Subgroups — C₅×#87799 #14522623

Order 2000.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#6029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₅⋊D₅	C₄	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	C₅×#1039	C₄	1	1	yes	characteristic
7	#87799	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×#676	—	5	6	no	maximal
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₅×C₅⋊D₅	—	2	1	no	—
11	C₄×C₅⋊D₅	C₂×C₅	1	1	yes	characteristic
12	C₄×C₅×D₅	—	5	6	no	—
13	C₅²×C₈	—	2	12	no	—
14	C₅²×C₈	D₅	1	6	yes	complemented
15	C₅²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
16	#6029	C₂×C₅	1	1	yes	characteristic, complemented
17	C₅×#168	—	5	6	no	—
18	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅⋊D₅	C₄×C₅	1	1	yes	characteristic
20	C₂×C₅×D₅	—	5	6	no	—
21	C₄×C₅²	—	2	12	no	—
22	C₄×C₅²	C₂×D₅	1	6	yes	—
23	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
24	#1039	C₄×C₅	1	1	yes	characteristic
25	C₅×Dic₅	—	5	6	no	—
26	C₅×M₁₆	—	25	1	no	—
27	#676	—	5	6	no	—
28	C₂×C₅²	—	2	12	no	—
29	C₂×C₅²	C₄×D₅	1	6	yes	—
30	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
31	C₅⋊D₅	—	2	1	no	—
32	C₅×D₅	—	10	6	no	—
33	C₂×C₄×C₅	—	25	1	no	—
34	C₄×D₅	—	5	6	no	—
35	C₅×C₈	—	2	12	no	—
36	C₅×C₈	—	25	1	no	—
37	C₅×C₈	C₅×D₅	1	6	yes	complemented
38	C₅×C₈	C₅⋊D₅	1	1	yes	characteristic, complemented
39	#168	—	5	6	no	—
40	C₅²	—	2	12	no	—
41	C₅²	#676	1	6	yes	complemented
42	C₅²	C₅×M₁₆	1	1	yes	characteristic, complemented
43	C₂²×C₅	—	25	1	no	—
44	C₂×D₅	—	5	6	no	—
45	C₄×C₅	—	2	12	no	—
46	C₄×C₅	—	25	1	no	—
47	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
48	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
49	Dic₅	—	5	6	no	—
50	M₁₆	—	25	1	no	Sylow
51	C₂×C₅	—	2	12	no	—
52	C₂×C₅	—	50	1	no	—
53	C₂×C₅	C₄×C₅×D₅	1	6	yes	—
54	C₂×C₅	C₄×C₅⋊D₅	1	1	yes	characteristic
55	D₅	—	10	6	no	—
56	C₂×C₄	—	25	1	no	—
57	C₈	—	25	1	no	—
58	C₈	C₅×C₅⋊D₅	1	1	yes	characteristic, complemented
59	C₅	—	2	12	no	—
60	C₅	C₅×#676	1	6	yes	complemented
61	C₅	#87799	1	1	yes	characteristic, direct product factor
62	C₂²	—	25	1	no	—
63	C₄	—	25	1	no	—
64	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
65	C₂	—	50	1	no	—
66	C₂	C₄×C₅×C₅⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅³×C₈	C₂	semidirect
3. C₅×#6029	C₂	semidirect
7. #87799	C₅	direct (N × H)
14. C₅²×C₈	D₅	semidirect
15. C₅²×C₈	C₂×C₅	semidirect
16. #6029	C₂×C₅	semidirect
18. C₅³	M₁₆	semidirect
37. C₅×C₈	C₅×D₅	semidirect
38. C₅×C₈	C₅⋊D₅	semidirect
41. C₅²	#676	semidirect
42. C₅²	C₅×M₁₆	semidirect
58. C₈	C₅×C₅⋊D₅	semidirect
60. C₅	C₅×#676	semidirect
61. C₅	#87799	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₅⋊D₅	2
C₅³×C₈	2
C₅×#6029	2
#87799	5
C₅×#676	5

Subgroups — C5×#87799 #14522623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87799 #14522623