Subgroups — C₄×#1043⋊C₅ #14522321

Order 2000.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1043⋊C₅	C₂	1	2	yes	maximal
2	C₄×(C₅⋊D₅)⋊C₅	C₂	1	1	yes	maximal, characteristic
3	C₂×(C₅⋊D₅)⋊C₅	C₂²	1	1	yes	characteristic
4	#1043⋊C₅	C₄	1	4	yes	direct product factor
5	C₄×H(3,𝔽₅)	C₄	1	1	yes	characteristic, complemented
6	#1039⋊C₅	C₄	1	1	yes	characteristic, complemented
7	C₄×#1043	C₅	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×AGL(1,𝔽₅)	—	5	1	no	maximal
9	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
10	(C₅⋊D₅)⋊C₅	C₂×C₄	1	2	yes	—
11	C₂×#1043	C₂×C₅	1	2	yes	—
12	C₂×C₅×AGL(1,𝔽₅)	—	5	2	no	—
13	C₄×C₅⋊D₅	C₂×C₅	1	1	yes	characteristic
14	C₄×C₅×D₅	—	5	1	no	—
15	H(3,𝔽₅)	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅⋊D₅	C₂²×C₅	1	1	yes	characteristic
17	C₂×C₅×D₅	—	5	1	no	—
18	#1043	C₄×C₅	1	4	yes	complemented
19	C₅×AGL(1,𝔽₅)	—	5	4	no	—
20	C₄×C₅²	—	4	1	no	—
21	C₄×C₅²	C₄×C₅	1	1	yes	characteristic, complemented
22	C₄×C₅²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
23	#1039	C₄×C₅	1	1	yes	characteristic, complemented
24	C₅×Dic₅	—	5	1	no	—
25	C₄×AGL(1,𝔽₅)	—	5	1	no	—
26	C₄×AGL(1,𝔽₅)	—	25	1	no	—
27	C₄²×C₅	—	25	1	no	—
28	C₂×C₅²	—	4	1	no	—
29	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
30	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₅⋊D₅	C₂×C₄×C₅	1	2	yes	—
32	C₅×D₅	—	5	2	no	—
33	C₂×AGL(1,𝔽₅)	—	5	2	no	—
34	C₂×AGL(1,𝔽₅)	—	25	2	no	—
35	C₂×C₄×C₅	—	25	1	no	—
36	C₂×C₄×C₅	—	25	2	no	—
37	C₄×D₅	—	5	1	no	—
38	C₄×D₅	—	25	1	no	—
39	C₅²	—	4	1	no	—
40	C₅²	C₄²×C₅	1	1	yes	characteristic, complemented
41	C₅²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
42	C₂²×C₅	—	25	1	no	—
43	C₂×D₅	—	5	1	no	—
44	C₂×D₅	—	25	1	no	—
45	AGL(1,𝔽₅)	—	5	4	no	—
46	AGL(1,𝔽₅)	—	25	4	no	—
47	C₄×C₅	—	5	1	no	—
48	C₄×C₅	—	5	1	no	—
49	C₄×C₅	—	20	1	no	—
50	C₄×C₅	—	25	1	no	—
51	C₄×C₅	—	25	4	no	—
52	C₄×C₅	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
53	Dic₅	—	5	1	no	—
54	Dic₅	—	25	1	no	—
55	C₄²	—	25	1	no	Sylow
56	C₂×C₅	—	5	1	no	—
57	C₂×C₅	—	5	1	no	—
58	C₂×C₅	—	20	1	no	—
59	C₂×C₅	—	25	2	no	—
60	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
61	D₅	—	5	2	no	—
62	D₅	—	25	2	no	—
63	C₂×C₄	—	25	2	no	—
64	C₂×C₄	—	25	1	no	—
65	C₅	—	5	1	no	—
66	C₅	—	5	1	no	—
67	C₅	—	20	1	no	—
68	C₅	C₄×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₂²	—	25	1	no	—
70	C₄	—	25	4	no	—
71	C₄	—	25	1	no	—
72	C₄	#1043⋊C₅	1	1	yes	characteristic, direct product factor
73	C₂	—	25	2	no	—
74	C₂	C₂×#1043⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#1043⋊C₅
commutator, hypocenter	C₅²	C₄²×C₅
Frattini, socle	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)
Fitting	C₄×H(3,𝔽₅)	C₄
prime radical	C₂×(C₅⋊D₅)⋊C₅	C₂²
cosocle	C₂×C₅⋊D₅	C₂²×C₅
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
4. #1043⋊C₅	C₄	direct (N × H)
5. C₄×H(3,𝔽₅)	C₄	semidirect
6. #1039⋊C₅	C₄	semidirect
7. C₄×#1043	C₅	semidirect
15. H(3,𝔽₅)	C₄²	semidirect
18. #1043	C₄×C₅	semidirect
21. C₄×C₅²	C₄×C₅	semidirect
22. C₄×C₅²	AGL(1,𝔽₅)	semidirect
23. #1039	C₄×C₅	semidirect
40. C₅²	C₄²×C₅	semidirect
41. C₅²	C₄×AGL(1,𝔽₅)	semidirect
72. C₄	#1043⋊C₅	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×#1043⋊C₅	2
C₄×(C₅⋊D₅)⋊C₅	2
C₄×#1043	5
C₄×C₅×AGL(1,𝔽₅)	5

Subgroups — C4×#1043⋊C5 #14522321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#1043⋊C₅ #14522321