Subgroups — D₈₅⋊(D₁₉⋊C₃) #34084331

Order 19380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×C₅⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈₅⋊D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₁₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇×D₁₉⋊C₃	—	5	1	no	maximal, Hall
7	C₁₉×D₈₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₇×D₉₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₃₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₇⋊(D₁₉⋊C₃)	D₅	1	1	yes	characteristic, complemented
11	D₁₇×C₁₉⋊C₃	—	5	1	no	—
12	C₁₇×D₁₉⋊C₃	—	5	1	no	—
13	C₅×C₁₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₁₇×D₁₉	—	5	1	no	Hall
15	D₅×D₁₉⋊C₃	—	17	1	no	maximal, Hall
16	C₃×D₅×D₁₇	—	19	1	no	maximal, Hall
17	C₁₇×C₁₉⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	D₃₂₃	C₃×D₅	1	1	yes	characteristic, complemented
19	C₁₇×D₁₉	—	5	1	no	—
20	C₁₉×D₁₇	—	5	1	no	—
21	C₅⋊(D₁₉⋊C₃)	D₁₇	1	1	yes	characteristic, complemented
22	D₅×C₁₉⋊C₃	—	17	1	no	—
23	C₅×D₁₉⋊C₃	—	17	1	no	—
24	C₃×D₈₅	—	38	1	no	—
25	C₃×D₅×C₁₇	—	19	1	no	—
26	C₃×C₅×D₁₇	—	19	1	no	—
27	D₅×D₁₉	—	17	1	no	Hall
28	D₅×D₁₇	—	19	1	no	Hall
29	C₁₇×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₅×C₁₉⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₁₇	—	38	1	no	Hall
32	C₂×D₁₉⋊C₃	—	85	1	no	Hall
33	C₂×C₃×D₁₇	—	95	1	no	Hall
34	D₉₅	C₃×D₁₇	1	1	yes	characteristic, complemented
35	C₅×D₁₉	—	17	1	no	—
36	D₅×C₁₉	—	17	1	no	—
37	D₈₅	D₁₉⋊C₃	1	1	yes	characteristic, complemented
38	C₅×D₁₇	—	19	1	no	—
39	D₅×C₁₇	—	19	1	no	—
40	C₂×C₁₉⋊C₃	—	85	1	no	—
41	D₁₉⋊C₃	—	5	1	no	—
42	D₁₉⋊C₃	—	17	1	no	—
43	C₂×C₃×C₁₇	—	95	1	no	—
44	C₃×D₁₇	—	19	1	no	—
45	C₃×D₁₇	—	190	1	no	—
46	C₅×C₁₉	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
47	C₅×C₁₇	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
48	C₂×D₁₉	—	85	1	no	Hall
49	C₂×D₁₇	—	95	1	no	Hall
50	C₂×C₃×D₅	—	323	1	no	Hall
51	C₁₉⋊C₃	D₅×D₁₇	1	1	yes	characteristic, complemented, Hall
52	C₃×C₁₇	—	38	1	no	Hall
53	C₂×C₁₉	—	85	1	no	—
54	D₁₉	—	5	1	no	—
55	D₁₉	—	17	1	no	—
56	C₂×C₁₇	—	95	1	no	—
57	D₁₇	—	5	1	no	—
58	D₁₇	—	19	1	no	—
59	C₂×C₃×C₅	—	323	1	no	—
60	C₃×D₅	—	19	1	no	—
61	C₃×D₅	—	646	1	no	—
62	C₂×D₅	—	323	1	no	Hall
63	C₁₉	C₃×D₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
64	C₁₇	D₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	38	1	no	Hall
66	C₂²×C₃	—	1615	1	no	Hall
67	C₂×C₅	—	323	1	no	—
68	D₅	—	17	1	no	—
69	D₅	—	19	1	no	—
70	C₂×C₃	—	323	1	no	—
71	C₂×C₃	—	95	1	no	—
72	C₂×C₃	—	3230	1	no	—
73	C₅	D₁₇×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1615	1	no	Sylow
75	C₃	—	38	1	no	Sylow
76	C₂	—	323	1	no	—
77	C₂	—	85	1	no	—
78	C₂	—	95	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇×C₁₉	C₂²×C₃
LCS	G ▷ C₅×C₁₇×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₃×D₈₅	C₂	semidirect
2. C₁₇×C₅⋊(D₁₉⋊C₃)	C₂	semidirect
3. C₅×C₁₇⋊(D₁₉⋊C₃)	C₂	semidirect
4. D₈₅⋊D₁₉	C₃	semidirect
5. C₅×C₁₇×C₁₉⋊C₃	C₂²	semidirect
7. C₁₉×D₈₅	C₂×C₃	semidirect
8. C₁₇×D₉₅	C₂×C₃	semidirect
9. C₅×D₃₂₃	C₂×C₃	semidirect
10. C₁₇⋊(D₁₉⋊C₃)	D₅	semidirect
13. C₅×C₁₇×C₁₉	C₂²×C₃	semidirect
17. C₁₇×C₁₉⋊C₃	C₂×D₅	semidirect
18. D₃₂₃	C₃×D₅	semidirect
21. C₅⋊(D₁₉⋊C₃)	D₁₇	semidirect
29. C₁₇×C₁₉	C₂×C₃×D₅	semidirect
30. C₅×C₁₉⋊C₃	C₂×D₁₇	semidirect
34. D₉₅	C₃×D₁₇	semidirect
37. D₈₅	D₁₉⋊C₃	semidirect
46. C₅×C₁₉	C₂×C₃×D₁₇	semidirect
47. C₅×C₁₇	C₂×D₁₉⋊C₃	semidirect
51. C₁₉⋊C₃	D₅×D₁₇	semidirect
63. C₁₉	C₃×D₅×D₁₇	semidirect
64. C₁₇	D₅×D₁₉⋊C₃	semidirect
73. C₅	D₁₇×D₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊C₃×D₈₅	2
C₁₇×C₅⋊(D₁₉⋊C₃)	2
C₅×C₁₇⋊(D₁₉⋊C₃)	2
D₈₅⋊D₁₉	3
D₁₇×D₁₉⋊C₃	5
D₅×D₁₉⋊C₃	17
C₃×D₅×D₁₇	19

Subgroups — D85⋊(D19⋊C3) #34084331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈₅⋊(D₁₉⋊C₃) #34084331