Subgroups — C₁₉×D₁₅⋊D₁₁ #27160087

Order 12540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₉×D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₉×D₁₁	—	5	1	no	maximal, Hall
7	C₁₉×D₅₅	D₃	1	1	yes	characteristic, complemented
8	D₅×C₁₁×C₁₉	—	3	1	no	—
9	C₅×C₁₉×D₁₁	—	3	1	no	—
10	C₁₉×D₃₃	D₅	1	1	yes	characteristic, complemented
11	D₃×C₁₁×C₁₉	—	5	1	no	—
12	C₃×C₁₉×D₁₁	—	5	1	no	—
13	D₃×D₅×C₁₉	—	11	1	no	maximal, Hall
14	C₅×C₁₁×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₉×D₁₁	—	15	1	no	Hall
16	D₁₅⋊D₁₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₁₁×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₁₉×D₁₅	D₁₁	1	1	yes	characteristic, complemented
19	C₅×D₃×C₁₉	—	11	1	no	—
20	C₃×D₅×C₁₉	—	11	1	no	—
21	C₂×C₁₁×C₁₉	—	15	1	no	—
22	C₁₉×D₁₁	—	3	1	no	—
23	C₁₉×D₁₁	—	5	1	no	—
24	C₂×D₅×C₁₉	—	33	1	no	Hall
25	C₁₁×D₁₅	C₂×C₁₉	1	1	yes	characteristic, complemented
26	C₅×D₃₃	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₃×D₅₅	C₂×C₁₉	1	1	yes	characteristic, complemented
28	C₃×C₅×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂×D₃×C₁₉	—	55	1	no	Hall
30	D₅×D₁₁	—	3	1	no	Hall
31	C₁₁×C₁₉	D₃×D₅	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅×C₁₉	—	33	1	no	—
33	D₅×C₁₉	—	3	1	no	—
34	D₅×C₁₉	—	11	1	no	—
35	C₃×C₅×C₁₁	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₁	—	5	1	no	Hall
37	C₂×C₃×C₁₉	—	55	1	no	—
38	D₃×C₁₉	—	5	1	no	—
39	D₃×C₁₉	—	11	1	no	—
40	D₅₅	D₃×C₁₉	1	1	yes	characteristic, complemented
41	C₅×D₁₁	—	3	1	no	—
42	D₅×C₁₁	—	3	1	no	—
43	C₅×C₁₉	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
44	C₂²×C₁₉	—	165	1	no	Hall
45	D₃₃	D₅×C₁₉	1	1	yes	characteristic, complemented
46	C₃×D₁₁	—	5	1	no	—
47	D₃×C₁₁	—	5	1	no	—
48	D₃×D₅	—	11	1	no	Hall
49	C₃×C₁₉	D₅×D₁₁	1	1	yes	characteristic, complemented, Hall
50	C₅×C₁₁	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₁	—	15	1	no	Hall
52	C₂×C₁₉	—	15	1	no	—
53	C₂×C₁₉	—	33	1	no	—
54	C₂×C₁₉	—	55	1	no	—
55	C₃×C₁₁	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
56	D₁₅	C₁₉×D₁₁	1	1	yes	characteristic, complemented
57	C₃×D₅	—	11	1	no	—
58	C₅×D₃	—	11	1	no	—
59	C₂×C₁₁	—	15	1	no	—
60	D₁₁	—	3	1	no	—
61	D₁₁	—	5	1	no	—
62	C₂×D₅	—	33	1	no	Hall
63	C₁₉	D₁₅⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×C₅	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
65	C₂×D₃	—	55	1	no	Hall
66	C₁₁	D₃×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	33	1	no	—
68	D₅	—	3	1	no	—
69	D₅	—	11	1	no	—
70	C₂×C₃	—	55	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	11	1	no	—
73	C₅	D₃×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	165	1	no	Sylow
75	C₃	D₅×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	33	1	no	—
78	C₂	—	55	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₁₅⋊D₁₁
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×D₁₅	C₂	semidirect
2. C₅×C₁₉×D₃₃	C₂	semidirect
3. C₃×C₁₉×D₅₅	C₂	semidirect
5. C₃×C₅×C₁₁×C₁₉	C₂²	semidirect
7. C₁₉×D₅₅	D₃	semidirect
10. C₁₉×D₃₃	D₅	semidirect
14. C₅×C₁₁×C₁₉	C₂×D₃	semidirect
16. D₁₅⋊D₁₁	C₁₉	direct (N × H)
17. C₃×C₁₁×C₁₉	C₂×D₅	semidirect
18. C₁₉×D₁₅	D₁₁	semidirect
25. C₁₁×D₁₅	C₂×C₁₉	semidirect
26. C₅×D₃₃	C₂×C₁₉	semidirect
27. C₃×D₅₅	C₂×C₁₉	semidirect
28. C₃×C₅×C₁₉	C₂×D₁₁	semidirect
31. C₁₁×C₁₉	D₃×D₅	semidirect
35. C₃×C₅×C₁₁	C₂²×C₁₉	semidirect
40. D₅₅	D₃×C₁₉	semidirect
43. C₅×C₁₉	D₃×D₁₁	semidirect
45. D₃₃	D₅×C₁₉	semidirect
49. C₃×C₁₉	D₅×D₁₁	semidirect
50. C₅×C₁₁	C₂×D₃×C₁₉	semidirect
55. C₃×C₁₁	C₂×D₅×C₁₉	semidirect
56. D₁₅	C₁₉×D₁₁	semidirect
63. C₁₉	D₁₅⋊D₁₁	direct (N × H)
64. C₃×C₅	C₂×C₁₉×D₁₁	semidirect
66. C₁₁	D₃×D₅×C₁₉	semidirect
73. C₅	D₃×C₁₉×D₁₁	semidirect
75. C₃	D₅×C₁₉×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×D₁₅	2
C₅×C₁₉×D₃₃	2
C₃×C₁₉×D₅₅	2
D₅×C₁₉×D₁₁	3
D₃×C₁₉×D₁₁	5
D₃×D₅×C₁₉	11
D₁₅⋊D₁₁	19

Subgroups — C19×D15⋊D11 #27160087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₁₅⋊D₁₁ #27160087