Subgroups — C₅×C₁₉×#4379 #30685948

Order 17100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#4379	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₁₉×#157	—	5	1	no	maximal
5	C₅²×D₃×C₁₉	—	6	2	no	—
6	C₅×C₁₉×Dic₅	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₃×C₁₉	—	2	2	no	—
8	C₅×C₃⋊D₃×C₁₉	D₅	1	1	yes	characteristic
9	C₅×C₃⋊D₃×C₁₉	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₉	—	2	2	no	—
11	C₂×C₅²×C₁₉	—	9	1	no	—
12	C₅×#4379	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅×C₁₉	—	2	2	no	—
14	C₃²×C₅×C₁₉	Dic₅	1	1	yes	characteristic, complemented
15	C₃²×C₅×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented
16	C₁₉×#157	—	5	1	no	Hall
17	C₅×D₃×C₁₉	—	6	2	no	—
18	C₅×D₃×C₁₉	—	6	2	no	—
19	C₅×D₃×C₁₉	—	6	8	no	—
20	C₅²×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
21	C₅²×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic
22	C₄×C₅×C₁₉	—	45	1	no	—
23	C₁₉×Dic₅	—	9	1	no	—
24	C₃⋊D₃×C₁₉	C₅×D₅	1	1	yes	characteristic
25	C₃×C₅×C₁₉	—	2	8	no	—
26	C₃×C₅×C₁₉	—	2	2	no	—
27	C₃×C₅×C₁₉	—	2	2	no	—
28	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₁₉	—	9	1	no	—
30	C₂×C₅×C₁₉	—	9	1	no	—
31	C₂×C₅×C₁₉	—	18	2	no	—
32	#4379	C₅×C₁₉	1	1	yes	characteristic, direct product factor
33	C₅×#157	—	5	1	no	—
34	C₃²×C₁₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
35	C₅²×D₃	—	6	2	no	—
36	D₃×C₁₉	—	6	2	no	—
37	C₅×Dic₅	—	9	1	no	Hall
38	C₅×C₁₉	—	2	2	no	—
39	C₅×C₁₉	C₅×#157	1	1	yes	characteristic, complemented
40	C₅×C₁₉	#4379	1	1	yes	characteristic, direct product factor
41	C₅×C₃⋊D₃	—	2	2	no	—
42	C₅×C₃⋊D₃	D₅×C₁₉	1	1	yes	characteristic
43	C₅×C₃⋊D₃	C₂×C₅×C₁₉	1	1	yes	characteristic
44	C₄×C₁₉	—	45	1	no	Hall
45	C₃×C₅²	—	2	2	no	—
46	C₃×C₁₉	—	2	2	no	—
47	C₂×C₅²	—	9	1	no	—
48	C₃²×C₅	—	2	2	no	—
49	C₃²×C₅	C₁₉×Dic₅	1	1	yes	characteristic, complemented
50	C₃²×C₅	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented
51	C₂×C₁₉	—	9	1	no	—
52	#157	—	5	1	no	Hall
53	C₅×D₃	—	6	2	no	—
54	C₅×D₃	—	6	2	no	—
55	C₅×D₃	—	6	8	no	—
56	C₅²	C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
57	C₄×C₅	—	45	1	no	—
58	Dic₅	—	9	1	no	—
59	C₁₉	C₅×#4379	1	1	yes	characteristic, direct product factor, Sylow
60	C₃⋊D₃	C₅×D₅×C₁₉	1	1	yes	characteristic
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₂×C₅	—	9	1	no	—
65	C₂×C₅	—	9	1	no	—
66	C₂×C₅	—	18	2	no	—
67	C₃²	C₅×C₁₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	6	2	no	—
69	C₅	—	2	2	no	—
70	C₅	C₅×C₁₉×#157	1	1	yes	characteristic, complemented
71	C₅	C₁₉×#4379	1	1	yes	characteristic, direct product factor
72	C₄	—	45	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₉	#4379
commutator, hypocenter	C₃²×C₅	C₄×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₄
prime radical	C₅²×C₃⋊D₃×C₁₉	C₂
cosocle	C₅×C₃⋊D₃	C₂×C₅×C₁₉
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₉	C₄	semidirect
3. C₁₉×#4379	C₅	direct (N × H)
12. C₅×#4379	C₁₉	direct (N × H)
14. C₃²×C₅×C₁₉	Dic₅	semidirect
15. C₃²×C₅×C₁₉	C₄×C₅	semidirect
20. C₅²×C₁₉	#157	semidirect
28. C₃²×C₅²	C₄×C₁₉	semidirect
32. #4379	C₅×C₁₉	direct (N × H)
34. C₃²×C₁₉	C₅×Dic₅	semidirect
39. C₅×C₁₉	C₅×#157	semidirect
40. C₅×C₁₉	#4379	direct (N × H)
49. C₃²×C₅	C₁₉×Dic₅	semidirect
50. C₃²×C₅	C₄×C₅×C₁₉	semidirect
56. C₅²	C₁₉×#157	semidirect
59. C₁₉	C₅×#4379	direct (N × H)
67. C₃²	C₅×C₁₉×Dic₅	semidirect
70. C₅	C₅×C₁₉×#157	semidirect
71. C₅	C₁₉×#4379	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₃⋊D₃×C₁₉	2
C₁₉×#4379	5
C₅×C₁₉×#157	5
C₅×C₁₉×Dic₅	9
C₅×#4379	19

Subgroups — C5×C19×#4379 #30685948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×#4379 #30685948