Subgroups — C₂×D₅×C₂₃×C₁₉⋊C₃ #39910752

Order 26220.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₃×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₉×C₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₂₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₂₃×C₁₉⋊C₃	—	5	1	no	maximal, Hall
6	D₅×C₁₉×C₂₃	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₂₃×C₁₉⋊C₃	—	5	2	no	—
9	C₂×C₂₃×C₁₉⋊C₃	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₁₉×C₂₃	—	5	1	no	Hall
12	C₂×C₃×D₅×C₂₃	—	19	1	no	maximal, Hall
13	C₂₃×C₁₉⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×D₅×C₁₉⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₁₉×C₂₃	—	5	2	no	—
16	C₂×C₁₉×C₂₃	C₃×D₅	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×C₂₃	—	19	1	no	—
18	C₃×D₅×C₂₃	—	19	2	no	—
19	C₂×C₅×C₁₉⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented
20	D₅×C₁₉⋊C₃	C₂×C₂₃	1	2	yes	direct product factor
21	C₂×D₅×C₂₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
22	C₁₉×C₂₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₉	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₂₃	—	19	1	no	Hall
25	C₅×C₁₉⋊C₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₃×C₂₃	—	95	1	no	Hall
27	C₂×C₅×C₂₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
28	D₅×C₂₃	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
29	C₂²×C₁₉⋊C₃	—	5	1	no	Hall
30	C₂×C₅×C₁₉	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
31	D₅×C₁₉	C₂×C₃×C₂₃	1	2	yes	complemented
32	C₂×C₃×C₂₃	—	19	1	no	—
33	C₂×C₃×C₂₃	—	95	2	no	—
34	C₅×C₂₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₉⋊C₃	—	5	2	no	—
36	C₂×C₁₉⋊C₃	D₅×C₂₃	1	1	yes	characteristic, direct product factor
37	C₅×C₁₉	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₂₃	—	5	1	no	Hall
39	C₂²×C₁₉	—	5	1	no	Hall
40	C₃×C₂₃	—	19	1	no	Hall
41	C₂×C₃×D₅	—	19	1	no	Hall
42	C₁₉⋊C₃	C₂×D₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₂₃	—	5	2	no	—
44	C₂×C₂₃	D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
45	C₂×C₁₉	—	5	2	no	—
46	C₂×C₁₉	C₃×D₅×C₂₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₅	—	19	1	no	—
48	C₃×D₅	—	19	2	no	—
49	C₂₃	C₂×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×D₅	C₂₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
51	C₁₉	C₂×C₃×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	—	19	1	no	Hall
53	C₂²×C₃	—	95	1	no	Hall
54	C₂×C₅	C₂×C₂₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
55	D₅	C₂×C₂₃×C₁₉⋊C₃	1	2	yes	direct product factor
56	C₂×C₃	—	19	1	no	—
57	C₂×C₃	—	95	2	no	—
58	C₅	C₂²×C₂₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	—	19	1	no	Sylow
61	C₂	—	5	2	no	—
62	C₂	D₅×C₂₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₂₃	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. D₅×C₂₃×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₂₃×C₁₉⋊C₃	C₂	semidirect
3. C₂×D₅×C₁₉×C₂₃	C₃	semidirect
4. C₅×C₂₃×C₁₉⋊C₃	C₂²	semidirect
6. D₅×C₁₉×C₂₃	C₂×C₃	semidirect
7. C₂×C₅×C₁₉×C₂₃	C₂×C₃	semidirect
9. C₂×C₂₃×C₁₉⋊C₃	D₅	direct (N × H)
10. C₅×C₁₉×C₂₃	C₂²×C₃	semidirect
13. C₂₃×C₁₉⋊C₃	C₂×D₅	direct (N × H)
14. C₂×D₅×C₁₉⋊C₃	C₂₃	direct (N × H)
16. C₂×C₁₉×C₂₃	C₃×D₅	semidirect
19. C₂×C₅×C₁₉⋊C₃	C₂×C₂₃	semidirect
20. D₅×C₁₉⋊C₃	C₂×C₂₃	direct (N × H)
21. C₂×D₅×C₂₃	C₁₉⋊C₃	direct (N × H)
22. C₁₉×C₂₃	C₂×C₃×D₅	semidirect
23. C₂×D₅×C₁₉	C₃×C₂₃	semidirect
25. C₅×C₁₉⋊C₃	C₂²×C₂₃	semidirect
27. C₂×C₅×C₂₃	C₂×C₁₉⋊C₃	semidirect
28. D₅×C₂₃	C₂×C₁₉⋊C₃	direct (N × H)
30. C₂×C₅×C₁₉	C₂×C₃×C₂₃	semidirect
31. D₅×C₁₉	C₂×C₃×C₂₃	semidirect
34. C₅×C₂₃	C₂²×C₁₉⋊C₃	semidirect
36. C₂×C₁₉⋊C₃	D₅×C₂₃	direct (N × H)
37. C₅×C₁₉	C₂²×C₃×C₂₃	semidirect
42. C₁₉⋊C₃	C₂×D₅×C₂₃	direct (N × H)
44. C₂×C₂₃	D₅×C₁₉⋊C₃	direct (N × H)
46. C₂×C₁₉	C₃×D₅×C₂₃	semidirect
49. C₂₃	C₂×D₅×C₁₉⋊C₃	direct (N × H)
50. C₂×D₅	C₂₃×C₁₉⋊C₃	direct (N × H)
51. C₁₉	C₂×C₃×D₅×C₂₃	semidirect
54. C₂×C₅	C₂×C₂₃×C₁₉⋊C₃	semidirect
55. D₅	C₂×C₂₃×C₁₉⋊C₃	direct (N × H)
58. C₅	C₂²×C₂₃×C₁₉⋊C₃	semidirect
62. C₂	D₅×C₂₃×C₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₅×C₂₃×C₁₉⋊C₃	2
C₂×C₅×C₂₃×C₁₉⋊C₃	2
C₂×D₅×C₁₉×C₂₃	3
C₂²×C₂₃×C₁₉⋊C₃	5
C₂×C₃×D₅×C₂₃	19
C₂×D₅×C₁₉⋊C₃	23

Subgroups — C2×D5×C23×C19⋊C3 #39910752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₂₃×C₁₉⋊C₃ #39910752