Subgroups — D₅×D₁₉×C₆₁ #37550819

Order 23180.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₉×C₆₁	—	5	1	no	maximal, Hall
6	C₂×C₁₉×C₆₁	—	5	1	no	—
7	D₁₉×C₆₁	—	5	1	no	—
8	D₁₉×C₆₁	D₅	1	1	yes	characteristic, direct product factor
9	C₂×D₅×C₆₁	—	19	1	no	maximal, Hall
10	C₁₉×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₆₁	—	19	1	no	—
12	D₅×C₆₁	—	19	1	no	—
13	D₅×C₆₁	D₁₉	1	1	yes	characteristic, direct product factor
14	D₅×D₁₉	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₆₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₆₁	—	95	1	no	Hall
17	D₉₅	C₂×C₆₁	1	1	yes	characteristic, complemented
18	C₅×D₁₉	C₂×C₆₁	1	1	yes	characteristic, complemented
19	D₅×C₁₉	C₂×C₆₁	1	1	yes	characteristic, complemented
20	C₂×C₆₁	—	5	1	no	—
21	C₂×C₆₁	—	19	1	no	—
22	C₂×C₆₁	—	95	1	no	—
23	C₅×C₁₉	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₉	—	5	1	no	Hall
25	C₆₁	D₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₁₉	—	5	1	no	—
27	D₁₉	—	5	1	no	—
28	D₁₉	D₅×C₆₁	1	1	yes	characteristic, direct product factor
29	C₂×D₅	—	19	1	no	Hall
30	C₁₉	C₂×D₅×C₆₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	19	1	no	—
32	D₅	—	19	1	no	—
33	D₅	D₁₉×C₆₁	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₁₉×C₆₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	95	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	19	1	no	—
38	C₂	—	95	1	no	—

	subgroup	G/H
center, hypercenter	C₆₁	D₅×D₁₉
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₆₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₆₁	C₂²
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₆₁

Complements

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

N	H ≅ G/N	type
1. C₆₁×D₉₅	C₂	semidirect
2. D₅×C₁₉×C₆₁	C₂	semidirect
3. C₅×D₁₉×C₆₁	C₂	semidirect
4. C₅×C₁₉×C₆₁	C₂²	semidirect
8. D₁₉×C₆₁	D₅	direct (N × H)
10. C₁₉×C₆₁	C₂×D₅	semidirect
13. D₅×C₆₁	D₁₉	direct (N × H)
14. D₅×D₁₉	C₆₁	direct (N × H)
15. C₅×C₆₁	C₂×D₁₉	semidirect
17. D₉₅	C₂×C₆₁	semidirect
18. C₅×D₁₉	C₂×C₆₁	semidirect
19. D₅×C₁₉	C₂×C₆₁	semidirect
23. C₅×C₁₉	C₂²×C₆₁	semidirect
25. C₆₁	D₅×D₁₉	direct (N × H)
28. D₁₉	D₅×C₆₁	direct (N × H)
30. C₁₉	C₂×D₅×C₆₁	semidirect
33. D₅	D₁₉×C₆₁	direct (N × H)
34. C₅	C₂×D₁₉×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×D₉₅	2
D₅×C₁₉×C₆₁	2
C₅×D₁₉×C₆₁	2
C₂×D₁₉×C₆₁	5
C₂×D₅×C₆₁	19
D₅×D₁₉	61

Subgroups — D5×D19×C61 #37550819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₉×C₆₁ #37550819