Subgroups — D₁₉×C₅⋊D₅₅ #35229921

Order 20900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₅⋊D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊D₁₀₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₉×D₅₅	—	5	6	no	maximal
6	D₁₀₄₅	—	5	6	no	—
7	C₁₉×D₅₅	—	5	6	no	—
8	C₅×C₁₁×D₁₉	D₅	1	6	yes	complemented
9	D₁₉×C₅⋊D₅	—	11	1	no	maximal, Hall
10	C₂×C₅⋊D₅₅	—	19	1	no	maximal, Hall
11	C₅×C₁₁×C₁₉	C₂×D₅	1	6	yes	complemented
12	C₅⋊D₉₅	—	11	1	no	—
13	C₁₉×C₅⋊D₅	—	11	1	no	—
14	C₅²×D₁₉	D₁₁	1	1	yes	characteristic, complemented
15	D₁₁×D₁₉	—	25	1	no	Hall
16	C₂×C₅²×C₁₁	—	19	1	no	—
17	C₅⋊D₅₅	—	19	1	no	—
18	C₅⋊D₅₅	D₁₉	1	1	yes	characteristic, direct product factor
19	C₅²×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₂₀₉	—	25	1	no	—
21	C₁₁×D₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented
22	C₁₉×D₁₁	—	25	1	no	—
23	D₅×D₁₉	—	55	6	no	—
24	C₅²×C₁₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₅₅	—	95	6	no	—
26	C₁₁×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	D₉₅	—	55	6	no	—
28	C₅×D₁₉	D₅₅	1	6	yes	complemented
29	D₅×C₁₉	—	55	6	no	—
30	C₂×C₅×C₁₁	—	19	6	no	—
31	D₅₅	—	5	6	no	—
32	D₅₅	—	95	6	no	—
33	C₂×C₅⋊D₅	—	209	1	no	Hall
34	C₅×C₁₉	C₂×D₅₅	1	6	yes	complemented
35	C₂×D₁₉	—	275	1	no	Hall
36	C₅×C₁₁	D₅×D₁₉	1	6	yes	complemented
37	C₂×C₅²	—	19	1	no	—
38	C₅⋊D₅	—	11	1	no	—
39	C₅⋊D₅	—	209	1	no	—
40	C₂×D₁₁	—	475	1	no	Hall
41	C₂×C₁₉	—	275	1	no	—
42	D₁₉	—	275	1	no	—
43	D₁₉	C₅⋊D₅₅	1	1	yes	characteristic, direct product factor
44	C₅²	D₁₁×D₁₉	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	19	1	no	—
46	D₁₁	—	25	1	no	—
47	D₁₁	—	475	1	no	—
48	C₂×D₅	—	1045	6	no	—
49	C₁₉	C₂×C₅⋊D₅₅	1	1	yes	characteristic, complemented, Sylow
50	C₁₁	D₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	19	6	no	—
52	D₅	—	1045	6	no	—
53	D₅	—	55	6	no	—
54	C₅	D₁₉×D₅₅	1	6	yes	complemented
55	C₂²	—	5225	1	no	Sylow
56	C₂	—	19	1	no	—
57	C₂	—	275	1	no	—
58	C₂	—	5225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁×C₁₉	C₂²
LCS	G ▷ C₅²×C₁₁×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₁×D₁₉	C₂	semidirect
2. C₁₉×C₅⋊D₅₅	C₂	semidirect
3. C₅⋊D₁₀₄₅	C₂	semidirect
4. C₅²×C₁₁×C₁₉	C₂²	semidirect
8. C₅×C₁₁×D₁₉	D₅	semidirect
11. C₅×C₁₁×C₁₉	C₂×D₅	semidirect
14. C₅²×D₁₉	D₁₁	semidirect
18. C₅⋊D₅₅	D₁₉	direct (N × H)
19. C₅²×C₁₉	C₂×D₁₁	semidirect
21. C₁₁×D₁₉	C₅⋊D₅	semidirect
24. C₅²×C₁₁	C₂×D₁₉	semidirect
26. C₁₁×C₁₉	C₂×C₅⋊D₅	semidirect
28. C₅×D₁₉	D₅₅	semidirect
34. C₅×C₁₉	C₂×D₅₅	semidirect
36. C₅×C₁₁	D₅×D₁₉	semidirect
43. D₁₉	C₅⋊D₅₅	direct (N × H)
44. C₅²	D₁₁×D₁₉	semidirect
49. C₁₉	C₂×C₅⋊D₅₅	semidirect
50. C₁₁	D₁₉×C₅⋊D₅	semidirect
54. C₅	D₁₉×D₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₅²×C₁₁×D₁₉	2
C₁₉×C₅⋊D₅₅	2
C₅⋊D₁₀₄₅	2
D₁₉×D₅₅	5
D₁₉×C₅⋊D₅	11
C₂×C₅⋊D₅₅	19

Subgroups — D19×C5⋊D55 #35229921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×C₅⋊D₅₅ #35229921