Subgroups — C₂×C₅×#6039 #14522859

Order 2000.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1039	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅²×Dic₅	C₂	1	2	yes	maximal
3	C₅×#6039	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅³	C₂²	1	1	yes	characteristic
5	C₅×#1039	C₂²	1	2	yes	—
6	C₅²×Dic₅	C₂²	1	4	yes	—
7	C₂×C₅×Dic₁₀	—	5	2	no	maximal
8	C₂×#6039	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅³	Q₈	1	2	yes	complemented
10	C₂×C₅³	C₂³	1	1	yes	characteristic
11	C₂×C₄×C₅²	—	5	2	no	—
12	C₂×#1039	C₂×C₅	1	1	yes	characteristic
13	C₂×C₅×Dic₅	—	2	4	no	—
14	C₂×C₅×Dic₅	—	5	2	no	—
15	C₂×C₅×Dic₅	—	10	2	no	—
16	C₂×C₅×Dic₅	D₅	1	2	yes	—
17	C₂×C₅×Dic₅	C₂×C₅	1	2	yes	—
18	C₅×Dic₁₀	—	5	8	no	—
19	#6039	C₂×C₅	1	4	yes	direct product factor
20	C₅³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅²	—	2	2	no	—
22	C₂²×C₅²	—	2	4	no	—
23	C₂²×C₅²	—	4	4	no	—
24	C₂²×C₅²	C₂×D₅	1	2	yes	—
25	C₂²×C₅²	C₂²×C₅	1	1	yes	characteristic
26	C₄×C₅²	—	5	4	no	—
27	#1039	C₂²×C₅	1	2	yes	—
28	C₅×Dic₅	—	2	8	no	—
29	C₅×Dic₅	—	5	4	no	—
30	C₅×Dic₅	—	10	4	no	—
31	C₅×Dic₅	C₂×D₅	1	4	yes	—
32	C₅×Dic₅	C₂²×C₅	1	4	yes	—
33	C₂×C₅×Q₈	—	25	1	no	—
34	C₂×Dic₁₀	—	5	2	no	—
35	C₂×C₅²	—	2	4	no	—
36	C₂×C₅²	—	2	8	no	—
37	C₂×C₅²	—	2	2	no	—
38	C₂×C₅²	—	2	4	no	—
39	C₂×C₅²	—	4	8	no	—
40	C₂×C₅²	—	4	4	no	—
41	C₂×C₅²	Dic₁₀	1	4	yes	complemented
42	C₂×C₅²	C₅×Q₈	1	2	yes	complemented
43	C₂×C₅²	C₂²×D₅	1	2	yes	—
44	C₂×C₅²	C₂³×C₅	1	1	yes	characteristic
45	C₅×Q₈	—	25	4	no	—
46	C₂×C₄×C₅	—	5	2	no	—
47	C₂×C₄×C₅	—	5	2	no	—
48	C₂×C₄×C₅	—	10	4	no	—
49	C₂×C₄×C₅	—	25	1	no	—
50	C₂×Dic₅	—	5	2	no	—
51	C₂×Dic₅	—	10	2	no	—
52	C₂×Dic₅	C₅×D₅	1	2	yes	—
53	Dic₁₀	—	5	8	no	—
54	C₅²	—	2	2	no	—
55	C₅²	—	2	4	no	—
56	C₅²	—	4	4	no	—
57	C₅²	C₂×Dic₁₀	1	2	yes	complemented
58	C₅²	C₂×C₅×Q₈	1	1	yes	characteristic, complemented
59	C₂²×C₅	—	2	4	no	—
60	C₂²×C₅	—	2	2	no	—
61	C₂²×C₅	—	4	4	no	—
62	C₂²×C₅	D₅²	1	1	yes	characteristic
63	C₂²×C₅	C₂×C₅×D₅	1	2	yes	—
64	C₄×C₅	—	5	4	no	—
65	C₄×C₅	—	5	4	no	—
66	C₄×C₅	—	10	8	no	—
67	C₄×C₅	—	25	2	no	—
68	Dic₅	—	5	4	no	—
69	Dic₅	—	10	4	no	—
70	Dic₅	C₂×C₅×D₅	1	4	yes	—
71	C₂×Q₈	—	25	1	no	Sylow
72	C₂×C₅	—	2	8	no	—
73	C₂×C₅	—	2	4	no	—
74	C₂×C₅	—	2	4	no	—
75	C₂×C₅	—	2	2	no	—
76	C₂×C₅	—	4	8	no	—
77	C₂×C₅	—	4	4	no	—
78	C₂×C₅	#6039	1	2	yes	direct product factor
79	C₂×C₅	C₅×Dic₁₀	1	4	yes	complemented
80	C₂×C₅	C₂×D₅²	1	1	yes	characteristic
81	C₂×C₅	C₂²×C₅×D₅	1	2	yes	—
82	Q₈	—	25	4	no	—
83	C₂×C₄	—	5	2	no	—
84	C₂×C₄	—	25	1	no	—
85	C₅	—	2	4	no	—
86	C₅	—	2	2	no	—
87	C₅	—	4	4	no	—
88	C₅	C₂×#6039	1	1	yes	characteristic, direct product factor
89	C₅	C₂×C₅×Dic₁₀	1	2	yes	complemented
90	C₂²	C₅×D₅²	1	1	yes	characteristic
91	C₄	—	5	4	no	—
92	C₄	—	25	2	no	—
93	C₂	C₅×#6039	1	2	yes	direct product factor
94	C₂	C₂×C₅×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₅	D₅²
commutator, cosocle	C₂×C₅²	C₂³×C₅
Frattini	C₂	C₂×C₅×D₅²
Fitting, socle, prime radical	C₂²×C₅³	C₂²
hypocenter	C₅²	C₂×C₅×Q₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×#6039	C₂	direct (N × H)
8. C₂×#6039	C₅	direct (N × H)
9. C₂×C₅³	Q₈	semidirect
19. #6039	C₂×C₅	direct (N × H)
20. C₅³	C₂×Q₈	semidirect
41. C₂×C₅²	Dic₁₀	semidirect
42. C₂×C₅²	C₅×Q₈	semidirect
57. C₅²	C₂×Dic₁₀	semidirect
58. C₅²	C₂×C₅×Q₈	semidirect
78. C₂×C₅	#6039	direct (N × H)
79. C₂×C₅	C₅×Dic₁₀	semidirect
88. C₅	C₂×#6039	direct (N × H)
89. C₅	C₂×C₅×Dic₁₀	semidirect
93. C₂	C₅×#6039	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×C₅×#1039	2
C₂×C₅²×Dic₅	2
C₅×#6039	2
C₂×C₅×Dic₁₀	5
C₂×#6039	5

Subgroups — C2×C5×#6039 #14522859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#6039 #14522859