Subgroups — C₅×#87810 #14522634

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	C₅×#6045	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#6029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅³	—	2	1	no	—
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	C₅×#1039	—	2	1	no	—
7	#87810	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×#687	—	5	6	no	maximal
9	C₂×C₅³	—	4	1	no	—
10	C₂×C₅³	D₄	1	1	yes	characteristic
11	C₅²×D₄	—	2	12	no	—
12	C₅²×D₄	D₅	1	6	yes	—
13	C₅²×D₄	C₂×C₅	1	1	yes	characteristic
14	#6045	C₂×C₅	1	1	yes	characteristic, complemented
15	C₅×Dic₁₀	—	5	6	no	—
16	#6029	C₂×C₅	1	1	yes	characteristic, complemented
17	C₅×#168	—	5	6	no	—
18	C₅³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	—	2	24	no	—
20	C₂²×C₅²	—	2	6	no	—
21	C₂²×C₅²	—	2	1	no	—
22	C₄×C₅²	—	2	12	no	—
23	C₄×C₅²	C₂×D₅	1	6	yes	—
24	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
25	#1039	—	2	1	no	—
26	C₅×Dic₅	—	10	6	no	—
27	C₅×SD₁₆	—	25	1	no	—
28	#687	—	5	6	no	—
29	C₂×C₅²	—	2	12	no	—
30	C₂×C₅²	—	4	24	no	—
31	C₂×C₅²	—	4	6	no	—
32	C₂×C₅²	—	4	1	no	—
33	C₂×C₅²	C₂²⋊D₅	1	6	yes	—
34	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
35	C₅×Q₈	—	25	1	no	—
36	C₅×D₄	—	2	12	no	—
37	C₅×D₄	C₅×D₅	1	6	yes	—
38	C₅×D₄	C₅⋊D₅	1	1	yes	characteristic
39	Dic₁₀	—	5	6	no	—
40	C₅×C₈	—	25	1	no	—
41	#168	—	5	6	no	—
42	C₅²	—	2	12	no	—
43	C₅²	#687	1	6	yes	complemented
44	C₅²	C₅×SD₁₆	1	1	yes	characteristic, 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	—	50	1	no	—
50	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
51	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
52	Dic₅	—	10	6	no	—
53	SD₁₆	—	25	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	C₂²⋊(C₅⋊D₅)	1	1	yes	characteristic
60	Q₈	—	25	1	no	—
61	D₄	C₅×C₅⋊D₅	1	1	yes	characteristic
62	C₈	—	25	1	no	—
63	C₅	—	2	12	no	—
64	C₅	C₅×#687	1	6	yes	complemented
65	C₅	#87810	1	1	yes	characteristic, direct product factor
66	C₂²	—	2	1	no	—
67	C₄	—	50	1	no	—
68	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
69	C₂	—	4	1	no	—
70	C₂	C₅×C₂²⋊(C₅⋊D₅)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×#6045	C₂	semidirect
3. C₅×#6029	C₂	semidirect
7. #87810	C₅	direct (N × H)
14. #6045	C₂×C₅	semidirect
16. #6029	C₂×C₅	semidirect
18. C₅³	SD₁₆	semidirect
43. C₅²	#687	semidirect
44. C₅²	C₅×SD₁₆	semidirect
64. C₅	C₅×#687	semidirect
65. C₅	#87810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅³×D₄	2
C₅×#6045	2
C₅×#6029	2
#87810	5
C₅×#687	5

Subgroups — C5×#87810 #14522634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87810 #14522634