Subgroups — C₂×C₅×#6045 #14522909

Order 2000.

496 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	C₅×#6045	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅³	C₂²	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	2	yes	—
6	C₅×#1039	C₂²	1	4	yes	—
7	C₂×#6045	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₅×Dic₁₀	—	5	6	no	maximal
9	C₂×C₅³	Q₈	1	2	yes	complemented
10	C₂×C₅³	C₂³	1	1	yes	characteristic
11	C₂×C₄×C₅²	—	2	12	no	—
12	C₂×C₄×C₅²	D₅	1	6	yes	—
13	C₂×C₄×C₅²	C₂×C₅	1	1	yes	characteristic
14	C₂×#1039	C₂×C₅	1	2	yes	—
15	#6045	C₂×C₅	1	4	yes	direct product factor
16	C₂×C₅×Dic₅	—	5	12	no	—
17	C₅×Dic₁₀	—	5	24	no	—
18	C₅³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	—	2	12	no	—
20	C₂²×C₅²	C₂×D₅	1	6	yes	—
21	C₂²×C₅²	C₂²×C₅	1	1	yes	characteristic
22	C₄×C₅²	—	2	24	no	—
23	C₄×C₅²	C₂×D₅	1	12	yes	—
24	C₄×C₅²	C₂²×C₅	1	2	yes	—
25	#1039	C₂²×C₅	1	4	yes	—
26	C₅×Dic₅	—	5	24	no	—
27	C₂×C₅×Q₈	—	25	1	no	—
28	C₂×Dic₁₀	—	5	6	no	—
29	C₂×C₅²	—	2	24	no	—
30	C₂×C₅²	—	2	12	no	—
31	C₂×C₅²	Dic₁₀	1	12	yes	complemented
32	C₂×C₅²	C₅×Q₈	1	2	yes	complemented
33	C₂×C₅²	C₂²×D₅	1	6	yes	—
34	C₂×C₅²	C₂³×C₅	1	1	yes	characteristic
35	C₅×Q₈	—	25	4	no	—
36	C₂×C₄×C₅	—	2	12	no	—
37	C₂×C₄×C₅	—	25	2	no	—
38	C₂×C₄×C₅	C₅×D₅	1	6	yes	—
39	C₂×C₄×C₅	C₅⋊D₅	1	1	yes	characteristic
40	C₂×Dic₅	—	5	12	no	—
41	Dic₁₀	—	5	24	no	—
42	C₅²	—	2	12	no	—
43	C₅²	C₂×Dic₁₀	1	6	yes	complemented
44	C₅²	C₂×C₅×Q₈	1	1	yes	characteristic, complemented
45	C₂²×C₅	—	2	12	no	—
46	C₂²×C₅	C₂×C₅×D₅	1	6	yes	—
47	C₂²×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
48	C₄×C₅	—	2	24	no	—
49	C₄×C₅	—	25	4	no	—
50	C₄×C₅	C₂×C₅×D₅	1	12	yes	—
51	C₄×C₅	C₂×C₅⋊D₅	1	2	yes	—
52	Dic₅	—	5	24	no	—
53	C₂×Q₈	—	25	1	no	Sylow
54	C₂×C₅	—	2	24	no	—
55	C₂×C₅	—	2	12	no	—
56	C₂×C₅	C₅×Dic₁₀	1	12	yes	complemented
57	C₂×C₅	#6045	1	2	yes	direct product factor
58	C₂×C₅	C₂²×C₅×D₅	1	6	yes	—
59	C₂×C₅	C₂²×C₅⋊D₅	1	1	yes	characteristic
60	Q₈	—	25	4	no	—
61	C₂×C₄	—	25	2	no	—
62	C₂×C₄	C₅×C₅⋊D₅	1	1	yes	characteristic
63	C₅	—	2	12	no	—
64	C₅	C₂×C₅×Dic₁₀	1	6	yes	complemented
65	C₅	C₂×#6045	1	1	yes	characteristic, direct product factor
66	C₂²	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
67	C₄	—	25	4	no	—
68	C₄	C₂×C₅×C₅⋊D₅	1	2	yes	—
69	C₂	C₅×#6045	1	2	yes	direct product factor
70	C₂	C₂²×C₅×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×C₅⋊D₅
commutator, cosocle	C₂×C₅²	C₂³×C₅
Frattini	C₂	C₂²×C₅×C₅⋊D₅
Fitting	C₂×C₄×C₅³	C₂
socle, prime radical	C₂²×C₅³	C₂²
hypercenter	C₂×C₄×C₅	C₅⋊D₅
hypocenter	C₅²	C₂×C₅×Q₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×#6045	C₂	direct (N × H)
7. C₂×#6045	C₅	direct (N × H)
9. C₂×C₅³	Q₈	semidirect
15. #6045	C₂×C₅	direct (N × H)
18. C₅³	C₂×Q₈	semidirect
31. C₂×C₅²	Dic₁₀	semidirect
32. C₂×C₅²	C₅×Q₈	semidirect
43. C₅²	C₂×Dic₁₀	semidirect
44. C₅²	C₂×C₅×Q₈	semidirect
56. C₂×C₅	C₅×Dic₁₀	semidirect
57. C₂×C₅	#6045	direct (N × H)
64. C₅	C₂×C₅×Dic₁₀	semidirect
65. C₅	C₂×#6045	direct (N × H)
69. C₂	C₅×#6045	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
C₅×#6045	2
C₂×#6045	5
C₂×C₅×Dic₁₀	5

Subgroups — C2×C5×#6045 #14522909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#6045 #14522909