Subgroups — C₉×C₂₃×#1044 #35208011

Order 20700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃×#1044	C₃	1	1	yes	maximal, characteristic
3	C₅²×C₉×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×AGL(1,𝔽₅)×C₂₃	—	5	2	no	maximal
5	C₃×C₂₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₂₃×#1044	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×D₅×C₂₃	—	5	2	no	—
8	C₉×D₅×C₂₃	—	10	2	no	—
9	C₃×C₅²×C₂₃	C₃×C₄	1	1	yes	characteristic
10	C₃×AGL(1,𝔽₅)×C₂₃	—	5	2	no	—
11	C₂₃×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
12	C₅×C₉×C₂₃	—	2	2	no	—
13	C₅×C₉×C₂₃	AGL(1,𝔽₅)	1	2	yes	complemented
14	C₉×#1044	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₄×C₉×C₂₃	—	25	1	no	Hall
16	C₃×D₅×C₂₃	—	5	2	no	—
17	C₃×D₅×C₂₃	—	10	2	no	—
18	C₅²×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	AGL(1,𝔽₅)×C₂₃	—	5	2	no	—
20	C₉×C₅⋊D₅	C₂×C₂₃	1	1	yes	characteristic
21	C₂×C₉×C₂₃	—	25	1	no	—
22	C₃×C₅×C₂₃	—	2	2	no	—
23	C₃×C₅×C₂₃	C₃×AGL(1,𝔽₅)	1	2	yes	—
24	C₃×#1044	C₃×C₂₃	1	1	yes	characteristic
25	C₃×C₄×C₂₃	—	25	1	no	—
26	D₅×C₂₃	—	5	2	no	—
27	D₅×C₂₃	—	10	2	no	—
28	C₅²×C₉	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
29	C₉×C₂₃	#1044	1	1	yes	characteristic, direct product factor, Hall
30	C₉×AGL(1,𝔽₅)	—	5	2	no	—
31	C₃×C₅⋊D₅	C₂×C₃×C₂₃	1	1	yes	characteristic
32	C₂×C₃×C₂₃	—	25	1	no	—
33	C₅×C₂₃	—	2	2	no	—
34	C₅×C₂₃	C₉×AGL(1,𝔽₅)	1	2	yes	complemented
35	#1044	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
36	C₄×C₂₃	—	25	1	no	Hall
37	C₉×D₅	—	5	2	no	—
38	C₉×D₅	—	10	2	no	—
39	C₃×C₅²	C₃×C₄×C₂₃	1	1	yes	characteristic
40	C₃×C₂₃	C₃×#1044	1	1	yes	characteristic
41	C₃×AGL(1,𝔽₅)	—	5	2	no	—
42	C₅⋊D₅	C₂×C₉×C₂₃	1	1	yes	characteristic
43	C₂×C₂₃	—	25	1	no	—
44	C₅×C₉	—	2	2	no	—
45	C₅×C₉	AGL(1,𝔽₅)×C₂₃	1	2	yes	complemented
46	C₄×C₉	—	25	1	no	Hall
47	C₃×D₅	—	5	2	no	—
48	C₃×D₅	—	10	2	no	—
49	C₅²	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
50	C₂₃	C₉×#1044	1	1	yes	characteristic, direct product factor, Sylow
51	AGL(1,𝔽₅)	—	5	2	no	—
52	C₂×C₉	—	25	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₃×AGL(1,𝔽₅)×C₂₃	1	2	yes	—
55	C₃×C₄	—	25	1	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₉	C₂₃×#1044	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₃	—	25	1	no	—
60	C₅	—	2	2	no	—
61	C₅	C₉×AGL(1,𝔽₅)×C₂₃	1	2	yes	complemented
62	C₄	—	25	1	no	Sylow
63	C₃	C₃×C₂₃×#1044	1	1	yes	characteristic
64	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₂₃	#1044
commutator, hypocenter	C₅²	C₄×C₉×C₂₃
Frattini	C₃	C₃×C₂₃×#1044
Fitting	C₅²×C₉×C₂₃	C₄
socle	C₃×C₅²×C₂₃	C₃×C₄
prime radical	C₃×C₂₃×C₅⋊D₅	C₂×C₃
cosocle	C₃×C₅⋊D₅	C₂×C₃×C₂₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₉×C₂₃

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₂₃	C₄	semidirect
6. C₂₃×#1044	C₉	direct (N × H)
13. C₅×C₉×C₂₃	AGL(1,𝔽₅)	semidirect
14. C₉×#1044	C₂₃	direct (N × H)
18. C₅²×C₂₃	C₄×C₉	semidirect
28. C₅²×C₉	C₄×C₂₃	semidirect
29. C₉×C₂₃	#1044	direct (N × H)
34. C₅×C₂₃	C₉×AGL(1,𝔽₅)	semidirect
35. #1044	C₉×C₂₃	direct (N × H)
45. C₅×C₉	AGL(1,𝔽₅)×C₂₃	semidirect
49. C₅²	C₄×C₉×C₂₃	semidirect
50. C₂₃	C₉×#1044	direct (N × H)
58. C₉	C₂₃×#1044	direct (N × H)
61. C₅	C₉×AGL(1,𝔽₅)×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₂₃×C₅⋊D₅	2
C₃×C₂₃×#1044	3
C₉×AGL(1,𝔽₅)×C₂₃	5
C₉×#1044	23

Subgroups — C9×C23×#1044 #35208011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂₃×#1044 #35208011