Subgroups — C₁₉×#685 #13095074

Order 1520.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×D₅×C₁₉	—	2	1	no	—
6	C₂×D₅×C₁₉	—	2	1	no	—
7	C₂×D₅×C₁₉	C₄	1	2	yes	complemented
8	C₄×C₅×C₁₉	—	2	1	no	—
9	C₁₉×Dic₅	—	2	1	no	—
10	C₂²⋊C₄×C₁₉	—	5	1	no	maximal, Hall
11	C₂×C₅×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₅×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₅×C₁₉	D₄	1	1	yes	characteristic
14	D₅×C₁₉	—	2	2	no	—
15	C₂³×C₁₉	—	5	1	no	—
16	C₂×C₄×C₁₉	—	5	1	no	—
17	C₂×C₄×C₁₉	D₅	1	1	yes	characteristic, complemented
18	C₅×C₁₉	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
19	#685	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₁₉	—	5	2	no	—
21	C₂²×C₁₉	—	10	1	no	—
22	C₂²×C₁₉	—	10	1	no	—
23	C₂²×C₁₉	C₂×D₅	1	1	yes	characteristic
24	C₄×C₁₉	—	2	1	no	—
25	C₄×C₁₉	—	10	1	no	—
26	C₂²×D₅	C₂×C₁₉	1	1	yes	characteristic
27	C₂×C₄×C₅	C₂×C₁₉	1	1	yes	characteristic, complemented
28	C₂×Dic₅	C₂×C₁₉	1	1	yes	characteristic, complemented
29	C₂×C₁₉	—	10	2	no	—
30	C₂×C₁₉	C₄×D₅	1	1	yes	characteristic
31	C₂×C₁₉	D₂₀	1	1	yes	characteristic
32	C₂×C₁₉	C₂²⋊D₅	1	1	yes	characteristic
33	C₂²×C₅	C₂²×C₁₉	1	1	yes	characteristic
34	C₂×D₅	—	2	1	no	—
35	C₂×D₅	—	2	1	no	—
36	C₂×D₅	C₄×C₁₉	1	2	yes	complemented
37	C₄×C₅	—	2	1	no	—
38	Dic₅	—	2	1	no	—
39	C₁₉	#685	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²⋊C₄	—	5	1	no	Sylow
41	C₂×C₅	C₂×C₄×C₁₉	1	1	yes	characteristic
42	C₂×C₅	D₄×C₁₉	1	1	yes	characteristic
43	C₂×C₅	D₄×C₁₉	1	1	yes	characteristic
44	D₅	—	2	2	no	—
45	C₂³	—	5	1	no	—
46	C₂×C₄	—	5	1	no	—
47	C₂×C₄	D₅×C₁₉	1	1	yes	characteristic, complemented
48	C₅	C₂²⋊C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	5	2	no	—
50	C₂²	—	10	1	no	—
51	C₂²	—	10	1	no	—
52	C₂²	C₂×D₅×C₁₉	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	10	1	no	—
55	C₂	—	10	2	no	—
56	C₂	C₄×D₅×C₁₉	1	1	yes	characteristic
57	C₂	C₁₉×D₂₀	1	1	yes	characteristic
58	C₂	C₁₉×C₂²⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×C₁₉	C₂	semidirect
3. C₂×C₁₉×Dic₅	C₂	semidirect
7. C₂×D₅×C₁₉	C₄	semidirect
17. C₂×C₄×C₁₉	D₅	semidirect
18. C₅×C₁₉	C₂²⋊C₄	semidirect
19. #685	C₁₉	direct (N × H)
27. C₂×C₄×C₅	C₂×C₁₉	semidirect
28. C₂×Dic₅	C₂×C₁₉	semidirect
36. C₂×D₅	C₄×C₁₉	semidirect
39. C₁₉	#685	direct (N × H)
47. C₂×C₄	D₅×C₁₉	semidirect
48. C₅	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₁₉	2
C₂×C₄×C₅×C₁₉	2
C₂×C₁₉×Dic₅	2
C₂²⋊C₄×C₁₉	5
#685	19

Subgroups — C19×#685 #13095074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#685 #13095074