Subgroups — D₁₉⋊C₃×D₆₅ #28414835

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊((C₁₉⋊C₃)⋊D₁₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉⋊C₃×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₁₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃×D₁₉⋊C₃	—	5	1	no	maximal, Hall
7	D₁₂₃₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₉×D₆₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	(C₁₉⋊C₃)⋊D₁₃	—	5	1	no	—
11	D₁₃×C₁₉⋊C₃	—	5	1	no	—
12	C₁₃×D₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₁₉⋊C₃	—	13	1	no	maximal, Hall
15	D₁₃×D₁₉	—	5	1	no	Hall
16	C₂×C₃×D₆₅	—	19	1	no	maximal, Hall
17	C₁₃×C₁₉⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₅⋊(D₁₉⋊C₃)	—	13	1	no	—
19	D₅×C₁₉⋊C₃	—	13	1	no	—
20	C₅×D₁₉⋊C₃	D₁₃	1	1	yes	characteristic, complemented
21	D₂₄₇	—	5	1	no	—
22	C₁₃×D₁₉	C₃×D₅	1	1	yes	characteristic, complemented
23	C₁₉×D₁₃	—	5	1	no	—
24	C₂×C₃×C₅×C₁₃	—	19	1	no	—
25	C₃×D₆₅	—	19	1	no	—
26	C₃×D₆₅	—	38	1	no	—
27	D₅×D₁₉	—	13	1	no	Hall
28	C₅×C₁₉⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₆₅	—	19	1	no	Hall
30	C₁₃×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₂×D₁₉⋊C₃	—	65	1	no	Hall
32	C₃×C₅×C₁₃	—	38	1	no	Hall
33	D₉₅	—	13	1	no	—
34	C₅×D₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
35	D₅×C₁₉	—	13	1	no	—
36	C₂×C₃×D₁₃	—	95	1	no	Hall
37	C₂×C₅×C₁₃	—	19	1	no	—
38	D₆₅	—	19	1	no	—
39	D₆₅	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₁₉⋊C₃	—	65	1	no	—
41	D₁₉⋊C₃	—	65	1	no	—
42	D₁₉⋊C₃	D₆₅	1	1	yes	characteristic, direct product factor
43	C₅×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₃	—	19	1	no	—
45	C₃×D₁₃	—	95	1	no	—
46	C₃×D₁₃	—	190	1	no	—
47	C₂×D₁₉	—	65	1	no	Hall
48	C₅×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₃×D₅	—	247	1	no	Hall
50	C₁₉⋊C₃	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	95	1	no	Hall
52	C₃×C₁₃	—	38	1	no	Hall
53	C₂×C₁₉	—	65	1	no	—
54	D₁₉	—	65	1	no	—
55	D₁₉	C₃×D₆₅	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅	—	19	1	no	—
57	C₃×D₅	—	494	1	no	—
58	C₃×D₅	—	247	1	no	—
59	C₂×C₁₃	—	19	1	no	—
60	D₁₃	—	5	1	no	—
61	D₁₃	—	95	1	no	—
62	C₂×D₅	—	247	1	no	Hall
63	C₁₉	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₅	—	38	1	no	Hall
65	C₁₃	D₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	1235	1	no	Hall
67	C₂×C₅	—	19	1	no	—
68	D₅	—	13	1	no	—
69	D₅	—	247	1	no	—
70	C₂×C₃	—	19	1	no	—
71	C₂×C₃	—	1235	1	no	—
72	C₂×C₃	—	1235	1	no	—
73	C₅	D₁₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1235	1	no	Sylow
75	C₃	—	19	1	no	Sylow
76	C₂	—	19	1	no	—
77	C₂	—	65	1	no	—
78	C₂	—	1235	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₅×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊((C₁₉⋊C₃)⋊D₁₃)	C₂	semidirect
2. C₁₉⋊C₃×D₆₅	C₂	semidirect
3. C₅×C₁₃×D₁₉⋊C₃	C₂	semidirect
4. D₁₉×D₆₅	C₃	semidirect
5. C₅×C₁₃×C₁₉⋊C₃	C₂²	semidirect
7. D₁₂₃₅	C₂×C₃	semidirect
8. C₁₉×D₆₅	C₂×C₃	semidirect
9. C₅×C₁₃×D₁₉	C₂×C₃	semidirect
12. C₁₃×D₁₉⋊C₃	D₅	semidirect
13. C₅×C₁₃×C₁₉	C₂²×C₃	semidirect
17. C₁₃×C₁₉⋊C₃	C₂×D₅	semidirect
20. C₅×D₁₉⋊C₃	D₁₃	semidirect
22. C₁₃×D₁₉	C₃×D₅	semidirect
28. C₅×C₁₉⋊C₃	C₂×D₁₃	semidirect
30. C₁₃×C₁₉	C₂×C₃×D₅	semidirect
34. C₅×D₁₉	C₃×D₁₃	semidirect
39. D₆₅	D₁₉⋊C₃	direct (N × H)
42. D₁₉⋊C₃	D₆₅	direct (N × H)
43. C₅×C₁₉	C₂×C₃×D₁₃	semidirect
48. C₅×C₁₃	C₂×D₁₉⋊C₃	semidirect
50. C₁₉⋊C₃	C₂×D₆₅	semidirect
55. D₁₉	C₃×D₆₅	semidirect
63. C₁₉	C₂×C₃×D₆₅	semidirect
65. C₁₃	D₅×D₁₉⋊C₃	semidirect
73. C₅	D₁₃×D₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊((C₁₉⋊C₃)⋊D₁₃)	2
C₁₉⋊C₃×D₆₅	2
C₅×C₁₃×D₁₉⋊C₃	2
D₁₉×D₆₅	3
D₁₃×D₁₉⋊C₃	5
D₅×D₁₉⋊C₃	13
C₂×C₃×D₆₅	19

Subgroups — D19⋊C3×D65 #28414835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉⋊C₃×D₆₅ #28414835