Subgroups — C₅×C₁₉×Dic₅₅ #35229869

Order 20900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×Dic₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₁₉×Dic₁₁	—	5	1	no	maximal
5	C₂×C₅×C₁₁×C₁₉	—	2	2	no	—
6	C₂×C₅×C₁₁×C₁₉	D₅	1	1	yes	characteristic
7	C₂×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₉×Dic₅	—	11	1	no	maximal, Hall
9	C₅×Dic₅₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₁×C₁₉	—	2	2	no	—
11	C₅×C₁₁×C₁₉	Dic₅	1	1	yes	characteristic, complemented
12	C₅×C₁₁×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅²×C₁₉	D₁₁	1	1	yes	characteristic
14	C₁₉×Dic₁₁	—	5	1	no	Hall
15	C₂×C₅²×C₁₁	C₂×C₁₉	1	1	yes	characteristic
16	C₅²×C₁₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₁₉	C₅×D₅	1	1	yes	characteristic
18	C₄×C₅×C₁₉	—	55	1	no	—
19	C₁₉×Dic₅	—	11	1	no	—
20	C₅²×C₁₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
21	Dic₅₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
22	C₅×Dic₁₁	—	5	1	no	—
23	C₁₁×C₁₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₉	—	2	2	no	—
25	C₂×C₅×C₁₉	C₅×D₁₁	1	1	yes	characteristic
26	C₂×C₅×C₁₉	D₅₅	1	1	yes	characteristic
27	C₂×C₅×C₁₁	—	2	2	no	—
28	C₂×C₅×C₁₁	D₅×C₁₉	1	1	yes	characteristic
29	C₂×C₅×C₁₁	C₂×C₅×C₁₉	1	1	yes	characteristic
30	C₅×Dic₅	—	11	1	no	Hall
31	C₅×C₁₉	—	2	2	no	—
32	C₅×C₁₉	C₅×Dic₁₁	1	1	yes	characteristic, complemented
33	C₅×C₁₉	Dic₅₅	1	1	yes	characteristic, direct product factor
34	C₄×C₁₉	—	55	1	no	Hall
35	C₅×C₁₁	—	2	2	no	—
36	C₅×C₁₁	C₁₉×Dic₅	1	1	yes	characteristic, complemented
37	C₅×C₁₁	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented
38	C₂×C₅²	C₁₉×D₁₁	1	1	yes	characteristic
39	Dic₁₁	—	5	1	no	Hall
40	C₂×C₁₉	C₅×D₅₅	1	1	yes	characteristic
41	C₅²	C₁₉×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁	C₅×D₅×C₁₉	1	1	yes	characteristic
43	C₄×C₅	—	55	1	no	—
44	Dic₅	—	11	1	no	—
45	C₁₉	C₅×Dic₅₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₁₁	C₅×C₁₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	C₅×C₁₉×D₁₁	1	1	yes	characteristic
49	C₂×C₅	C₁₉×D₅₅	1	1	yes	characteristic
50	C₅	—	2	2	no	—
51	C₅	C₅×C₁₉×Dic₁₁	1	1	yes	characteristic, complemented
52	C₅	C₁₉×Dic₅₅	1	1	yes	characteristic, direct product factor
53	C₄	—	55	1	no	Sylow
54	C₂	C₅×C₁₉×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₅₅
commutator, hypocenter	C₅×C₁₁	C₄×C₅×C₁₉
Frattini	C₂	C₅×C₁₉×D₅₅
Fitting, socle, prime radical	C₂×C₅²×C₁₁×C₁₉	C₂
cosocle	C₂×C₅×C₁₁	C₂×C₅×C₁₉
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₉	C₄	semidirect
3. C₁₉×Dic₅₅	C₅	direct (N × H)
9. C₅×Dic₅₅	C₁₉	direct (N × H)
11. C₅×C₁₁×C₁₉	Dic₅	semidirect
12. C₅×C₁₁×C₁₉	C₄×C₅	semidirect
16. C₅²×C₁₉	Dic₁₁	semidirect
20. C₅²×C₁₁	C₄×C₁₉	semidirect
21. Dic₅₅	C₅×C₁₉	direct (N × H)
23. C₁₁×C₁₉	C₅×Dic₅	semidirect
32. C₅×C₁₉	C₅×Dic₁₁	semidirect
33. C₅×C₁₉	Dic₅₅	direct (N × H)
36. C₅×C₁₁	C₁₉×Dic₅	semidirect
37. C₅×C₁₁	C₄×C₅×C₁₉	semidirect
41. C₅²	C₁₉×Dic₁₁	semidirect
45. C₁₉	C₅×Dic₅₅	direct (N × H)
46. C₁₁	C₅×C₁₉×Dic₅	semidirect
51. C₅	C₅×C₁₉×Dic₁₁	semidirect
52. C₅	C₁₉×Dic₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₁₁×C₁₉	2
C₁₉×Dic₅₅	5
C₅×C₁₉×Dic₁₁	5
C₅×C₁₉×Dic₅	11
C₅×Dic₅₅	19

Subgroups — C5×C19×Dic55 #35229869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×Dic₅₅ #35229869