Subgroups — C₅²×#687 #14522618

Order 2000.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅²×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅³	—	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×#687	C₅	1	6	yes	maximal, direct product factor
9	C₂×C₅³	—	4	1	no	—
10	C₂×C₅³	D₄	1	1	yes	characteristic
11	C₅²×Q₈	—	5	1	no	—
12	C₅²×D₄	—	2	12	no	—
13	C₅²×D₄	D₅	1	1	yes	characteristic
14	C₅²×D₄	C₂×C₅	1	6	yes	—
15	C₅×Dic₁₀	C₂×C₅	1	6	yes	complemented
16	C₅²×C₈	—	5	1	no	—
17	C₅×#168	C₂×C₅	1	6	yes	complemented
18	C₅³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	—	2	24	no	—
20	C₂²×C₅²	—	2	1	no	—
21	C₂²×C₅²	—	2	6	no	—
22	C₄×C₅²	—	2	12	no	—
23	C₄×C₅²	—	10	1	no	—
24	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
25	C₄×C₅²	C₂²×C₅	1	6	yes	—
26	C₅×Dic₅	—	2	6	no	—
27	C₅×SD₁₆	—	5	6	no	—
28	#687	C₅²	1	1	yes	characteristic, direct product factor
29	C₂×C₅²	—	2	12	no	—
30	C₂×C₅²	—	4	24	no	—
31	C₂×C₅²	—	4	1	no	—
32	C₂×C₅²	—	4	6	no	—
33	C₂×C₅²	C₂²⋊D₅	1	1	yes	characteristic
34	C₂×C₅²	C₅×D₄	1	6	yes	—
35	C₅×Q₈	—	5	6	no	—
36	C₅×D₄	—	2	12	no	—
37	C₅×D₄	C₅×D₅	1	6	yes	—
38	C₅×D₄	C₂×C₅²	1	1	yes	characteristic
39	Dic₁₀	C₂×C₅²	1	1	yes	characteristic, complemented
40	C₅×C₈	—	5	6	no	—
41	#168	C₂×C₅²	1	1	yes	characteristic, complemented
42	C₅²	—	2	12	no	—
43	C₅²	#687	1	1	yes	characteristic, direct product factor
44	C₅²	C₅×SD₁₆	1	6	yes	complemented
45	C₂²×C₅	—	2	24	no	—
46	C₂²×C₅	—	2	6	no	—
47	C₂²×C₅	—	2	1	no	—
48	C₄×C₅	—	2	12	no	—
49	C₄×C₅	—	10	6	no	—
50	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
51	C₄×C₅	C₂²×C₅²	1	1	yes	characteristic
52	Dic₅	—	2	1	no	—
53	SD₁₆	—	5	1	no	Sylow
54	C₂×C₅	—	2	12	no	—
55	C₂×C₅	—	4	24	no	—
56	C₂×C₅	—	4	1	no	—
57	C₂×C₅	—	4	6	no	—
58	C₂×C₅	C₅×C₂²⋊D₅	1	6	yes	—
59	C₂×C₅	C₅²×D₄	1	1	yes	characteristic
60	Q₈	—	5	1	no	—
61	D₄	C₅²×D₅	1	1	yes	characteristic
62	C₈	—	5	1	no	—
63	C₅	—	2	12	no	—
64	C₅	C₅×#687	1	6	yes	direct product factor
65	C₅	C₅²×SD₁₆	1	1	yes	characteristic, complemented
66	C₂²	—	2	1	no	—
67	C₄	—	10	1	no	—
68	C₄	C₂×C₅²×D₅	1	1	yes	characteristic
69	C₂	—	4	1	no	—
70	C₂	C₅²×C₂²⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅²×Dic₁₀	C₂	semidirect
3. C₅²×#168	C₂	semidirect
8. C₅×#687	C₅	direct (N × H)
15. C₅×Dic₁₀	C₂×C₅	semidirect
17. C₅×#168	C₂×C₅	semidirect
18. C₅³	SD₁₆	semidirect
28. #687	C₅²	direct (N × H)
39. Dic₁₀	C₂×C₅²	semidirect
41. #168	C₂×C₅²	semidirect
43. C₅²	#687	direct (N × H)
44. C₅²	C₅×SD₁₆	semidirect
64. C₅	C₅×#687	direct (N × H)
65. 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
C₅³×D₄	2
C₅²×Dic₁₀	2
C₅²×#168	2
C₅²×SD₁₆	5
C₅×#687	5

Subgroups — C52×#687 #14522618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#687 #14522618