Subgroups — C₅²×#677 #14522608

Order 2000.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₅²×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×D₅	—	2	1	no	—
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	C₅²×Dic₅	—	2	1	no	—
7	C₅²×SD₁₆	—	5	1	no	maximal
8	C₅×#677	C₅	1	6	yes	maximal, direct product factor
9	C₂×C₅³	D₄	1	1	yes	characteristic
10	C₅²×D₅	—	4	1	no	—
11	C₅²×Q₈	—	5	1	no	—
12	C₅²×D₄	—	5	1	no	—
13	C₅×D₂₀	C₂×C₅	1	6	yes	—
14	C₅×Dic₁₀	C₂×C₅	1	6	yes	complemented
15	C₅²×C₈	—	2	12	no	—
16	C₅²×C₈	D₅	1	1	yes	characteristic, complemented
17	C₅²×C₈	C₂×C₅	1	6	yes	complemented
18	C₅³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	—	10	1	no	—
20	C₂×C₅×D₅	—	2	6	no	—
21	C₄×C₅²	—	2	12	no	—
22	C₄×C₅²	—	10	1	no	—
23	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅²	C₂²×C₅	1	6	yes	—
25	C₅×Dic₅	—	2	6	no	—
26	C₅×SD₁₆	—	5	6	no	—
27	#677	C₅²	1	1	yes	characteristic, direct product factor
28	C₂×C₅²	—	2	12	no	—
29	C₂×C₅²	—	20	1	no	—
30	C₂×C₅²	D₂₀	1	1	yes	characteristic
31	C₂×C₅²	C₅×D₄	1	6	yes	—
32	C₅×D₅	—	4	6	no	—
33	C₅×Q₈	—	5	6	no	—
34	C₅×D₄	—	5	6	no	—
35	D₂₀	C₂×C₅²	1	1	yes	characteristic
36	Dic₁₀	C₂×C₅²	1	1	yes	characteristic, complemented
37	C₅×C₈	—	2	12	no	—
38	C₅×C₈	C₅×D₅	1	6	yes	complemented
39	C₅×C₈	C₂×C₅²	1	1	yes	characteristic, complemented
40	C₅²	—	2	12	no	—
41	C₅²	#677	1	1	yes	characteristic, direct product factor
42	C₅²	C₅×SD₁₆	1	6	yes	complemented
43	C₂²×C₅	—	10	6	no	—
44	C₂×D₅	—	2	1	no	—
45	C₄×C₅	—	2	12	no	—
46	C₄×C₅	—	10	6	no	—
47	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
48	C₄×C₅	C₂²×C₅²	1	1	yes	characteristic
49	Dic₅	—	2	1	no	—
50	SD₁₆	—	5	1	no	Sylow
51	C₂×C₅	—	2	12	no	—
52	C₂×C₅	—	20	6	no	—
53	C₂×C₅	C₅×D₂₀	1	6	yes	—
54	C₂×C₅	C₅²×D₄	1	1	yes	characteristic
55	D₅	—	4	1	no	—
56	Q₈	—	5	1	no	—
57	D₄	—	5	1	no	—
58	C₈	C₅²×D₅	1	1	yes	characteristic, complemented
59	C₅	—	2	12	no	—
60	C₅	C₅×#677	1	6	yes	direct product factor
61	C₅	C₅²×SD₁₆	1	1	yes	characteristic, complemented
62	C₂²	—	10	1	no	—
63	C₄	—	10	1	no	—
64	C₄	C₂×C₅²×D₅	1	1	yes	characteristic
65	C₂	—	20	1	no	—
66	C₂	C₅²×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅²	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₅²
Frattini	C₄	C₂×C₅²×D₅
Fitting	C₅³×C₈	C₂
socle	C₂×C₅³	D₄
prime radical	C₅²×D₂₀	C₂
hypercenter	C₅²×C₈	D₅
hypocenter	C₅	C₅²×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅² ◁ C₄×C₅² ◁ C₅²×C₈

Complements

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

N	H ≅ G/N	type
2. C₅²×Dic₁₀	C₂	semidirect
3. C₅³×C₈	C₂	semidirect
8. C₅×#677	C₅	direct (N × H)
14. C₅×Dic₁₀	C₂×C₅	semidirect
16. C₅²×C₈	D₅	semidirect
17. C₅²×C₈	C₂×C₅	semidirect
18. C₅³	SD₁₆	semidirect
27. #677	C₅²	direct (N × H)
36. Dic₁₀	C₂×C₅²	semidirect
38. C₅×C₈	C₅×D₅	semidirect
39. C₅×C₈	C₂×C₅²	semidirect
41. C₅²	#677	direct (N × H)
42. C₅²	C₅×SD₁₆	semidirect
58. C₈	C₅²×D₅	semidirect
60. C₅	C₅×#677	direct (N × H)
61. C₅	C₅²×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₂₀	2
C₅²×Dic₁₀	2
C₅³×C₈	2
C₅²×SD₁₆	5
C₅×#677	5

Subgroups — C52×#677 #14522608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#677 #14522608