Subgroups — C₅×#87811 #14522635

Order 2000.

304 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, complemented
2	C₅×C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic
3	C₅×#6029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₅⋊D₅	—	2	1	no	—
5	C₄×C₅³	—	2	1	no	—
6	C₄×C₅³	C₂²	1	1	yes	characteristic
7	#87811	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×#688	—	5	6	no	maximal
9	C₂×C₅³	D₄	1	1	yes	characteristic
10	C₅×C₅⋊D₅	—	4	1	no	—
11	C₅²×Q₈	—	2	12	no	—
12	C₅²×Q₈	D₅	1	6	yes	complemented
13	C₅²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
14	C₄⋊(C₅⋊D₅)	C₂×C₅	1	1	yes	characteristic
15	C₅×D₂₀	—	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	C₂×C₅⋊D₅	—	2	1	no	—
20	C₂×C₅×D₅	—	10	6	no	—
21	C₄×C₅²	—	2	24	no	—
22	C₄×C₅²	—	2	12	no	—
23	C₄×C₅²	—	2	6	no	—
24	C₄×C₅²	—	2	1	no	—
25	C₄×C₅²	C₂×D₅	1	6	yes	—
26	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
27	C₅×SD₁₆	—	25	1	no	—
28	#688	—	5	6	no	—
29	C₂×C₅²	—	2	12	no	—
30	C₂×C₅²	C₂²⋊D₅	1	6	yes	—
31	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
32	C₅⋊D₅	—	4	1	no	—
33	C₅×D₅	—	20	6	no	—
34	C₅×Q₈	—	2	12	no	—
35	C₅×Q₈	C₅×D₅	1	6	yes	complemented
36	C₅×Q₈	C₅⋊D₅	1	1	yes	characteristic, complemented
37	C₅×D₄	—	25	1	no	—
38	D₂₀	—	5	6	no	—
39	C₅×C₈	—	25	1	no	—
40	#168	—	5	6	no	—
41	C₅²	—	2	12	no	—
42	C₅²	#688	1	6	yes	complemented
43	C₅²	C₅×SD₁₆	1	1	yes	characteristic, complemented
44	C₂²×C₅	—	50	1	no	—
45	C₂×D₅	—	10	6	no	—
46	C₄×C₅	—	2	24	no	—
47	C₄×C₅	—	2	6	no	—
48	C₄×C₅	—	2	1	no	—
49	C₄×C₅	—	2	12	no	—
50	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
51	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
52	SD₁₆	—	25	1	no	Sylow
53	C₂×C₅	—	2	12	no	—
54	C₂×C₅	—	100	1	no	—
55	C₂×C₅	C₅×C₂²⋊D₅	1	6	yes	—
56	C₂×C₅	C₂²⋊(C₅⋊D₅)	1	1	yes	characteristic
57	D₅	—	20	6	no	—
58	Q₈	C₅×C₅⋊D₅	1	1	yes	characteristic, complemented
59	D₄	—	25	1	no	—
60	C₈	—	25	1	no	—
61	C₅	—	2	12	no	—
62	C₅	C₅×#688	1	6	yes	complemented
63	C₅	#87811	1	1	yes	characteristic, direct product factor
64	C₂²	—	50	1	no	—
65	C₄	—	2	1	no	—
66	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
67	C₂	—	100	1	no	—
68	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	C₂×C₅³	D₄
prime radical	C₅×C₄⋊(C₅⋊D₅)	C₂
hypercenter	C₅×Q₈	C₅⋊D₅
hypocenter	C₅²	C₅×SD₁₆
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
1. C₅³×Q₈	C₂	semidirect
3. C₅×#6029	C₂	semidirect
7. #87811	C₅	direct (N × H)
12. C₅²×Q₈	D₅	semidirect
13. C₅²×Q₈	C₂×C₅	semidirect
16. #6029	C₂×C₅	semidirect
18. C₅³	SD₁₆	semidirect
35. C₅×Q₈	C₅×D₅	semidirect
36. C₅×Q₈	C₅⋊D₅	semidirect
42. C₅²	#688	semidirect
43. C₅²	C₅×SD₁₆	semidirect
58. Q₈	C₅×C₅⋊D₅	semidirect
62. C₅	C₅×#688	semidirect
63. C₅	#87811	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×C₄⋊(C₅⋊D₅)	2
C₅×#6029	2
#87811	5
C₅×#688	5

Subgroups — C5×#87811 #14522635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87811 #14522635