Subgroups — C₄×C₅×#1039 #14522629

Order 2000.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#1039	C₂	1	2	yes	maximal
3	C₂²×C₅³	C₂²	1	1	yes	characteristic
4	C₄×C₅³	C₄	1	2	yes	complemented
5	C₅×#1039	C₄	1	4	yes	direct product factor
6	C₄×#1039	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₄×C₅×Dic₅	—	5	6	no	maximal
8	C₂×C₅³	C₂×C₄	1	2	yes	—
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₅²	—	2	12	no	—
11	C₂×C₄×C₅²	D₅	1	6	yes	—
12	C₂×C₄×C₅²	C₂×C₅	1	1	yes	characteristic
13	C₂×#1039	C₂×C₅	1	2	yes	—
14	C₂×C₅×Dic₅	—	5	12	no	—
15	C₅³	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅²	—	2	12	no	—
17	C₂²×C₅²	C₂×D₅	1	6	yes	—
18	C₂²×C₅²	C₂²×C₅	1	1	yes	characteristic
19	C₄×C₅²	—	2	24	no	—
20	C₄×C₅²	Dic₅	1	12	yes	complemented
21	C₄×C₅²	C₄×C₅	1	2	yes	complemented
22	#1039	C₄×C₅	1	4	yes	direct product factor
23	C₅×Dic₅	—	5	24	no	—
24	C₄²×C₅	—	25	1	no	—
25	C₄×Dic₅	—	5	6	no	—
26	C₂×C₅²	—	2	24	no	—
27	C₂×C₅²	—	2	12	no	—
28	C₂×C₅²	C₄×D₅	1	12	yes	—
29	C₂×C₅²	C₂×Dic₅	1	6	yes	—
30	C₂×C₅²	C₂×C₄×C₅	1	2	yes	—
31	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
32	C₂×C₄×C₅	—	2	12	no	—
33	C₂×C₄×C₅	—	25	2	no	—
34	C₂×C₄×C₅	C₅×D₅	1	6	yes	—
35	C₂×C₄×C₅	C₅⋊D₅	1	1	yes	characteristic
36	C₂×Dic₅	—	5	12	no	—
37	C₅²	—	2	12	no	—
38	C₅²	C₄×Dic₅	1	6	yes	complemented
39	C₅²	C₄²×C₅	1	1	yes	characteristic, complemented
40	C₂²×C₅	—	2	12	no	—
41	C₂²×C₅	C₂×C₅×D₅	1	6	yes	—
42	C₂²×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
43	C₄×C₅	—	2	24	no	—
44	C₄×C₅	—	25	4	no	—
45	C₄×C₅	C₅×Dic₅	1	12	yes	complemented
46	C₄×C₅	#1039	1	2	yes	direct product factor
47	Dic₅	—	5	24	no	—
48	C₄²	—	25	1	no	Sylow
49	C₂×C₅	—	2	24	no	—
50	C₂×C₅	—	2	12	no	—
51	C₂×C₅	C₄×C₅×D₅	1	12	yes	—
52	C₂×C₅	C₂×C₅×Dic₅	1	6	yes	—
53	C₂×C₅	C₄×C₅⋊D₅	1	2	yes	—
54	C₂×C₅	C₂×#1039	1	1	yes	characteristic
55	C₂×C₄	—	25	2	no	—
56	C₂×C₄	C₅×C₅⋊D₅	1	1	yes	characteristic
57	C₅	—	2	12	no	—
58	C₅	C₄×C₅×Dic₅	1	6	yes	complemented
59	C₅	C₄×#1039	1	1	yes	characteristic, direct product factor
60	C₂²	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
61	C₄	—	25	4	no	—
62	C₄	C₅×#1039	1	2	yes	direct product factor
63	C₂	C₄×C₅×C₅⋊D₅	1	2	yes	—
64	C₂	C₂×C₅×#1039	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	C₅⋊D₅
commutator, hypocenter	C₅²	C₄²×C₅
Frattini	C₂²	C₂×C₅×C₅⋊D₅
Fitting	C₂×C₄×C₅³	C₂
socle, prime radical	C₂²×C₅³	C₂²
cosocle	C₂²×C₅²	C₂²×C₅
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
4. C₄×C₅³	C₄	semidirect
5. C₅×#1039	C₄	direct (N × H)
6. C₄×#1039	C₅	direct (N × H)
15. C₅³	C₄²	semidirect
20. C₄×C₅²	Dic₅	semidirect
21. C₄×C₅²	C₄×C₅	semidirect
22. #1039	C₄×C₅	direct (N × H)
38. C₅²	C₄×Dic₅	semidirect
39. C₅²	C₄²×C₅	semidirect
45. C₄×C₅	C₅×Dic₅	semidirect
46. C₄×C₅	#1039	direct (N × H)
58. C₅	C₄×C₅×Dic₅	semidirect
59. C₅	C₄×#1039	direct (N × H)
62. C₄	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
C₂×C₄×C₅³	2
C₂×C₅×#1039	2
C₄×#1039	5
C₄×C₅×Dic₅	5

Subgroups — C4×C5×#1039 #14522629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#1039 #14522629