Subgroups — C₂×D₅×C₁₉×C₅₉ #36375780

Order 22420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₉×C₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₉×C₅₉	—	5	1	no	maximal, Hall
5	C₂×C₁₉×C₅₉	—	5	2	no	—
6	C₂×C₁₉×C₅₉	D₅	1	1	yes	characteristic, direct product factor
7	C₂×D₅×C₅₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₅₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₅₉	C₂×C₁₉	1	1	yes	characteristic, complemented
10	D₅×C₅₉	C₂×C₁₉	1	2	yes	direct product factor
11	C₂×D₅×C₁₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₅₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₅₉	—	5	1	no	Hall
14	C₂×C₅×C₁₉	C₂×C₅₉	1	1	yes	characteristic, complemented
15	D₅×C₁₉	C₂×C₅₉	1	2	yes	direct product factor
16	C₂×C₅₉	—	5	2	no	—
17	C₂×C₅₉	D₅×C₁₉	1	1	yes	characteristic, direct product factor
18	C₅×C₁₉	C₂²×C₅₉	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₁₉	—	5	1	no	Hall
20	C₅₉	C₂×D₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₉	—	5	2	no	—
22	C₂×C₁₉	D₅×C₅₉	1	1	yes	characteristic, direct product factor
23	C₂×D₅	C₁₉×C₅₉	1	1	yes	characteristic, direct product factor, Hall
24	C₁₉	C₂×D₅×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₂×C₁₉×C₅₉	1	1	yes	characteristic, complemented
26	D₅	C₂×C₁₉×C₅₉	1	2	yes	direct product factor
27	C₅	C₂²×C₁₉×C₅₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	5	1	no	Sylow
29	C₂	—	5	2	no	—
30	C₂	D₅×C₁₉×C₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₅₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₁₉×C₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₅₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₉×C₅₉

Complements

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

N	H ≅ G/N	type
1. D₅×C₁₉×C₅₉	C₂	direct (N × H)
2. C₂×C₅×C₁₉×C₅₉	C₂	semidirect
3. C₅×C₁₉×C₅₉	C₂²	semidirect
6. C₂×C₁₉×C₅₉	D₅	direct (N × H)
7. C₂×D₅×C₅₉	C₁₉	direct (N × H)
8. C₁₉×C₅₉	C₂×D₅	direct (N × H)
9. C₂×C₅×C₅₉	C₂×C₁₉	semidirect
10. D₅×C₅₉	C₂×C₁₉	direct (N × H)
11. C₂×D₅×C₁₉	C₅₉	direct (N × H)
12. C₅×C₅₉	C₂²×C₁₉	semidirect
14. C₂×C₅×C₁₉	C₂×C₅₉	semidirect
15. D₅×C₁₉	C₂×C₅₉	direct (N × H)
17. C₂×C₅₉	D₅×C₁₉	direct (N × H)
18. C₅×C₁₉	C₂²×C₅₉	semidirect
20. C₅₉	C₂×D₅×C₁₉	direct (N × H)
22. C₂×C₁₉	D₅×C₅₉	direct (N × H)
23. C₂×D₅	C₁₉×C₅₉	direct (N × H)
24. C₁₉	C₂×D₅×C₅₉	direct (N × H)
25. C₂×C₅	C₂×C₁₉×C₅₉	semidirect
26. D₅	C₂×C₁₉×C₅₉	direct (N × H)
27. C₅	C₂²×C₁₉×C₅₉	semidirect
30. C₂	D₅×C₁₉×C₅₉	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×C₁₉×C₅₉	2
C₂×C₅×C₁₉×C₅₉	2
C₂²×C₁₉×C₅₉	5
C₂×D₅×C₅₉	19
C₂×D₅×C₁₉	59

Subgroups — C2×D5×C19×C59 #36375780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₁₉×C₅₉ #36375780