Subgroups — C₃×C₂₃×#66775 #37553296

Order 23460.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#66775	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₇×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×#595	—	5	1	no	maximal, Hall
5	C₂₃×D₈₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₂₃×D₁₇	—	5	1	no	—
7	C₅×C₁₇×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂₃×#595	—	5	1	no	Hall
9	C₃×AGL(1,𝔽₅)×C₂₃	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₂₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×#66775	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂₃×D₁₇	—	5	1	no	—
13	C₃×D₅×C₂₃	—	17	1	no	—
14	C₃×D₈₅	C₂×C₂₃	1	1	yes	characteristic
15	AGL(1,𝔽₅)×C₂₃	—	17	1	no	Hall
16	C₁₇×C₂₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₂₃	#595	1	1	yes	characteristic, complemented, Hall
18	#66775	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄×C₂₃	—	85	1	no	Hall
20	C₃×C₅×C₁₇	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
21	D₅×C₂₃	—	17	1	no	—
22	C₃×#595	—	5	1	no	Hall
23	D₈₅	C₂×C₃×C₂₃	1	1	yes	characteristic
24	C₂×C₃×C₂₃	—	85	1	no	—
25	C₅×C₂₃	C₃×#595	1	1	yes	characteristic, complemented, Hall
26	C₃×D₁₇	—	5	1	no	—
27	C₄×C₂₃	—	85	1	no	Hall
28	C₅×C₁₇	C₃×C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₃	#66775	1	1	yes	characteristic, direct product factor, Hall
30	#595	—	5	1	no	Hall
31	C₃×AGL(1,𝔽₅)	—	17	1	no	Hall
32	C₃×C₁₇	AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	—	85	1	no	—
34	D₁₇	—	5	1	no	—
35	C₃×D₅	—	17	1	no	—
36	C₂₃	C₃×#66775	1	1	yes	characteristic, direct product factor, Sylow
37	AGL(1,𝔽₅)	—	17	1	no	Hall
38	C₁₇	C₃×AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₂₃×#595	1	1	yes	characteristic, complemented, Hall
40	C₃×C₄	—	85	1	no	Hall
41	D₅	—	17	1	no	—
42	C₂×C₃	—	85	1	no	—
43	C₅	C₃×C₂₃×#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	85	1	no	Sylow
45	C₃	C₂₃×#66775	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₃	#66775
commutator, hypocenter	C₅×C₁₇	C₃×C₄×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₂₃	C₄
prime radical	C₃×C₂₃×D₈₅	C₂
cosocle	D₈₅	C₂×C₃×C₂₃
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
2. C₂₃×#66775	C₃	direct (N × H)
3. C₃×C₅×C₁₇×C₂₃	C₄	semidirect
7. C₅×C₁₇×C₂₃	C₃×C₄	semidirect
10. C₃×C₁₇×C₂₃	AGL(1,𝔽₅)	semidirect
11. C₃×#66775	C₂₃	direct (N × H)
16. C₁₇×C₂₃	C₃×AGL(1,𝔽₅)	semidirect
17. C₃×C₅×C₂₃	#595	semidirect
18. #66775	C₃×C₂₃	direct (N × H)
20. C₃×C₅×C₁₇	C₄×C₂₃	semidirect
25. C₅×C₂₃	C₃×#595	semidirect
28. C₅×C₁₇	C₃×C₄×C₂₃	semidirect
29. C₃×C₂₃	#66775	direct (N × H)
32. C₃×C₁₇	AGL(1,𝔽₅)×C₂₃	semidirect
36. C₂₃	C₃×#66775	direct (N × H)
38. C₁₇	C₃×AGL(1,𝔽₅)×C₂₃	semidirect
39. C₃×C₅	C₂₃×#595	semidirect
43. C₅	C₃×C₂₃×#595	semidirect
45. C₃	C₂₃×#66775	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂₃×D₈₅	2
C₂₃×#66775	3
C₃×C₂₃×#595	5
C₃×AGL(1,𝔽₅)×C₂₃	17
C₃×#66775	23

Subgroups — C3×C23×#66775 #37553296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₃×#66775 #37553296