Subgroups — C₅×D₅₇⋊D₁₉ #36343255

Order 21660.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×D₅₇	C₂	1	2	yes	maximal, complemented
3	C₅×D₁₉²	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₉²	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₇⋊D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₉⋊D₁₉	D₃	1	1	yes	characteristic, complemented
7	C₅×C₁₉×D₁₉	—	3	2	no	—
8	C₁₉×D₅₇	C₂×C₅	1	2	yes	complemented
9	C₃×C₁₉⋊D₁₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×C₁₉²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₉²	—	3	1	no	Hall
12	C₅×D₃×D₁₉	—	19	2	no	maximal
13	C₃×C₁₉²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₁₉⋊D₁₉	C₅×D₃	1	1	yes	characteristic, complemented
15	C₁₉×D₁₉	—	3	2	no	—
16	C₅×D₅₇	D₁₉	1	2	yes	complemented
17	C₅×D₃×C₁₉	—	19	2	no	—
18	C₃×C₅×D₁₉	—	19	2	no	—
19	C₃×C₅×D₁₉	—	38	9	no	—
20	C₂×C₅×D₁₉	—	57	2	no	—
21	C₁₉²	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₅×C₁₉	—	2	9	no	—
23	C₃×C₅×C₁₉	C₂×D₁₉	1	2	yes	complemented
24	D₃×D₁₉	—	19	2	no	—
25	C₂×C₅×C₁₉	—	57	2	no	—
26	C₅×D₁₉	—	3	2	no	—
27	C₅×D₁₉	—	19	2	no	—
28	C₅×D₁₉	—	38	9	no	—
29	D₅₇	C₅×D₁₉	1	2	yes	complemented
30	C₃×D₁₉	—	19	2	no	—
31	C₃×D₁₉	—	38	9	no	—
32	D₃×C₁₉	—	19	2	no	—
33	C₅×C₁₉	—	2	9	no	—
34	C₅×C₁₉	D₃×D₁₉	1	2	yes	complemented
35	C₂×D₁₉	—	57	2	no	—
36	C₂×C₅×D₃	—	361	1	no	Hall
37	C₃×C₁₉	—	2	9	no	—
38	C₃×C₁₉	C₂×C₅×D₁₉	1	2	yes	complemented
39	C₂×C₁₉	—	57	2	no	—
40	D₁₉	—	3	2	no	—
41	D₁₉	—	19	2	no	—
42	D₁₉	—	38	9	no	—
43	C₂×C₃×C₅	—	361	1	no	—
44	C₅×D₃	—	19	2	no	—
45	C₂²×C₅	—	1083	1	no	Hall
46	C₁₉	—	2	9	no	—
47	C₁₉	C₅×D₃×D₁₉	1	2	yes	complemented
48	C₃×C₅	D₁₉²	1	1	yes	characteristic, complemented, Hall
49	C₂×D₃	—	361	1	no	Hall
50	C₂×C₅	—	57	2	no	—
51	C₂×C₅	—	361	1	no	—
52	C₂×C₃	—	361	1	no	—
53	D₃	—	19	2	no	—
54	C₅	D₅₇⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²	—	1083	1	no	Sylow
56	C₃	C₅×D₁₉²	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	57	2	no	—
58	C₂	—	361	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅₇⋊D₁₉
commutator, cosocle, hypocenter	C₃×C₁₉²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂²
LCS	G ▷ C₃×C₁₉²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉⋊D₁₉	C₂	semidirect
2. C₅×C₁₉×D₅₇	C₂	semidirect
4. C₃×C₅×C₁₉²	C₂²	semidirect
5. D₅₇⋊D₁₉	C₅	direct (N × H)
6. C₅×C₁₉⋊D₁₉	D₃	semidirect
8. C₁₉×D₅₇	C₂×C₅	semidirect
9. C₃×C₁₉⋊D₁₉	C₂×C₅	semidirect
10. C₅×C₁₉²	C₂×D₃	semidirect
13. C₃×C₁₉²	C₂²×C₅	semidirect
14. C₁₉⋊D₁₉	C₅×D₃	semidirect
16. C₅×D₅₇	D₁₉	semidirect
21. C₁₉²	C₂×C₅×D₃	semidirect
23. C₃×C₅×C₁₉	C₂×D₁₉	semidirect
29. D₅₇	C₅×D₁₉	semidirect
34. C₅×C₁₉	D₃×D₁₉	semidirect
38. C₃×C₁₉	C₂×C₅×D₁₉	semidirect
47. C₁₉	C₅×D₃×D₁₉	semidirect
48. C₃×C₅	D₁₉²	semidirect
54. C₅	D₅₇⋊D₁₉	direct (N × H)
56. C₃	C₅×D₁₉²	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉⋊D₁₉	2
C₅×C₁₉×D₅₇	2
C₅×D₁₉²	3
D₅₇⋊D₁₉	5
C₅×D₃×D₁₉	19

Subgroups — C5×D57⋊D19 #36343255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅₇⋊D₁₉ #36343255