Subgroups — C₈×D₅×C₁₉ #13095064

Order 1520.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₅×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×Dic₅	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₉	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₉	C₂×C₄	1	1	yes	characteristic
9	D₅×C₁₉	C₈	1	2	yes	direct product factor
10	C₂×C₄×C₁₉	—	5	1	no	—
11	C₈×C₁₉	—	5	1	no	—
12	C₈×C₁₉	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₁₉	C₂×C₈	1	1	yes	characteristic, complemented, Hall
14	C₈×D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₁₉	—	5	1	no	—
16	C₄×C₁₉	—	5	1	no	—
17	C₄×C₁₉	C₂×D₅	1	1	yes	characteristic
18	C₄×D₅	C₂×C₁₉	1	1	yes	characteristic
19	C₅×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
20	#168	C₂×C₁₉	1	1	yes	characteristic, complemented
21	C₂×C₁₉	—	5	2	no	—
22	C₂×C₁₉	C₄×D₅	1	1	yes	characteristic
23	C₂×D₅	C₄×C₁₉	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₁₉	1	1	yes	characteristic
25	Dic₅	C₄×C₁₉	1	1	yes	characteristic
26	C₁₉	C₈×D₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₈	—	5	1	no	Sylow
28	C₂×C₅	C₂×C₄×C₁₉	1	1	yes	characteristic
29	D₅	C₈×C₁₉	1	2	yes	direct product factor
30	C₂×C₄	—	5	1	no	—
31	C₈	—	5	1	no	—
32	C₈	D₅×C₁₉	1	1	yes	characteristic, direct product factor
33	C₅	C₂×C₈×C₁₉	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	5	1	no	—
35	C₄	—	5	1	no	—
36	C₄	C₂×D₅×C₁₉	1	1	yes	characteristic
37	C₂	—	5	2	no	—
38	C₂	C₄×D₅×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₁₉	D₅
commutator, hypocenter	C₅	C₂×C₈×C₁₉
Frattini	C₄	C₂×D₅×C₁₉
Fitting	C₅×C₈×C₁₉	C₂
socle	C₂×C₅×C₁₉	C₂×C₄
prime radical	C₂×D₅×C₁₉	C₄
cosocle	C₄×C₅	C₂²×C₁₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₈×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₈×C₁₉	C₂	semidirect
3. C₁₉×#168	C₂	semidirect
9. D₅×C₁₉	C₈	direct (N × H)
12. C₈×C₁₉	D₅	direct (N × H)
13. C₅×C₁₉	C₂×C₈	semidirect
14. C₈×D₅	C₁₉	direct (N × H)
19. C₅×C₈	C₂×C₁₉	semidirect
20. #168	C₂×C₁₉	semidirect
26. C₁₉	C₈×D₅	direct (N × H)
29. D₅	C₈×C₁₉	direct (N × H)
32. C₈	D₅×C₁₉	direct (N × H)
33. C₅	C₂×C₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₅×C₁₉	2
C₅×C₈×C₁₉	2
C₁₉×#168	2
C₂×C₈×C₁₉	5
C₈×D₅	19

Subgroups — C8×D5×C19 #13095064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₅×C₁₉ #13095064