Subgroups — C₂₃×C₃⋊#66772 #37553327

Order 23460.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#66772	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₃×C₃⋊#595	—	5	1	no	maximal, Hall
5	C₅×C₂₃×D₁₇	D₃	1	1	yes	characteristic
6	C₃×C₂₃×D₁₇	D₅	1	1	yes	characteristic
7	C₅×C₁₇×C₂₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₂₃×#595	—	15	1	no	Hall
9	C₂₃×Dic₁₅	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₂₃	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#66772	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂₃×D₁₇	D₁₅	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂₃	—	17	1	no	—
14	C₃×C₅×D₁₇	C₂×C₂₃	1	1	yes	characteristic
15	Dic₅×C₂₃	—	51	1	no	Hall
16	C₁₇×C₂₃	Dic₁₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₂₃	#595	1	1	yes	characteristic, complemented, Hall
18	#66772	—	3	1	no	Hall
19	Dic₃×C₂₃	—	85	1	no	Hall
20	C₃×C₅×C₁₇	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₂₃	—	17	1	no	—
22	C₃⋊#595	—	5	1	no	Hall
23	C₅×D₁₇	D₃×C₂₃	1	1	yes	characteristic
24	C₂×C₃×C₂₃	—	17	1	no	—
25	C₅×C₂₃	C₃⋊#595	1	1	yes	characteristic, complemented, Hall
26	C₃×D₁₇	D₅×C₂₃	1	1	yes	characteristic
27	C₄×C₂₃	—	255	1	no	Hall
28	C₅×C₁₇	Dic₃×C₂₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₃	#66772	1	1	yes	characteristic, complemented, Hall
30	#595	—	15	1	no	Hall
31	Dic₁₅	—	17	1	no	Hall
32	C₃×C₁₇	Dic₅×C₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	—	17	1	no	—
34	D₁₇	C₂₃×D₁₅	1	1	yes	characteristic
35	C₂×C₃×C₅	—	17	1	no	—
36	C₂₃	C₃⋊#66772	1	1	yes	characteristic, direct product factor, Sylow
37	Dic₅	—	51	1	no	Hall
38	C₁₇	C₂₃×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₂₃×#595	1	1	yes	characteristic, complemented, Hall
40	Dic₃	—	85	1	no	Hall
41	C₂×C₅	—	17	1	no	—
42	C₂×C₃	—	17	1	no	—
43	C₅	C₂₃×C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	255	1	no	Sylow
45	C₃	C₂₃×#66772	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	C₃⋊#66772
commutator, hypocenter	C₃×C₅×C₁₇	C₄×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₂₃	C₄
prime radical	C₃×C₅×C₂₃×D₁₇	C₂
cosocle	C₃×C₅×D₁₇	C₂×C₂₃
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇×C₂₃	C₄	semidirect
7. C₅×C₁₇×C₂₃	Dic₃	semidirect
10. C₃×C₁₇×C₂₃	Dic₅	semidirect
11. C₃⋊#66772	C₂₃	direct (N × H)
16. C₁₇×C₂₃	Dic₁₅	semidirect
17. C₃×C₅×C₂₃	#595	semidirect
20. C₃×C₅×C₁₇	C₄×C₂₃	semidirect
25. C₅×C₂₃	C₃⋊#595	semidirect
28. C₅×C₁₇	Dic₃×C₂₃	semidirect
29. C₃×C₂₃	#66772	semidirect
32. C₃×C₁₇	Dic₅×C₂₃	semidirect
36. C₂₃	C₃⋊#66772	direct (N × H)
38. C₁₇	C₂₃×Dic₁₅	semidirect
39. C₃×C₅	C₂₃×#595	semidirect
43. C₅	C₂₃×C₃⋊#595	semidirect
45. C₃	C₂₃×#66772	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂₃×D₁₇	2
C₂₃×#66772	3
C₂₃×C₃⋊#595	5
C₂₃×Dic₁₅	17
C₃⋊#66772	23

Subgroups — C23×C3⋊#66772 #37553327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×C₃⋊#66772 #37553327