Subgroups — C₂×C₁₉×(C₅⋊D₅)⋊C₉ #30685566

Order 17100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×(C₅⋊D₅)⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
4	C₁₉×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×C₁₉×C₅⋊D₅	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₃×D₅×C₁₉	—	15	2	no	—
10	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
11	C₁₉×C₅⋊D₅	C₂×C₉	1	2	yes	complemented
12	C₂×(C₅⋊D₅)⋊C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₉×C₁₉	—	25	1	no	maximal, Hall
14	C₂×C₃×C₅×C₁₉	—	3	2	no	—
15	C₃×D₅×C₁₉	—	15	4	no	—
16	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅²⋊C₉	C₂×C₁₉	1	1	yes	characteristic, complemented
18	(C₅⋊D₅)⋊C₉	C₂×C₁₉	1	2	yes	direct product factor
19	C₂×D₅×C₁₉	—	15	2	no	—
20	C₂×C₉×C₁₉	—	25	2	no	—
21	C₂×C₉×C₁₉	—	25	1	no	—
22	C₂×C₃×C₅⋊D₅	C₃×C₁₉	1	1	yes	characteristic
23	C₃×C₅×C₁₉	—	3	2	no	—
24	C₂²×C₃×C₁₉	—	25	1	no	—
25	C₅²⋊C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₁₉	—	3	2	no	—
27	D₅×C₁₉	—	15	4	no	—
28	C₉×C₁₉	—	25	1	no	Hall
29	C₂×C₃×C₅²	C₂×C₃×C₁₉	1	1	yes	characteristic
30	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	2	yes	—
31	C₂×C₃×C₁₉	—	25	2	no	—
32	C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
33	C₂×C₅⋊D₅	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
34	C₅×C₁₉	—	3	2	no	—
35	C₂²×C₁₉	—	25	1	no	Hall
36	C₃×C₅²	C₂²×C₃×C₁₉	1	1	yes	characteristic
37	C₂×C₃×D₅	—	15	2	no	—
38	C₃×C₁₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
39	C₂×C₅²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
40	C₅⋊D₅	C₂×C₉×C₁₉	1	2	yes	complemented
41	C₂×C₁₉	—	25	2	no	—
42	C₂×C₁₉	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, direct product factor
43	C₂²×C₉	—	25	1	no	Hall
44	C₂×C₃×C₅	—	3	2	no	—
45	C₃×D₅	—	15	4	no	—
46	C₅²	C₂²×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₅	—	15	2	no	—
48	C₁₉	C₂×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₉	—	25	2	no	—
50	C₂×C₉	—	25	1	no	—
51	C₃×C₅	—	3	2	no	—
52	C₂²×C₃	—	25	1	no	—
53	C₂×C₅	—	3	2	no	—
54	D₅	—	15	4	no	—
55	C₉	—	25	1	no	Sylow
56	C₂×C₃	—	25	2	no	—
57	C₂×C₃	C₁₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
58	C₅	—	3	2	no	—
59	C₂²	—	25	1	no	Sylow
60	C₃	C₂×C₁₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
61	C₂	—	25	2	no	—
62	C₂	C₁₉×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×(C₅⋊D₅)⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₅⋊D₅	C₃
cosocle	C₃×C₅²	C₂²×C₃×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₅²⋊C₉	C₂	semidirect
2. C₁₉×(C₅⋊D₅)⋊C₉	C₂	direct (N × H)
4. C₁₉×C₅²⋊C₉	C₂²	semidirect
7. C₂×C₁₉×C₅⋊D₅	C₉	semidirect
10. C₂×C₅²×C₁₉	C₂×C₉	semidirect
11. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
12. C₂×(C₅⋊D₅)⋊C₉	C₁₉	direct (N × H)
16. C₅²×C₁₉	C₂²×C₉	semidirect
17. C₂×C₅²⋊C₉	C₂×C₁₉	semidirect
18. (C₅⋊D₅)⋊C₉	C₂×C₁₉	direct (N × H)
25. C₅²⋊C₉	C₂²×C₁₉	semidirect
33. C₂×C₅⋊D₅	C₉×C₁₉	semidirect
39. C₂×C₅²	C₂×C₉×C₁₉	semidirect
40. C₅⋊D₅	C₂×C₉×C₁₉	semidirect
42. C₂×C₁₉	(C₅⋊D₅)⋊C₉	direct (N × H)
46. C₅²	C₂²×C₉×C₁₉	semidirect
48. C₁₉	C₂×(C₅⋊D₅)⋊C₉	direct (N × H)
62. C₂	C₁₉×(C₅⋊D₅)⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×C₅²⋊C₉	2
C₁₉×(C₅⋊D₅)⋊C₉	2
C₂×C₃×C₁₉×C₅⋊D₅	3
C₂×(C₅⋊D₅)⋊C₉	19
C₂²×C₉×C₁₉	25

Subgroups — C2×C19×(C5⋊D5)⋊C9 #30685566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×(C₅⋊D₅)⋊C₉ #30685566