Subgroups — C₂×C₅×C₄⋊(C₅⋊D₅) #14522911

Order 2000.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₅⋊D₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅³	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄⋊(C₅⋊D₅)	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅³	C₂²	1	1	yes	characteristic
5	C₂×C₅×C₅⋊D₅	—	2	4	no	—
6	C₂×C₅×C₅⋊D₅	C₂²	1	4	yes	complemented
7	C₄×C₅³	C₂²	1	2	yes	complemented
8	C₂×C₄⋊(C₅⋊D₅)	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅×D₂₀	—	5	6	no	maximal
10	C₂×C₅³	D₄	1	2	yes	complemented
11	C₂×C₅³	C₂³	1	1	yes	characteristic
12	C₅×C₅⋊D₅	—	2	4	no	—
13	C₂²×C₅⋊D₅	C₂×C₅	1	2	yes	complemented
14	C₂²×C₅×D₅	—	5	12	no	—
15	C₂×C₄×C₅²	—	2	12	no	—
16	C₂×C₄×C₅²	D₅	1	6	yes	complemented
17	C₂×C₄×C₅²	C₂×C₅	1	1	yes	characteristic, complemented
18	C₄⋊(C₅⋊D₅)	C₂×C₅	1	4	yes	direct product factor
19	C₅×D₂₀	—	5	24	no	—
20	C₅³	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅²	—	2	12	no	—
22	C₂²×C₅²	C₂×D₅	1	6	yes	—
23	C₂²×C₅²	C₂²×C₅	1	1	yes	characteristic
24	C₂×C₅⋊D₅	—	2	4	no	—
25	C₂×C₅⋊D₅	C₂²×C₅	1	4	yes	complemented
26	C₂×C₅×D₅	—	5	24	no	—
27	C₂×C₅×D₅	—	10	24	no	—
28	C₄×C₅²	—	2	24	no	—
29	C₄×C₅²	C₂×D₅	1	12	yes	complemented
30	C₄×C₅²	C₂²×C₅	1	2	yes	complemented
31	C₂×C₅×D₄	—	25	1	no	—
32	C₂×D₂₀	—	5	6	no	—
33	C₂×C₅²	—	2	24	no	—
34	C₂×C₅²	—	2	12	no	—
35	C₂×C₅²	D₂₀	1	12	yes	complemented
36	C₂×C₅²	C₅×D₄	1	2	yes	complemented
37	C₂×C₅²	C₂²×D₅	1	6	yes	—
38	C₂×C₅²	C₂³×C₅	1	1	yes	characteristic
39	C₅⋊D₅	—	2	4	no	—
40	C₅×D₅	—	10	24	no	—
41	C₂³×C₅	—	25	2	no	—
42	C₂²×D₅	—	5	12	no	—
43	C₅×D₄	—	25	4	no	—
44	C₂×C₄×C₅	—	2	12	no	—
45	C₂×C₄×C₅	C₅×D₅	1	6	yes	complemented
46	C₂×C₄×C₅	C₅⋊D₅	1	1	yes	characteristic, complemented
47	D₂₀	—	5	24	no	—
48	C₅²	—	2	12	no	—
49	C₅²	C₂×D₂₀	1	6	yes	complemented
50	C₅²	C₂×C₅×D₄	1	1	yes	characteristic, complemented
51	C₂²×C₅	—	2	12	no	—
52	C₂²×C₅	—	25	4	no	—
53	C₂²×C₅	—	50	4	no	—
54	C₂²×C₅	C₂×C₅×D₅	1	6	yes	—
55	C₂²×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
56	C₂×D₅	—	5	24	no	—
57	C₂×D₅	—	10	24	no	—
58	C₄×C₅	—	2	24	no	—
59	C₄×C₅	C₂×C₅×D₅	1	12	yes	complemented
60	C₄×C₅	C₂×C₅⋊D₅	1	2	yes	complemented
61	C₂×D₄	—	25	1	no	Sylow
62	C₂×C₅	—	2	24	no	—
63	C₂×C₅	—	2	12	no	—
64	C₂×C₅	—	50	4	no	—
65	C₂×C₅	C₅×D₂₀	1	12	yes	complemented
66	C₂×C₅	C₄⋊(C₅⋊D₅)	1	2	yes	direct product factor
67	C₂×C₅	C₂²×C₅×D₅	1	6	yes	—
68	C₂×C₅	C₂²×C₅⋊D₅	1	1	yes	characteristic
69	D₅	—	10	24	no	—
70	C₂³	—	25	2	no	—
71	D₄	—	25	4	no	—
72	C₂×C₄	C₅×C₅⋊D₅	1	1	yes	characteristic, complemented
73	C₅	—	2	12	no	—
74	C₅	C₂×C₅×D₂₀	1	6	yes	complemented
75	C₅	C₂×C₄⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
76	C₂²	—	25	4	no	—
77	C₂²	—	50	4	no	—
78	C₂²	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
79	C₄	C₂×C₅×C₅⋊D₅	1	2	yes	complemented
80	C₂	—	50	4	no	—
81	C₂	C₅×C₄⋊(C₅⋊D₅)	1	2	yes	direct product factor
82	C₂	C₂²×C₅×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×C₅⋊D₅
commutator, cosocle	C₂×C₅²	C₂³×C₅
Frattini	C₂	C₂²×C₅×C₅⋊D₅
Fitting	C₂×C₄×C₅³	C₂
socle	C₂²×C₅³	C₂²
hypercenter	C₂×C₄×C₅	C₅⋊D₅
hypocenter	C₅²	C₂×C₅×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₅⋊D₅	C₂	semidirect
2. C₂×C₄×C₅³	C₂	semidirect
3. C₅×C₄⋊(C₅⋊D₅)	C₂	direct (N × H)
6. C₂×C₅×C₅⋊D₅	C₂²	semidirect
7. C₄×C₅³	C₂²	semidirect
8. C₂×C₄⋊(C₅⋊D₅)	C₅	direct (N × H)
10. C₂×C₅³	D₄	semidirect
13. C₂²×C₅⋊D₅	C₂×C₅	semidirect
16. C₂×C₄×C₅²	D₅	semidirect
17. C₂×C₄×C₅²	C₂×C₅	semidirect
18. C₄⋊(C₅⋊D₅)	C₂×C₅	direct (N × H)
20. C₅³	C₂×D₄	semidirect
25. C₂×C₅⋊D₅	C₂²×C₅	semidirect
29. C₄×C₅²	C₂×D₅	semidirect
30. C₄×C₅²	C₂²×C₅	semidirect
35. C₂×C₅²	D₂₀	semidirect
36. C₂×C₅²	C₅×D₄	semidirect
45. C₂×C₄×C₅	C₅×D₅	semidirect
46. C₂×C₄×C₅	C₅⋊D₅	semidirect
49. C₅²	C₂×D₂₀	semidirect
50. C₅²	C₂×C₅×D₄	semidirect
59. C₄×C₅	C₂×C₅×D₅	semidirect
60. C₄×C₅	C₂×C₅⋊D₅	semidirect
65. C₂×C₅	C₅×D₂₀	semidirect
66. C₂×C₅	C₄⋊(C₅⋊D₅)	direct (N × H)
72. C₂×C₄	C₅×C₅⋊D₅	semidirect
74. C₅	C₂×C₅×D₂₀	semidirect
75. C₅	C₂×C₄⋊(C₅⋊D₅)	direct (N × H)
79. C₄	C₂×C₅×C₅⋊D₅	semidirect
81. C₂	C₅×C₄⋊(C₅⋊D₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₅⋊D₅	2
C₂×C₄×C₅³	2
C₅×C₄⋊(C₅⋊D₅)	2
C₂×C₄⋊(C₅⋊D₅)	5
C₂×C₅×D₂₀	5

Subgroups — C2×C5×C4⋊(C5⋊D5) #14522911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₄⋊(C₅⋊D₅) #14522911