Subgroups — C₃×C₅×C₁₉×Dic₂₃ #39910713

Order 26220.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×Dic₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₉×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×Dic₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₉×C₂₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₉×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₁₉×Dic₂₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×Dic₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₉×C₂₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₅×C₁₉	—	23	1	no	maximal, Hall
12	C₂×C₁₉×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂₃	C₂×C₁₉	1	1	yes	characteristic
14	C₂×C₃×C₅×C₁₉	D₂₃	1	1	yes	characteristic
15	C₅×Dic₂₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₁₉×C₂₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	C₄×C₅×C₁₉	—	23	1	no	Hall
18	C₃×C₅×C₂₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×C₁₉	Dic₂₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×Dic₂₃	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₂₃	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₃×C₄×C₁₉	—	23	1	no	Hall
23	C₂×C₅×C₁₉	C₃×D₂₃	1	1	yes	characteristic
24	C₂×C₃×C₂₃	C₂×C₅×C₁₉	1	1	yes	characteristic
25	C₅×C₂₃	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₉	C₅×D₂₃	1	1	yes	characteristic
27	C₅×C₁₉	C₃×Dic₂₃	1	1	yes	characteristic, direct product factor, Hall
28	Dic₂₃	C₃×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₄×C₁₉	—	23	1	no	Hall
30	C₃×C₂₃	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄×C₅	—	23	1	no	Hall
32	C₃×C₁₉	C₅×Dic₂₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₂₃	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic
34	C₂×C₁₉	C₃×C₅×D₂₃	1	1	yes	characteristic
35	C₂×C₃×C₅	C₁₉×D₂₃	1	1	yes	characteristic
36	C₂₃	C₃×C₄×C₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
37	C₄×C₅	—	23	1	no	Hall
38	C₁₉	C₃×C₅×Dic₂₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₁₉×Dic₂₃	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₄	—	23	1	no	Hall
41	C₂×C₅	C₃×C₁₉×D₂₃	1	1	yes	characteristic
42	C₂×C₃	C₅×C₁₉×D₂₃	1	1	yes	characteristic
43	C₅	C₃×C₁₉×Dic₂₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	23	1	no	Sylow
45	C₃	C₅×C₁₉×Dic₂₃	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₅×C₁₉×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₉	D₂₃
commutator, hypocenter	C₂₃	C₃×C₄×C₅×C₁₉
Frattini	C₂	C₃×C₅×C₁₉×D₂₃
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₉×C₂₃	C₂
cosocle	C₂×C₂₃	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₉×Dic₂₃	C₃	direct (N × H)
3. C₃×C₅×C₁₉×C₂₃	C₄	semidirect
4. C₃×C₁₉×Dic₂₃	C₅	direct (N × H)
7. C₅×C₁₉×C₂₃	C₃×C₄	semidirect
8. C₁₉×Dic₂₃	C₃×C₅	direct (N × H)
9. C₃×C₅×Dic₂₃	C₁₉	direct (N × H)
10. C₃×C₁₉×C₂₃	C₄×C₅	semidirect
15. C₅×Dic₂₃	C₃×C₁₉	direct (N × H)
16. C₁₉×C₂₃	C₃×C₄×C₅	semidirect
18. C₃×C₅×C₂₃	C₄×C₁₉	semidirect
19. C₃×C₅×C₁₉	Dic₂₃	direct (N × H)
20. C₃×Dic₂₃	C₅×C₁₉	direct (N × H)
25. C₅×C₂₃	C₃×C₄×C₁₉	semidirect
27. C₅×C₁₉	C₃×Dic₂₃	direct (N × H)
28. Dic₂₃	C₃×C₅×C₁₉	direct (N × H)
30. C₃×C₂₃	C₄×C₅×C₁₉	semidirect
32. C₃×C₁₉	C₅×Dic₂₃	direct (N × H)
36. C₂₃	C₃×C₄×C₅×C₁₉	semidirect
38. C₁₉	C₃×C₅×Dic₂₃	direct (N × H)
39. C₃×C₅	C₁₉×Dic₂₃	direct (N × H)
43. C₅	C₃×C₁₉×Dic₂₃	direct (N × H)
45. C₃	C₅×C₁₉×Dic₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₉×C₂₃	2
C₅×C₁₉×Dic₂₃	3
C₃×C₁₉×Dic₂₃	5
C₃×C₅×Dic₂₃	19
C₃×C₄×C₅×C₁₉	23

Subgroups — C3×C5×C19×Dic23 #39910713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₉×Dic₂₃ #39910713