Subgroups — C₅×#87804 #14522628

Order 2000.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₅×#6029	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅³	C₄	1	1	yes	characteristic
4	C₄×C₅³	C₄	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	#87804	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×#681	—	5	6	no	maximal
8	C₂×C₅³	—	2	1	no	—
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₅²	—	2	12	no	—
11	C₂×C₄×C₅²	D₅	1	6	yes	—
12	C₂×C₄×C₅²	C₂×C₅	1	1	yes	characteristic
13	#6029	C₂×C₅	1	2	yes	complemented
14	C₅×#168	—	5	12	no	—
15	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅²	—	2	12	no	—
17	C₂²×C₅²	Dic₅	1	6	yes	—
18	C₂²×C₅²	C₄×C₅	1	1	yes	characteristic
19	C₄×C₅²	—	2	12	no	—
20	C₄×C₅²	—	2	12	no	—
21	C₄×C₅²	Dic₅	1	6	yes	—
22	C₄×C₅²	C₄×C₅	1	1	yes	characteristic
23	C₄×C₅²	C₂×D₅	1	6	yes	—
24	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
25	C₅×M₁₆	—	25	1	no	—
26	#681	—	5	6	no	—
27	C₂×C₅²	—	2	24	no	—
28	C₂×C₅²	—	2	6	no	—
29	C₂×C₅²	—	2	1	no	—
30	C₂×C₅²	—	2	12	no	—
31	C₂×C₅²	C₂×Dic₅	1	6	yes	—
32	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
33	C₂×C₄×C₅	—	2	12	no	—
34	C₂×C₄×C₅	C₅×D₅	1	6	yes	—
35	C₂×C₄×C₅	C₅⋊D₅	1	1	yes	characteristic
36	C₅×C₈	—	25	2	no	—
37	#168	—	5	12	no	—
38	C₅²	—	2	12	no	—
39	C₅²	#681	1	6	yes	complemented
40	C₅²	C₅×M₁₆	1	1	yes	characteristic, complemented
41	C₂²×C₅	—	2	12	no	—
42	C₂²×C₅	C₅×Dic₅	1	6	yes	—
43	C₂²×C₅	#1039	1	1	yes	characteristic
44	C₄×C₅	—	2	12	no	—
45	C₄×C₅	—	2	12	no	—
46	C₄×C₅	C₅×Dic₅	1	6	yes	—
47	C₄×C₅	#1039	1	1	yes	characteristic
48	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
49	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
50	M₁₆	—	25	1	no	Sylow
51	C₂×C₅	—	2	24	no	—
52	C₂×C₅	—	2	6	no	—
53	C₂×C₅	—	2	1	no	—
54	C₂×C₅	—	2	12	no	—
55	C₂×C₅	C₂×C₅×Dic₅	1	6	yes	—
56	C₂×C₅	C₂×#1039	1	1	yes	characteristic
57	C₂×C₄	C₅×C₅⋊D₅	1	1	yes	characteristic
58	C₈	—	25	2	no	—
59	C₅	—	2	12	no	—
60	C₅	C₅×#681	1	6	yes	complemented
61	C₅	#87804	1	1	yes	characteristic, direct product factor
62	C₂²	C₅×#1039	1	1	yes	characteristic
63	C₄	C₅×#1039	1	1	yes	characteristic
64	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
65	C₂	—	2	1	no	—
66	C₂	C₂×C₅×#1039	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	C₂×C₄×C₅³	C₂
socle	C₂×C₅³	C₂×C₄
prime radical	C₂²×C₅³	C₄
cosocle	C₄×C₅²	C₂²×C₅
hypercenter	C₂×C₄×C₅	C₅⋊D₅
hypocenter	C₅²	C₅×M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#6029	C₂	semidirect
6. #87804	C₅	direct (N × H)
13. #6029	C₂×C₅	semidirect
15. C₅³	M₁₆	semidirect
39. C₅²	#681	semidirect
40. C₅²	C₅×M₁₆	semidirect
60. C₅	C₅×#681	semidirect
61. C₅	#87804	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅³	2
C₅×#6029	2
#87804	5
C₅×#681	5

Subgroups — C5×#87804 #14522628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87804 #14522628