Subgroups — C₅×#64515 #13095049

Order 1520.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₁₉	C₄	1	1	yes	characteristic
5	C₄×C₅×C₁₉	C₂²	1	1	yes	characteristic
6	C₅×Dic₁₉	C₄	1	1	yes	characteristic
7	#64515	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₅×D₁₉	—	2	1	no	—
10	C₄×D₁₉	C₂×C₅	1	1	yes	characteristic
11	C₈×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₁₉⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₁₉	M₁₆	1	1	yes	characteristic, complemented, Hall
14	C₅×M₁₆	—	19	1	no	maximal, Hall
15	C₂×D₁₉	C₄×C₅	1	1	yes	characteristic
16	C₄×C₁₉	C₂²×C₅	1	1	yes	characteristic
17	Dic₁₉	C₄×C₅	1	1	yes	characteristic
18	C₂×C₄×C₅	—	19	1	no	—
19	C₅×C₈	—	19	1	no	—
20	C₅×C₈	D₁₉	1	1	yes	characteristic, complemented
21	C₂×C₁₉	C₂×C₄×C₅	1	1	yes	characteristic
22	D₁₉	—	2	1	no	—
23	C₂²×C₅	—	19	1	no	—
24	C₄×C₅	—	19	1	no	—
25	C₄×C₅	C₂×D₁₉	1	1	yes	characteristic
26	C₁₉	C₅×M₁₆	1	1	yes	characteristic, complemented, Sylow
27	M₁₆	—	19	1	no	Sylow
28	C₂×C₅	—	38	1	no	—
29	C₂×C₅	C₄×D₁₉	1	1	yes	characteristic
30	C₂×C₄	—	19	1	no	—
31	C₈	—	19	1	no	—
32	C₈	C₅×D₁₉	1	1	yes	characteristic, complemented
33	C₅	#64515	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	19	1	no	—
35	C₄	—	19	1	no	—
36	C₄	C₂×C₅×D₁₉	1	1	yes	characteristic
37	C₂	—	38	1	no	—
38	C₂	C₄×C₅×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₁₉
commutator	C₂×C₁₉	C₂×C₄×C₅
Frattini	C₄	C₂×C₅×D₁₉
Fitting	C₅×C₈×C₁₉	C₂
socle	C₂×C₅×C₁₉	C₂×C₄
prime radical	C₂×C₅×D₁₉	C₄
cosocle	C₄×C₁₉	C₂²×C₅
hypercenter	C₅×C₈	D₁₉
hypocenter	C₁₉	C₅×M₁₆
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄×C₅ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×C₈×C₁₉	C₂	semidirect
3. C₅×C₁₉⋊C₈	C₂	semidirect
7. #64515	C₅	direct (N × H)
11. C₈×C₁₉	C₂×C₅	semidirect
12. C₁₉⋊C₈	C₂×C₅	semidirect
13. C₅×C₁₉	M₁₆	semidirect
20. C₅×C₈	D₁₉	semidirect
26. C₁₉	C₅×M₁₆	semidirect
32. C₈	C₅×D₁₉	semidirect
33. C₅	#64515	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×D₁₉	2
C₅×C₈×C₁₉	2
C₅×C₁₉⋊C₈	2
#64515	5
C₅×M₁₆	19

Subgroups — C5×#64515 #13095049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64515 #13095049