Subgroups — C₂²×C₅×#1039 #14522917

Order 2000.

816 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#1039	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅³	C₄	1	4	yes	complemented
4	C₂²×C₅³	C₂²	1	3	yes	—
5	C₅×#1039	C₂²	1	4	yes	direct product factor
6	C₂²×#1039	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₅×Dic₅	—	5	6	no	maximal
8	C₂×C₅³	C₂×C₄	1	6	yes	complemented
9	C₂×C₅³	C₂³	1	1	yes	characteristic
10	C₂³×C₅²	—	2	12	no	—
11	C₂³×C₅²	D₅	1	6	yes	—
12	C₂³×C₅²	C₂×C₅	1	1	yes	characteristic
13	C₂×#1039	C₂×C₅	1	6	yes	direct product factor
14	C₂×C₅×Dic₅	—	5	36	no	—
15	C₅³	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅²	—	2	48	no	—
17	C₂²×C₅²	—	2	36	no	—
18	C₂²×C₅²	Dic₅	1	24	yes	complemented
19	C₂²×C₅²	C₄×C₅	1	4	yes	complemented
20	C₂²×C₅²	C₂×D₅	1	18	yes	—
21	C₂²×C₅²	C₂²×C₅	1	3	yes	—
22	#1039	C₂²×C₅	1	4	yes	direct product factor
23	C₅×Dic₅	—	5	24	no	—
24	C₂²×C₄×C₅	—	25	1	no	—
25	C₂²×Dic₅	—	5	6	no	—
26	C₂×C₅²	—	2	72	no	—
27	C₂×C₅²	—	2	12	no	—
28	C₂×C₅²	C₂×Dic₅	1	36	yes	complemented
29	C₂×C₅²	C₂×C₄×C₅	1	6	yes	complemented
30	C₂×C₅²	C₂²×D₅	1	6	yes	—
31	C₂×C₅²	C₂³×C₅	1	1	yes	characteristic
32	C₂³×C₅	—	2	12	no	—
33	C₂³×C₅	C₅×D₅	1	6	yes	—
34	C₂³×C₅	C₅⋊D₅	1	1	yes	characteristic
35	C₂×C₄×C₅	—	25	6	no	—
36	C₂×Dic₅	—	5	36	no	—
37	C₅²	—	2	12	no	—
38	C₅²	C₂²×Dic₅	1	6	yes	complemented
39	C₅²	C₂²×C₄×C₅	1	1	yes	characteristic, complemented
40	C₂²×C₅	—	2	48	no	—
41	C₂²×C₅	—	2	36	no	—
42	C₂²×C₅	C₅×Dic₅	1	24	yes	complemented
43	C₂²×C₅	#1039	1	4	yes	direct product factor
44	C₂²×C₅	C₂×C₅×D₅	1	18	yes	—
45	C₂²×C₅	C₂×C₅⋊D₅	1	3	yes	—
46	C₄×C₅	—	25	4	no	—
47	Dic₅	—	5	24	no	—
48	C₂²×C₄	—	25	1	no	Sylow
49	C₂×C₅	—	2	72	no	—
50	C₂×C₅	—	2	12	no	—
51	C₂×C₅	C₂×C₅×Dic₅	1	36	yes	complemented
52	C₂×C₅	C₂×#1039	1	6	yes	direct product factor
53	C₂×C₅	C₂²×C₅×D₅	1	6	yes	—
54	C₂×C₅	C₂²×C₅⋊D₅	1	1	yes	characteristic
55	C₂³	C₅×C₅⋊D₅	1	1	yes	characteristic
56	C₂×C₄	—	25	6	no	—
57	C₅	—	2	12	no	—
58	C₅	C₂²×C₅×Dic₅	1	6	yes	complemented
59	C₅	C₂²×#1039	1	1	yes	characteristic, direct product factor
60	C₂²	C₅×#1039	1	4	yes	direct product factor
61	C₂²	C₂×C₅×C₅⋊D₅	1	3	yes	—
62	C₄	—	25	4	no	—
63	C₂	C₂×C₅×#1039	1	6	yes	direct product factor
64	C₂	C₂²×C₅×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₅	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₄×C₅
Frattini	C₂	C₂²×C₅×C₅⋊D₅
Fitting, socle, prime radical	C₂³×C₅³	C₂
cosocle	C₂×C₅²	C₂³×C₅
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#1039	C₂	direct (N × H)
3. C₂²×C₅³	C₄	semidirect
5. C₅×#1039	C₂²	direct (N × H)
6. C₂²×#1039	C₅	direct (N × H)
8. C₂×C₅³	C₂×C₄	semidirect
13. C₂×#1039	C₂×C₅	direct (N × H)
15. C₅³	C₂²×C₄	semidirect
18. C₂²×C₅²	Dic₅	semidirect
19. C₂²×C₅²	C₄×C₅	semidirect
22. #1039	C₂²×C₅	direct (N × H)
28. C₂×C₅²	C₂×Dic₅	semidirect
29. C₂×C₅²	C₂×C₄×C₅	semidirect
38. C₅²	C₂²×Dic₅	semidirect
39. C₅²	C₂²×C₄×C₅	semidirect
42. C₂²×C₅	C₅×Dic₅	semidirect
43. C₂²×C₅	#1039	direct (N × H)
51. C₂×C₅	C₂×C₅×Dic₅	semidirect
52. C₂×C₅	C₂×#1039	direct (N × H)
58. C₅	C₂²×C₅×Dic₅	semidirect
59. C₅	C₂²×#1039	direct (N × H)
60. C₂²	C₅×#1039	direct (N × H)
63. C₂	C₂×C₅×#1039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅³	2
C₂×C₅×#1039	2
C₂²×#1039	5
C₂²×C₅×Dic₅	5

Subgroups — C22×C5×#1039 #14522917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#1039 #14522917