Subgroups — C₅×C₁₉×C₃⋊D₅₇ #44570633

Order 32490.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉×D₅₇	—	3	4	no	maximal
3	C₁₉×C₃⋊D₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	D₃	1	4	yes	complemented
5	C₅×C₁₉×D₁₉	—	9	1	no	Hall
6	C₃²×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₁₉×D₅₇	—	3	4	no	—
8	C₅×C₁₉²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₅×C₃⋊D₅₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor
10	C₅×C₃⋊D₃×C₁₉	—	19	1	no	maximal
11	C₃×C₁₉²	C₅×D₃	1	4	yes	complemented
12	C₃²×C₅×C₁₉	—	2	9	no	—
13	C₃²×C₅×C₁₉	D₁₉	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₁₉	C₂×C₁₉	1	1	yes	characteristic, complemented
15	C₁₉×D₁₉	—	9	1	no	Hall
16	C₅×D₅₇	—	3	4	no	—
17	C₅×D₃×C₁₉	—	57	4	no	—
18	C₁₉²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
19	C₃⋊D₅₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor
20	C₃⋊D₃×C₁₉	—	19	1	no	—
21	C₃×C₅×C₁₉	—	2	36	no	—
22	C₃×C₅×C₁₉	D₃×C₁₉	1	4	yes	complemented
23	C₃×C₅×C₁₉	D₅₇	1	4	yes	complemented
24	C₂×C₅×C₁₉	—	171	1	no	—
25	C₅×D₁₉	—	9	1	no	—
26	C₃²×C₁₉	—	2	9	no	—
27	C₃²×C₁₉	C₅×D₁₉	1	1	yes	characteristic, complemented
28	C₃²×C₁₉	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
29	D₅₇	—	3	4	no	—
30	D₃×C₁₉	—	57	4	no	—
31	C₅×C₁₉	—	2	9	no	—
32	C₅×C₁₉	C₃⋊D₃×C₁₉	1	1	yes	characteristic, complemented
33	C₅×C₁₉	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor
34	C₅×C₃⋊D₃	—	19	1	no	Hall
35	C₃×C₁₉	—	2	36	no	—
36	C₃×C₁₉	C₅×D₃×C₁₉	1	4	yes	complemented
37	C₃×C₁₉	C₅×D₅₇	1	4	yes	complemented
38	C₃²×C₅	C₁₉×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₁₉	—	171	1	no	—
40	D₁₉	—	9	1	no	—
41	C₅×D₃	—	57	4	no	—
42	C₁₉	—	2	9	no	—
43	C₁₉	C₅×C₃⋊D₃×C₁₉	1	1	yes	characteristic, complemented
44	C₁₉	C₅×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor
45	C₃⋊D₃	—	19	1	no	Hall
46	C₃×C₅	C₁₉×D₅₇	1	4	yes	complemented
47	C₂×C₅	—	171	1	no	Hall
48	C₃²	C₅×C₁₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
49	D₃	—	57	4	no	—
50	C₅	C₁₉×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₅×C₁₉×D₅₇	1	4	yes	complemented
52	C₂	—	171	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₃⋊D₅₇
commutator, cosocle, hypocenter	C₃²×C₁₉	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉²	C₂
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
3. C₁₉×C₃⋊D₅₇	C₅	direct (N × H)
4. C₃×C₅×C₁₉²	D₃	semidirect
6. C₃²×C₁₉²	C₂×C₅	semidirect
8. C₅×C₁₉²	C₃⋊D₃	semidirect
9. C₅×C₃⋊D₅₇	C₁₉	direct (N × H)
11. C₃×C₁₉²	C₅×D₃	semidirect
13. C₃²×C₅×C₁₉	D₁₉	semidirect
14. C₃²×C₅×C₁₉	C₂×C₁₉	semidirect
18. C₁₉²	C₅×C₃⋊D₃	semidirect
19. C₃⋊D₅₇	C₅×C₁₉	direct (N × H)
22. C₃×C₅×C₁₉	D₃×C₁₉	semidirect
23. C₃×C₅×C₁₉	D₅₇	semidirect
27. C₃²×C₁₉	C₅×D₁₉	semidirect
28. C₃²×C₁₉	C₂×C₅×C₁₉	semidirect
32. C₅×C₁₉	C₃⋊D₃×C₁₉	semidirect
33. C₅×C₁₉	C₃⋊D₅₇	direct (N × H)
36. C₃×C₁₉	C₅×D₃×C₁₉	semidirect
37. C₃×C₁₉	C₅×D₅₇	semidirect
38. C₃²×C₅	C₁₉×D₁₉	semidirect
43. C₁₉	C₅×C₃⋊D₃×C₁₉	semidirect
44. C₁₉	C₅×C₃⋊D₅₇	direct (N × H)
46. C₃×C₅	C₁₉×D₅₇	semidirect
48. C₃²	C₅×C₁₉×D₁₉	semidirect
50. C₅	C₁₉×C₃⋊D₅₇	direct (N × H)
51. C₃	C₅×C₁₉×D₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₉²	2
C₅×C₁₉×D₅₇	3
C₁₉×C₃⋊D₅₇	5
C₅×C₃⋊D₅₇	19
C₅×C₃⋊D₃×C₁₉	19

Subgroups — C5×C19×C3⋊D57 #44570633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×C₃⋊D₅₇ #44570633