Subgroups — #87856⋊C₅ #14522320

Order 2000.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×(C₅⋊D₅)⋊C₅	C₂	1	1	yes	maximal, characteristic
2	#6033⋊C₅	C₂	1	2	yes	maximal, complemented
3	C₂×(C₅⋊D₅)⋊C₅	C₄	1	1	yes	characteristic
4	C₄×H(3,𝔽₅)	C₄	1	1	yes	characteristic
5	#1039⋊C₅	C₂²	1	1	yes	characteristic
6	#87856	C₅	1	1	yes	maximal, characteristic, complemented
7	C₅×#700	—	5	1	no	maximal
8	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
9	(C₅⋊D₅)⋊C₅	—	2	1	no	—
10	C₄×C₅⋊D₅	C₂×C₅	1	1	yes	characteristic
11	C₄×C₅×D₅	—	5	1	no	—
12	#6033	C₂×C₅	1	2	yes	complemented
13	C₅×#170	—	5	2	no	—
14	H(3,𝔽₅)	M₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅⋊D₅	C₄×C₅	1	1	yes	characteristic
16	C₂×C₅×D₅	—	5	1	no	—
17	C₄×C₅²	—	4	1	no	—
18	C₄×C₅²	C₄×C₅	1	1	yes	characteristic
19	C₄×C₅²	AGL(1,𝔽₅)	1	1	yes	characteristic
20	#1039	C₂²×C₅	1	1	yes	characteristic
21	C₅×Dic₅	—	5	1	no	—
22	#700	—	5	1	no	—
23	#700	—	25	1	no	—
24	C₅×M₁₆	—	25	1	no	—
25	C₂×C₅²	—	4	1	no	—
26	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
27	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₅⋊D₅	—	2	1	no	—
29	C₅×D₅	—	10	1	no	—
30	C₂×C₄×C₅	—	25	1	no	—
31	C₄×D₅	—	5	1	no	—
32	C₄×D₅	—	25	1	no	—
33	#170	—	5	2	no	—
34	#170	—	25	2	no	—
35	C₅×C₈	—	25	2	no	—
36	C₅²	—	4	1	no	—
37	C₅²	C₅×M₁₆	1	1	yes	characteristic, complemented
38	C₅²	#700	1	1	yes	characteristic, complemented
39	C₂²×C₅	—	25	1	no	—
40	C₂×D₅	—	5	1	no	—
41	C₂×D₅	—	25	1	no	—
42	C₄×C₅	—	5	1	no	—
43	C₄×C₅	—	5	1	no	—
44	C₄×C₅	—	20	1	no	—
45	C₄×C₅	—	25	1	no	—
46	C₄×C₅	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
47	Dic₅	—	5	1	no	—
48	Dic₅	—	25	1	no	—
49	M₁₆	—	25	1	no	Sylow
50	C₂×C₅	—	5	1	no	—
51	C₂×C₅	—	5	1	no	—
52	C₂×C₅	—	20	1	no	—
53	C₂×C₅	—	50	1	no	—
54	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
55	D₅	—	10	1	no	—
56	D₅	—	50	1	no	—
57	C₂×C₄	—	25	1	no	—
58	C₈	—	25	2	no	—
59	C₅	—	5	1	no	—
60	C₅	—	5	1	no	—
61	C₅	—	20	1	no	—
62	C₅	C₅×#700	1	1	yes	characteristic
63	C₂²	—	25	1	no	—
64	C₄	—	25	1	no	—
65	C₄	#1043⋊C₅	1	1	yes	characteristic
66	C₂	—	50	1	no	—
67	C₂	C₂×#1043⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#1043⋊C₅
commutator	C₂×C₅²	C₂×C₄×C₅
Frattini, socle	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)
Fitting	C₄×H(3,𝔽₅)	C₄
prime radical	C₂×(C₅⋊D₅)⋊C₅	C₄
cosocle	#1039	C₂²×C₅
hypercenter	C₄	#1043⋊C₅
hypocenter	C₅²	C₅×M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. #6033⋊C₅	C₂	semidirect
6. #87856	C₅	semidirect
12. #6033	C₂×C₅	semidirect
14. H(3,𝔽₅)	M₁₆	semidirect
37. C₅²	C₅×M₁₆	semidirect
38. C₅²	#700	semidirect

Maximal subgroups

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

subgroup	index
C₄×(C₅⋊D₅)⋊C₅	2
#6033⋊C₅	2
#87856	5
C₅×#700	5

Subgroups — #87856⋊C5 #14522320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #87856⋊C₅ #14522320