃	—	2	2	no	—
23	C₅×C₅₃	C₉×D₅	1	1	yes	characteristic, complemented
24	C₅×C₅₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented
25	C₅²×C₉	D₅₃	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅₃	C₃×C₅×D₅	1	1	yes	characteristic
27	C₃×C₅×D₅	—	53	1	no	—
28	D₅₃	—	5	1	no	Hall
29	C₂×C₅×C₉	—	265	1	no	—
30	C₉×D₅	—	53	1	no	—
31	C₃×C₅²	C₃×D₅₃	1	1	yes	characteristic
32	C₅₃	C₅×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
33	C₅×D₅	—	53	1	no	Hall
34	C₅×C₉	—	2	2	no	—
35	C₅×C₉	C₅×D₅₃	1	1	yes	characteristic, complemented
36	C₅×C₉	D₂₆₅	1	1	yes	characteristic, direct product factor
37	C₂×C₃×C₅	—	265	1	no	—
38	C₃×D₅	—	53	1	no	—
39	C₅²	C₉×D₅₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₉	—	265	1	no	Hall
41	C₃×C₅	—	2	2	no	—
42	C₃×C₅	C₃×C₅×D₅₃	1	1	yes	characteristic
43	C₃×C₅	C₃×D₂₆₅	1	1	yes	characteristic
44	C₂×C₅	—	265	1	no	—
45	D₅	—	53	1	no	—
46	C₉	C₅×D₂₆₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	265	1	no	—
48	C₅	—	2	2	no	—
49	C₅	C₅×C₉×D₅₃	1	1	yes	characteristic, complemented
50	C₅	C₉×D₂₆₅	1	1	yes	characteristic, direct product factor
51	C₃	C₃×C₅×D₂₆₅	1	1	yes	characteristic
52	C₂	—	265	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉	D₂₆₅
commutator, hypocenter	C₅×C₅₃	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₂₆₅
Fitting	C₅²×C₉×C₅₃	C₂
socle	C₃×C₅²×C₅₃	C₂×C₃
prime radical	C₃×C₅×D₂₆₅	C₃
cosocle	C₃×C₅×C₅₃	C₂×C₃×C₅
LCS	G ▷ C₅×C₅₃
UCS	C₁ ◁ C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₅²×C₉×C₅₃	C₂	semidirect
3. C₉×D₂₆₅	C₅	direct (N × H)
6. C₅×D₂₆₅	C₉	direct (N × H)
8. C₅×C₉×C₅₃	D₅	semidirect
9. C₅×C₉×C₅₃	C₂×C₅	semidirect
12. C₅²×C₅₃	C₂×C₉	semidirect
17. D₂₆₅	C₅×C₉	direct (N × H)
19. C₉×C₅₃	C₅×D₅	semidirect
23. C₅×C₅₃	C₉×D₅	semidirect
24. C₅×C₅₃	C₂×C₅×C₉	semidirect
25. C₅²×C₉	D₅₃	semidirect
32. C₅₃	C₅×C₉×D₅	semidirect
35. C₅×C₉	C₅×D₅₃	semidirect
36. C₅×C₉	D₂₆₅	direct (N × H)
39. C₅²	C₉×D₅₃	semidirect
46. C₉	C₅×D₂₆₅	direct (N × H)
49. C₅	C₅×C₉×D₅₃	semidirect
50. C₅	C₉×D₂₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₉×C₅₃	2
C₃×C₅×D₂₆₅	3
C₉×D₂₆₅	5
C₅×C₉×D₅₃	5
C₅×C₉×D₅	53

Subgroups — C5×C9×D265 #37558701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₂₆₅ #37558701