Subgroups — C₉×C₂₃×#1043 #35208009

Order 20700.

144 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×#1043	C₃	1	1	yes	maximal, characteristic
3	C₅²×C₉×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×AGL(1,𝔽₅)×C₂₃	—	5	6	no	maximal
5	C₃×C₂₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₂₃×#1043	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×D₅×C₂₃	—	5	6	no	—
8	C₃×C₅²×C₂₃	C₃×C₄	1	1	yes	characteristic
9	C₃×AGL(1,𝔽₅)×C₂₃	—	5	6	no	—
10	C₂₃×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
11	C₅×C₉×C₂₃	AGL(1,𝔽₅)	1	6	yes	complemented
12	C₉×#1043	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₉×C₂₃	—	25	1	no	Hall
14	C₃×D₅×C₂₃	—	5	6	no	—
15	C₅²×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	AGL(1,𝔽₅)×C₂₃	—	5	6	no	—
17	C₉×C₅⋊D₅	C₂×C₂₃	1	1	yes	characteristic
18	C₂×C₉×C₂₃	—	25	1	no	—
19	C₃×C₅×C₂₃	C₃×AGL(1,𝔽₅)	1	6	yes	—
20	C₃×#1043	C₃×C₂₃	1	1	yes	characteristic
21	C₃×C₄×C₂₃	—	25	1	no	—
22	D₅×C₂₃	—	5	6	no	—
23	C₅²×C₉	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₉×C₂₃	#1043	1	1	yes	characteristic, direct product factor, Hall
25	C₉×AGL(1,𝔽₅)	—	5	6	no	—
26	C₃×C₅⋊D₅	C₂×C₃×C₂₃	1	1	yes	characteristic
27	C₂×C₃×C₂₃	—	25	1	no	—
28	C₅×C₂₃	C₉×AGL(1,𝔽₅)	1	6	yes	complemented
29	#1043	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
30	C₄×C₂₃	—	25	1	no	Hall
31	C₉×D₅	—	5	6	no	—
32	C₃×C₅²	C₃×C₄×C₂₃	1	1	yes	characteristic
33	C₃×C₂₃	C₃×#1043	1	1	yes	characteristic
34	C₃×AGL(1,𝔽₅)	—	5	6	no	—
35	C₅⋊D₅	C₂×C₉×C₂₃	1	1	yes	characteristic
36	C₂×C₂₃	—	25	1	no	—
37	C₅×C₉	AGL(1,𝔽₅)×C₂₃	1	6	yes	complemented
38	C₄×C₉	—	25	1	no	Hall
39	C₃×D₅	—	5	6	no	—
40	C₅²	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂₃	C₉×#1043	1	1	yes	characteristic, direct product factor, Sylow
42	AGL(1,𝔽₅)	—	5	6	no	—
43	C₂×C₉	—	25	1	no	—
44	C₃×C₅	C₃×AGL(1,𝔽₅)×C₂₃	1	6	yes	—
45	C₃×C₄	—	25	1	no	—
46	D₅	—	5	6	no	—
47	C₉	C₂₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	—	25	1	no	—
49	C₅	C₉×AGL(1,𝔽₅)×C₂₃	1	6	yes	complemented
50	C₄	—	25	1	no	Sylow
51	C₃	C₃×C₂₃×#1043	1	1	yes	characteristic
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₂₃	#1043
commutator, hypocenter	C₅²	C₄×C₉×C₂₃
Frattini	C₃	C₃×C₂₃×#1043
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×#1043	C₉	direct (N × H)
11. C₅×C₉×C₂₃	AGL(1,𝔽₅)	semidirect
12. C₉×#1043	C₂₃	direct (N × H)
15. C₅²×C₂₃	C₄×C₉	semidirect
23. C₅²×C₉	C₄×C₂₃	semidirect
24. C₉×C₂₃	#1043	direct (N × H)
28. C₅×C₂₃	C₉×AGL(1,𝔽₅)	semidirect
29. #1043	C₉×C₂₃	direct (N × H)
37. C₅×C₉	AGL(1,𝔽₅)×C₂₃	semidirect
40. C₅²	C₄×C₉×C₂₃	semidirect
41. C₂₃	C₉×#1043	direct (N × H)
47. C₉	C₂₃×#1043	direct (N × H)
49. 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×#1043	3
C₉×AGL(1,𝔽₅)×C₂₃	5
C₉×#1043	23

Subgroups — C9×C23×#1043 #35208009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂₃×#1043 #35208009