Subgroups — C₂×C₅×C₁₉×D₈₃ #44538705

Order 31540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×D₈₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₉×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×C₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×D₈₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₉×C₈₃	C₂×C₅	1	1	yes	characteristic, complemented
6	C₁₉×D₈₃	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₅×D₈₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₈₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₈₃	C₂×C₁₉	1	1	yes	characteristic, complemented
10	C₅×D₈₃	C₂×C₁₉	1	2	yes	direct product factor
11	C₅×C₈₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₅×C₁₉	—	83	1	no	maximal, Hall
13	C₂×D₈₃	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₉	—	83	2	no	—
15	C₂×C₅×C₁₉	D₈₃	1	1	yes	characteristic, direct product factor
16	C₂×C₈₃	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
17	D₈₃	C₂×C₅×C₁₉	1	2	yes	direct product factor
18	C₅×C₁₉	C₂×D₈₃	1	1	yes	characteristic, direct product factor, Hall
19	C₈₃	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₁₉	—	83	1	no	Hall
21	C₂×C₁₉	—	83	2	no	—
22	C₂×C₁₉	C₅×D₈₃	1	1	yes	characteristic, direct product factor
23	C₂²×C₅	—	83	1	no	Hall
24	C₁₉	C₂×C₅×D₈₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	—	83	2	no	—
26	C₂×C₅	C₁₉×D₈₃	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₁₉×D₈₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	83	1	no	Sylow
29	C₂	—	83	2	no	—
30	C₂	C₅×C₁₉×D₈₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₈₃
commutator, cosocle, hypocenter	C₈₃	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₈₃	C₂
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₂×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×D₈₃	C₂	direct (N × H)
2. C₂×C₅×C₁₉×C₈₃	C₂	semidirect
3. C₅×C₁₉×C₈₃	C₂²	semidirect
4. C₂×C₁₉×D₈₃	C₅	direct (N × H)
5. C₂×C₁₉×C₈₃	C₂×C₅	semidirect
6. C₁₉×D₈₃	C₂×C₅	direct (N × H)
7. C₂×C₅×D₈₃	C₁₉	direct (N × H)
8. C₁₉×C₈₃	C₂²×C₅	semidirect
9. C₂×C₅×C₈₃	C₂×C₁₉	semidirect
10. C₅×D₈₃	C₂×C₁₉	direct (N × H)
11. C₅×C₈₃	C₂²×C₁₉	semidirect
13. C₂×D₈₃	C₅×C₁₉	direct (N × H)
15. C₂×C₅×C₁₉	D₈₃	direct (N × H)
16. C₂×C₈₃	C₂×C₅×C₁₉	semidirect
17. D₈₃	C₂×C₅×C₁₉	direct (N × H)
18. C₅×C₁₉	C₂×D₈₃	direct (N × H)
19. C₈₃	C₂²×C₅×C₁₉	semidirect
22. C₂×C₁₉	C₅×D₈₃	direct (N × H)
24. C₁₉	C₂×C₅×D₈₃	direct (N × H)
26. C₂×C₅	C₁₉×D₈₃	direct (N × H)
27. C₅	C₂×C₁₉×D₈₃	direct (N × H)
30. C₂	C₅×C₁₉×D₈₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×D₈₃	2
C₂×C₅×C₁₉×C₈₃	2
C₂×C₁₉×D₈₃	5
C₂×C₅×D₈₃	19
C₂²×C₅×C₁₉	83

Subgroups — C2×C5×C19×D83 #44538705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₉×D₈₃ #44538705