Subgroups — D₁₉×(C₅⋊D₅)⋊C₉ #30685558

Order 17100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₉×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#22555510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
5	C₁₉×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅⋊D₉₅	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₅²×D₁₉	C₂×C₃	1	1	yes	characteristic
9	D₁₉×C₅⋊D₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
11	C₃×D₅×D₁₉	—	15	2	no	—
12	C₅⋊D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅²×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×(C₅⋊D₅)⋊C₉	—	19	1	no	maximal, Hall
16	C₂×C₉×D₁₉	—	25	1	no	maximal, Hall
17	C₃×D₉₅	—	15	2	no	—
18	C₃×D₅×C₁₉	—	15	2	no	—
19	C₃×C₅×D₁₉	—	3	2	no	—
20	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²⋊C₉	—	19	1	no	—
22	(C₅⋊D₅)⋊C₉	—	19	1	no	—
23	(C₅⋊D₅)⋊C₉	D₁₉	1	1	yes	characteristic, direct product factor
24	D₅×D₁₉	—	15	2	no	—
25	C₂×C₉×C₁₉	—	25	1	no	—
26	C₉×D₁₉	—	25	1	no	—
27	C₉×D₁₉	—	25	1	no	—
28	C₂×C₃×C₅⋊D₅	—	19	1	no	—
29	C₃×C₅×C₁₉	—	3	2	no	—
30	C₂×C₃×D₁₉	—	75	1	no	—
31	C₅²⋊C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
32	D₉₅	—	15	2	no	—
33	C₅×D₁₉	—	3	2	no	—
34	D₅×C₁₉	—	15	2	no	—
35	C₉×C₁₉	—	25	1	no	Hall
36	C₂×C₃×C₅²	—	19	1	no	—
37	C₃×C₅⋊D₅	—	19	1	no	—
38	C₃×C₅⋊D₅	C₃×D₁₉	1	1	yes	characteristic
39	C₂×C₃×C₁₉	—	75	1	no	—
40	C₃×D₁₉	—	75	1	no	—
41	C₃×D₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
42	C₂×C₅⋊D₅	—	19	1	no	Hall
43	C₅×C₁₉	—	3	2	no	—
44	C₂×D₁₉	—	75	1	no	Hall
45	C₃×C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic
46	C₂×C₃×D₅	—	285	2	no	—
47	C₃×C₁₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
48	C₂×C₅²	—	19	1	no	—
49	C₅⋊D₅	—	19	1	no	—
50	C₅⋊D₅	C₉×D₁₉	1	1	yes	characteristic, complemented
51	C₂×C₁₉	—	75	1	no	—
52	D₁₉	—	75	1	no	—
53	D₁₉	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, direct product factor
54	C₂²×C₉	—	475	1	no	Hall
55	C₂×C₃×C₅	—	57	2	no	—
56	C₃×D₅	—	15	2	no	—
57	C₃×D₅	—	285	2	no	—
58	C₅²	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₅	—	285	2	no	—
60	C₁₉	C₂×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₉	—	25	1	no	—
62	C₂×C₉	—	475	1	no	—
63	C₂×C₉	—	475	1	no	—
64	C₃×C₅	—	3	2	no	—
65	C₂²×C₃	—	1425	1	no	—
66	C₂×C₅	—	57	2	no	—
67	D₅	—	15	2	no	—
68	D₅	—	285	2	no	—
69	C₉	—	25	1	no	Sylow
70	C₂×C₃	—	19	1	no	—
71	C₂×C₃	—	75	1	no	—
72	C₂×C₃	—	1425	1	no	—
73	C₅	—	3	2	no	—
74	C₂²	—	1425	1	no	Sylow
75	C₃	D₁₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
76	C₂	—	19	1	no	—
77	C₂	—	75	1	no	—
78	C₂	—	1425	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₉×(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅²×C₁₉	C₂²×C₃
prime radical	C₃×D₁₉×C₅⋊D₅	C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. D₁₉×C₅²⋊C₉	C₂	semidirect
2. #22555510	C₂	semidirect
3. C₁₉×(C₅⋊D₅)⋊C₉	C₂	semidirect
5. C₁₉×C₅²⋊C₉	C₂²	semidirect
9. D₁₉×C₅⋊D₅	C₉	semidirect
12. C₅⋊D₉₅	C₂×C₉	semidirect
13. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
14. C₅²×D₁₉	C₂×C₉	semidirect
20. C₅²×C₁₉	C₂²×C₉	semidirect
23. (C₅⋊D₅)⋊C₉	D₁₉	direct (N × H)
31. C₅²⋊C₉	C₂×D₁₉	semidirect
50. C₅⋊D₅	C₉×D₁₉	semidirect
53. D₁₉	(C₅⋊D₅)⋊C₉	direct (N × H)
58. C₅²	C₂×C₉×D₁₉	semidirect
60. C₁₉	C₂×(C₅⋊D₅)⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
D₁₉×C₅²⋊C₉	2
#22555510	2
C₁₉×(C₅⋊D₅)⋊C₉	2
C₃×D₁₉×C₅⋊D₅	3
C₂×(C₅⋊D₅)⋊C₉	19
C₂×C₉×D₁₉	25

Subgroups — D19×(C5⋊D5)⋊C9 #30685558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×(C₅⋊D₅)⋊C₉ #30685558