Subgroups — C₁₉×C₃⋊D₂₈₅ #44570636

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	C₁₉×D₂₈₅	—	3	4	no	maximal
3	C₁₉×C₃⋊D₅₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₉²	D₃	1	4	yes	complemented
5	C₁₉×D₉₅	—	9	1	no	Hall
6	C₃²×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
7	C₁₉×D₅₇	—	15	4	no	—
8	C₅×C₁₉²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊D₂₈₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor
10	C₁₉×C₃⋊D₁₅	—	19	1	no	maximal
11	C₃×C₁₉²	D₁₅	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	—	45	1	no	Hall
16	D₂₈₅	—	3	4	no	—
17	C₁₉×D₁₅	—	57	4	no	—
18	C₁₉²	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
19	C₃⋊D₅₇	—	5	1	no	—
20	C₃⋊D₃×C₁₉	—	95	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	D₉₅	—	9	1	no	—
25	D₅×C₁₉	—	171	1	no	—
26	C₃²×C₁₉	—	2	9	no	—
27	C₃²×C₁₉	D₅×C₁₉	1	1	yes	characteristic, complemented
28	C₃²×C₁₉	D₉₅	1	1	yes	characteristic, complemented
29	D₅₇	—	15	4	no	—
30	D₃×C₁₉	—	285	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, complemented
34	C₃⋊D₁₅	—	19	1	no	Hall
35	C₃×C₁₉	—	2	36	no	—
36	C₃×C₁₉	C₁₉×D₁₅	1	4	yes	complemented
37	C₃×C₁₉	D₂₈₅	1	4	yes	complemented
38	C₃²×C₅	C₁₉×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₁₉	—	855	1	no	—
40	D₁₉	—	45	1	no	—
41	D₁₅	—	57	4	no	—
42	C₁₉	—	2	9	no	—
43	C₁₉	C₁₉×C₃⋊D₁₅	1	1	yes	characteristic, complemented
44	C₁₉	C₃⋊D₂₈₅	1	1	yes	characteristic, direct product factor
45	C₃⋊D₃	—	95	1	no	Hall
46	C₃×C₅	C₁₉×D₅₇	1	4	yes	complemented
47	D₅	—	171	1	no	Hall
48	C₃²	C₁₉×D₉₅	1	1	yes	characteristic, complemented, Sylow
49	D₃	—	285	4	no	—
50	C₅	C₁₉×C₃⋊D₅₇	1	1	yes	characteristic, complemented, Sylow
51	C₃	C₁₉×D₂₈₅	1	4	yes	complemented
52	C₂	—	855	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊D₂₈₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₉	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉²	C₂
LCS	G ▷ C₃²×C₅×C₁₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
4. C₃×C₅×C₁₉²	D₃	semidirect
6. C₃²×C₁₉²	D₅	semidirect
8. C₅×C₁₉²	C₃⋊D₃	semidirect
9. C₃⋊D₂₈₅	C₁₉	direct (N × H)
11. C₃×C₁₉²	D₁₅	semidirect
13. C₃²×C₅×C₁₉	D₁₉	semidirect
14. C₃²×C₅×C₁₉	C₂×C₁₉	semidirect
18. C₁₉²	C₃⋊D₁₅	semidirect
22. C₃×C₅×C₁₉	D₃×C₁₉	semidirect
23. C₃×C₅×C₁₉	D₅₇	semidirect
27. C₃²×C₁₉	D₅×C₁₉	semidirect
28. C₃²×C₁₉	D₉₅	semidirect
32. C₅×C₁₉	C₃⋊D₃×C₁₉	semidirect
33. C₅×C₁₉	C₃⋊D₅₇	semidirect
36. C₃×C₁₉	C₁₉×D₁₅	semidirect
37. C₃×C₁₉	D₂₈₅	semidirect
38. C₃²×C₅	C₁₉×D₁₉	semidirect
43. C₁₉	C₁₉×C₃⋊D₁₅	semidirect
44. C₁₉	C₃⋊D₂₈₅	direct (N × H)
46. C₃×C₅	C₁₉×D₅₇	semidirect
48. C₃²	C₁₉×D₉₅	semidirect
50. C₅	C₁₉×C₃⋊D₅₇	semidirect
51. C₃	C₁₉×D₂₈₅	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
C₁₉×D₂₈₅	3
C₁₉×C₃⋊D₅₇	5
C₃⋊D₂₈₅	19
C₁₉×C₃⋊D₁₅	19

Subgroups — C19×C3⋊D285 #44570636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊D₂₈₅ #44570636