Subgroups — C₃×C₂₃⋊#66774 #37553301

Order 23460.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊#66774	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₇×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₃₉₁	—	5	1	no	maximal, Hall
5	D₅×C₁₇×C₂₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇×C₂₃	—	5	1	no	—
7	C₅×C₁₇×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₃₉₁	—	5	1	no	Hall
9	C₃×C₂₃⋊AGL(1,𝔽₅)	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₂₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×#66774	—	23	1	no	maximal, Hall
12	C₂×C₁₇×C₂₃	—	5	1	no	—
13	C₃×D₅×C₂₃	D₁₇	1	1	yes	characteristic
14	C₃×D₅×C₁₇	D₂₃	1	1	yes	characteristic
15	C₂₃⋊AGL(1,𝔽₅)	—	17	1	no	Hall
16	C₁₇×C₂₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₂₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
18	#66774	—	23	1	no	Hall
19	C₃×Dic₂₃	—	85	1	no	Hall
20	C₃×C₅×C₁₇	Dic₂₃	1	1	yes	characteristic, complemented, Hall
21	D₅×C₂₃	C₃×D₁₇	1	1	yes	characteristic
22	C₃×Dic₁₇	—	115	1	no	Hall
23	D₅×C₁₇	C₃×D₂₃	1	1	yes	characteristic
24	C₂×C₃×C₂₃	—	5	1	no	—
25	C₅×C₂₃	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₇	—	5	1	no	—
27	Dic₂₃	—	85	1	no	Hall
28	C₅×C₁₇	C₃×Dic₂₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₃	#66774	1	1	yes	characteristic, complemented, Hall
30	Dic₁₇	—	115	1	no	Hall
31	C₃×AGL(1,𝔽₅)	—	391	1	no	Hall
32	C₃×C₁₇	C₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	—	5	1	no	—
34	C₂×C₁₇	—	5	1	no	—
35	C₃×D₅	D₃₉₁	1	1	yes	characteristic
36	C₂₃	C₃×#66774	1	1	yes	characteristic, complemented, Sylow
37	AGL(1,𝔽₅)	—	391	1	no	Hall
38	C₁₇	C₃×C₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	Dic₃₉₁	1	1	yes	characteristic, complemented, Hall
40	C₃×C₄	—	1955	1	no	Hall
41	D₅	C₃×D₃₉₁	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₃×Dic₃₉₁	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	1955	1	no	Sylow
45	C₃	C₂₃⋊#66774	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂₃⋊#66774
commutator, hypocenter	C₅×C₁₇×C₂₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₂₃	C₄
prime radical	C₃×D₅×C₁₇×C₂₃	C₂
cosocle	D₅×C₁₇×C₂₃	C₂×C₃
LCS	G ▷ C₅×C₁₇×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₂₃⋊#66774	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
16. C₁₇×C₂₃	C₃×AGL(1,𝔽₅)	semidirect
17. C₃×C₅×C₂₃	Dic₁₇	semidirect
20. C₃×C₅×C₁₇	Dic₂₃	semidirect
25. C₅×C₂₃	C₃×Dic₁₇	semidirect
28. C₅×C₁₇	C₃×Dic₂₃	semidirect
29. C₃×C₂₃	#66774	semidirect
32. C₃×C₁₇	C₂₃⋊AGL(1,𝔽₅)	semidirect
36. C₂₃	C₃×#66774	semidirect
38. C₁₇	C₃×C₂₃⋊AGL(1,𝔽₅)	semidirect
39. C₃×C₅	Dic₃₉₁	semidirect
43. C₅	C₃×Dic₃₉₁	semidirect
45. C₃	C₂₃⋊#66774	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×D₅×C₁₇×C₂₃	2
C₂₃⋊#66774	3
C₃×Dic₃₉₁	5
C₃×C₂₃⋊AGL(1,𝔽₅)	17
C₃×#66774	23

Subgroups — C3×C23⋊#66774 #37553301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₃⋊#66774 #37553301