Subgroups — C₂×C₅×#6033 #14522792

Order 2000.

236 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	C₅×#6033	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₅³	C₄	1	1	yes	characteristic
4	C₅×#1039	C₄	1	1	yes	characteristic
5	C₅×#1039	C₂²	1	1	yes	characteristic
6	C₂×#6033	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅×#170	—	5	6	no	maximal
8	C₂×C₅³	C₈	1	2	yes	complemented
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₂×#1039	C₂×C₅	1	1	yes	characteristic
11	C₂×C₅×Dic₅	—	5	6	no	—
12	#6033	C₂×C₅	1	2	yes	direct product factor
13	C₅×#170	—	5	12	no	—
14	C₅³	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅²	—	4	6	no	—
16	C₂²×C₅²	C₄×C₅	1	1	yes	characteristic
17	C₂²×C₅²	AGL(1,𝔽₅)	1	6	yes	—
18	#1039	C₄×C₅	1	1	yes	characteristic
19	#1039	C₂²×C₅	1	1	yes	characteristic
20	C₅×Dic₅	—	5	6	no	—
21	C₅×Dic₅	—	5	6	no	—
22	C₂×#170	—	5	6	no	—
23	C₂×C₅×C₈	—	25	1	no	—
24	C₂×C₅²	—	4	12	no	—
25	C₂×C₅²	—	4	6	no	—
26	C₂×C₅²	C₅×C₈	1	2	yes	complemented
27	C₂×C₅²	#170	1	12	yes	complemented
28	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
29	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	6	yes	—
30	C₂×C₄×C₅	—	25	1	no	—
31	C₂×Dic₅	—	5	6	no	—
32	#170	—	5	12	no	—
33	C₅×C₈	—	25	2	no	—
34	C₅²	—	4	6	no	—
35	C₅²	C₂×C₅×C₈	1	1	yes	characteristic, complemented
36	C₅²	C₂×#170	1	6	yes	complemented
37	C₂²×C₅	—	4	6	no	—
38	C₂²×C₅	C₅×AGL(1,𝔽₅)	1	6	yes	—
39	C₂²×C₅	#1043	1	1	yes	characteristic
40	C₄×C₅	—	25	1	no	—
41	C₄×C₅	—	25	1	no	—
42	Dic₅	—	5	6	no	—
43	Dic₅	—	5	6	no	—
44	C₂×C₈	—	25	1	no	Sylow
45	C₂×C₅	—	4	12	no	—
46	C₂×C₅	—	4	6	no	—
47	C₂×C₅	C₅×#170	1	12	yes	complemented
48	C₂×C₅	#6033	1	2	yes	direct product factor
49	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	6	yes	—
50	C₂×C₅	C₂×#1043	1	1	yes	characteristic
51	C₂×C₄	—	25	1	no	—
52	C₈	—	25	2	no	—
53	C₅	—	4	6	no	—
54	C₅	C₂×C₅×#170	1	6	yes	complemented
55	C₅	C₂×#6033	1	1	yes	characteristic, direct product factor
56	C₂²	C₅×#1043	1	1	yes	characteristic
57	C₄	—	25	1	no	—
58	C₄	—	25	1	no	—
59	C₂	C₅×#6033	1	2	yes	direct product factor
60	C₂	C₂×C₅×#1043	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₅	#1043
commutator, hypocenter	C₅²	C₂×C₅×C₈
Frattini	C₂	C₂×C₅×#1043
Fitting, socle, prime radical	C₂²×C₅³	C₄
cosocle	#1039	C₂²×C₅
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#6033	C₂	direct (N × H)
6. C₂×#6033	C₅	direct (N × H)
8. C₂×C₅³	C₈	semidirect
12. #6033	C₂×C₅	direct (N × H)
14. C₅³	C₂×C₈	semidirect
26. C₂×C₅²	C₅×C₈	semidirect
27. C₂×C₅²	#170	semidirect
35. C₅²	C₂×C₅×C₈	semidirect
36. C₅²	C₂×#170	semidirect
47. C₂×C₅	C₅×#170	semidirect
48. C₂×C₅	#6033	direct (N × H)
54. C₅	C₂×C₅×#170	semidirect
55. C₅	C₂×#6033	direct (N × H)
59. C₂	C₅×#6033	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
C₅×#6033	2
C₂×#6033	5
C₂×C₅×#170	5

Subgroups — C2×C5×#6033 #14522792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#6033 #14522792