Subgroups — C₅×#87812 #14522636

Order 2000.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#6045	C₂	1	1	yes	maximal, characteristic
3	C₅×#6029	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅³	—	2	1	no	—
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	C₅×#1039	—	2	1	no	—
7	#87812	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×#689	—	5	6	no	maximal
9	C₂×C₅³	D₄	1	1	yes	characteristic
10	C₅²×Q₈	—	2	12	no	—
11	C₅²×Q₈	D₅	1	6	yes	—
12	C₅²×Q₈	C₂×C₅	1	1	yes	characteristic
13	#6045	C₂×C₅	1	1	yes	characteristic
14	C₅×Dic₁₀	—	5	6	no	—
15	#6029	C₂×C₅	1	1	yes	characteristic
16	C₅×#168	—	5	6	no	—
17	C₅³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅²	—	2	24	no	—
19	C₄×C₅²	—	2	12	no	—
20	C₄×C₅²	—	2	6	no	—
21	C₄×C₅²	—	2	1	no	—
22	C₄×C₅²	C₂×D₅	1	6	yes	—
23	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
24	#1039	—	2	1	no	—
25	C₅×Dic₅	—	10	6	no	—
26	C₅×Q₁₆	—	25	1	no	—
27	#689	—	5	6	no	—
28	C₂×C₅²	—	2	12	no	—
29	C₂×C₅²	C₂²⋊D₅	1	6	yes	—
30	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
31	C₅×Q₈	—	2	12	no	—
32	C₅×Q₈	—	25	1	no	—
33	C₅×Q₈	C₅×D₅	1	6	yes	—
34	C₅×Q₈	C₅⋊D₅	1	1	yes	characteristic
35	Dic₁₀	—	5	6	no	—
36	C₅×C₈	—	25	1	no	—
37	#168	—	5	6	no	—
38	C₅²	—	2	12	no	—
39	C₅²	#689	1	6	yes	complemented
40	C₅²	C₅×Q₁₆	1	1	yes	characteristic, complemented
41	C₄×C₅	—	2	24	no	—
42	C₄×C₅	—	2	6	no	—
43	C₄×C₅	—	2	1	no	—
44	C₄×C₅	—	2	12	no	—
45	C₄×C₅	—	50	1	no	—
46	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
47	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
48	Dic₅	—	10	6	no	—
49	Q₁₆	—	25	1	no	Sylow
50	C₂×C₅	—	2	12	no	—
51	C₂×C₅	C₅×C₂²⋊D₅	1	6	yes	—
52	C₂×C₅	C₂²⋊(C₅⋊D₅)	1	1	yes	characteristic
53	Q₈	—	25	1	no	—
54	Q₈	C₅×C₅⋊D₅	1	1	yes	characteristic
55	C₈	—	25	1	no	—
56	C₅	—	2	12	no	—
57	C₅	C₅×#689	1	6	yes	complemented
58	C₅	#87812	1	1	yes	characteristic, direct product factor
59	C₄	—	2	1	no	—
60	C₄	—	50	1	no	—
61	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
62	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	C₅³×Q₈	C₂
socle, prime radical	C₂×C₅³	D₄
hypercenter	C₅×Q₈	C₅⋊D₅
hypocenter	C₅²	C₅×Q₁₆
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₈

Complements

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

N	H ≅ G/N	type
7. #87812	C₅	direct (N × H)
17. C₅³	Q₁₆	semidirect
39. C₅²	#689	semidirect
40. C₅²	C₅×Q₁₆	semidirect
57. C₅	C₅×#689	semidirect
58. C₅	#87812	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×Q₈	2
C₅×#6045	2
C₅×#6029	2
#87812	5
C₅×#689	5

Subgroups — C5×#87812 #14522636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87812 #14522636