Subgroups — C₅²×#676 #14522607

Order 2000.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×D₅	C₄	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	C₅²×Dic₅	C₄	1	1	yes	characteristic
7	C₅²×M₁₆	—	5	1	no	maximal
8	C₅×#676	C₅	1	6	yes	maximal, direct product factor
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₅²×D₅	—	2	1	no	—
11	C₂×C₄×C₅²	—	5	1	no	—
12	C₄×C₅×D₅	C₂×C₅	1	6	yes	—
13	C₅²×C₈	—	2	12	no	—
14	C₅²×C₈	—	5	1	no	—
15	C₅²×C₈	D₅	1	1	yes	characteristic, complemented
16	C₅²×C₈	C₂×C₅	1	6	yes	complemented
17	C₅×#168	C₂×C₅	1	6	yes	complemented
18	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	—	5	1	no	—
20	C₂×C₅×D₅	C₄×C₅	1	6	yes	—
21	C₄×C₅²	—	2	12	no	—
22	C₄×C₅²	—	5	1	no	—
23	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅²	C₂²×C₅	1	6	yes	—
25	C₅×Dic₅	C₄×C₅	1	6	yes	—
26	C₅×M₁₆	—	5	6	no	—
27	#676	C₅²	1	1	yes	characteristic, direct product factor
28	C₂×C₅²	—	2	12	no	—
29	C₂×C₅²	—	10	1	no	—
30	C₂×C₅²	C₄×D₅	1	1	yes	characteristic
31	C₂×C₅²	C₂×C₄×C₅	1	6	yes	—
32	C₅×D₅	—	2	6	no	—
33	C₂×C₄×C₅	—	5	6	no	—
34	C₄×D₅	C₂×C₅²	1	1	yes	characteristic
35	C₅×C₈	—	2	12	no	—
36	C₅×C₈	—	5	6	no	—
37	C₅×C₈	C₅×D₅	1	6	yes	complemented
38	C₅×C₈	C₂×C₅²	1	1	yes	characteristic, complemented
39	#168	C₂×C₅²	1	1	yes	characteristic, complemented
40	C₅²	—	2	12	no	—
41	C₅²	#676	1	1	yes	characteristic, direct product factor
42	C₅²	C₅×M₁₆	1	6	yes	complemented
43	C₂²×C₅	—	5	6	no	—
44	C₂×D₅	C₄×C₅²	1	1	yes	characteristic
45	C₄×C₅	—	2	12	no	—
46	C₄×C₅	—	5	6	no	—
47	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
48	C₄×C₅	C₂²×C₅²	1	1	yes	characteristic
49	Dic₅	C₄×C₅²	1	1	yes	characteristic
50	M₁₆	—	5	1	no	Sylow
51	C₂×C₅	—	2	12	no	—
52	C₂×C₅	—	10	6	no	—
53	C₂×C₅	C₄×C₅×D₅	1	6	yes	—
54	C₂×C₅	C₂×C₄×C₅²	1	1	yes	characteristic
55	D₅	—	2	1	no	—
56	C₂×C₄	—	5	1	no	—
57	C₈	—	5	1	no	—
58	C₈	C₅²×D₅	1	1	yes	characteristic, complemented
59	C₅	—	2	12	no	—
60	C₅	C₅×#676	1	6	yes	direct product factor
61	C₅	C₅²×M₁₆	1	1	yes	characteristic, complemented
62	C₂²	—	5	1	no	—
63	C₄	—	5	1	no	—
64	C₄	C₂×C₅²×D₅	1	1	yes	characteristic
65	C₂	—	10	1	no	—
66	C₂	C₄×C₅²×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅²	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₅²
Frattini	C₄	C₂×C₅²×D₅
Fitting	C₅³×C₈	C₂
socle	C₂×C₅³	C₂×C₄
prime radical	C₂×C₅²×D₅	C₄
cosocle	C₄×C₅	C₂²×C₅²
hypercenter	C₅²×C₈	D₅
hypocenter	C₅	C₅²×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₅² ◁ C₅²×C₈

Complements

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

N	H ≅ G/N	type
2. C₅³×C₈	C₂	semidirect
3. C₅²×#168	C₂	semidirect
8. C₅×#676	C₅	direct (N × H)
15. C₅²×C₈	D₅	semidirect
16. C₅²×C₈	C₂×C₅	semidirect
17. C₅×#168	C₂×C₅	semidirect
18. C₅³	M₁₆	semidirect
27. #676	C₅²	direct (N × H)
37. C₅×C₈	C₅×D₅	semidirect
38. C₅×C₈	C₂×C₅²	semidirect
39. #168	C₂×C₅²	semidirect
41. C₅²	#676	direct (N × H)
42. C₅²	C₅×M₁₆	semidirect
58. C₈	C₅²×D₅	semidirect
60. C₅	C₅×#676	direct (N × H)
61. C₅	C₅²×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅²×D₅	2
C₅³×C₈	2
C₅²×#168	2
C₅²×M₁₆	5
C₅×#676	5

Subgroups — C52×#676 #14522607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#676 #14522607