Subgroups — C₂³×C₅×C₅⋊D₅ #14522998

Order 2000.

1456 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅³	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×C₅⋊D₅	C₂	1	14	yes	maximal, direct product factor
3	C₂²×C₅³	C₂²	1	7	yes	complemented
4	C₂×C₅×C₅⋊D₅	C₂²	1	28	yes	direct product factor
5	C₂³×C₅⋊D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂³×C₅×D₅	—	5	6	no	maximal
7	C₂×C₅³	C₂³	1	7	yes	complemented
8	C₅×C₅⋊D₅	C₂³	1	8	yes	direct product factor
9	C₂³×C₅²	—	2	12	no	—
10	C₂³×C₅²	D₅	1	6	yes	complemented
11	C₂³×C₅²	C₂×C₅	1	1	yes	characteristic, complemented
12	C₂²×C₅⋊D₅	C₂×C₅	1	14	yes	direct product factor
13	C₂²×C₅×D₅	—	5	84	no	—
14	C₅³	C₂⁴	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅²	—	2	84	no	—
16	C₂²×C₅²	C₂×D₅	1	42	yes	complemented
17	C₂²×C₅²	C₂²×C₅	1	7	yes	complemented
18	C₂×C₅⋊D₅	C₂²×C₅	1	28	yes	direct product factor
19	C₂×C₅×D₅	—	5	168	no	—
20	C₂⁴×C₅	—	25	1	no	—
21	C₂³×D₅	—	5	6	no	—
22	C₂×C₅²	—	2	84	no	—
23	C₂×C₅²	C₂²×D₅	1	42	yes	complemented
24	C₂×C₅²	C₂³×C₅	1	7	yes	complemented
25	C₅⋊D₅	C₂³×C₅	1	8	yes	direct product factor
26	C₅×D₅	—	5	48	no	—
27	C₂³×C₅	—	2	12	no	—
28	C₂³×C₅	—	25	14	no	—
29	C₂³×C₅	C₅×D₅	1	6	yes	complemented
30	C₂³×C₅	C₅⋊D₅	1	1	yes	characteristic, direct product factor
31	C₂²×D₅	—	5	84	no	—
32	C₅²	—	2	12	no	—
33	C₅²	C₂³×D₅	1	6	yes	complemented
34	C₅²	C₂⁴×C₅	1	1	yes	characteristic, complemented
35	C₂²×C₅	—	2	84	no	—
36	C₂²×C₅	—	25	28	no	—
37	C₂²×C₅	C₂×C₅×D₅	1	42	yes	complemented
38	C₂²×C₅	C₂×C₅⋊D₅	1	7	yes	direct product factor
39	C₂×D₅	—	5	168	no	—
40	C₂⁴	—	25	1	no	Sylow
41	C₂×C₅	—	2	84	no	—
42	C₂×C₅	—	25	8	no	—
43	C₂×C₅	C₂²×C₅×D₅	1	42	yes	complemented
44	C₂×C₅	C₂²×C₅⋊D₅	1	7	yes	direct product factor
45	D₅	—	5	48	no	—
46	C₂³	—	25	14	no	—
47	C₂³	C₅×C₅⋊D₅	1	1	yes	characteristic, direct product factor
48	C₅	—	2	12	no	—
49	C₅	C₂³×C₅×D₅	1	6	yes	complemented
50	C₅	C₂³×C₅⋊D₅	1	1	yes	characteristic, direct product factor
51	C₂²	—	25	28	no	—
52	C₂²	C₂×C₅×C₅⋊D₅	1	7	yes	direct product factor
53	C₂	—	25	8	no	—
54	C₂	C₂²×C₅×C₅⋊D₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₅	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂⁴×C₅
Frattini	C₁	G
Fitting, socle	C₂³×C₅³	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅³	C₂	semidirect
2. C₂²×C₅×C₅⋊D₅	C₂	direct (N × H)
3. C₂²×C₅³	C₂²	semidirect
4. C₂×C₅×C₅⋊D₅	C₂²	direct (N × H)
5. C₂³×C₅⋊D₅	C₅	direct (N × H)
7. C₂×C₅³	C₂³	semidirect
8. C₅×C₅⋊D₅	C₂³	direct (N × H)
10. C₂³×C₅²	D₅	semidirect
11. C₂³×C₅²	C₂×C₅	semidirect
12. C₂²×C₅⋊D₅	C₂×C₅	direct (N × H)
14. C₅³	C₂⁴	semidirect
16. C₂²×C₅²	C₂×D₅	semidirect
17. C₂²×C₅²	C₂²×C₅	semidirect
18. C₂×C₅⋊D₅	C₂²×C₅	direct (N × H)
23. C₂×C₅²	C₂²×D₅	semidirect
24. C₂×C₅²	C₂³×C₅	semidirect
25. C₅⋊D₅	C₂³×C₅	direct (N × H)
29. C₂³×C₅	C₅×D₅	semidirect
30. C₂³×C₅	C₅⋊D₅	direct (N × H)
33. C₅²	C₂³×D₅	semidirect
34. C₅²	C₂⁴×C₅	semidirect
37. C₂²×C₅	C₂×C₅×D₅	semidirect
38. C₂²×C₅	C₂×C₅⋊D₅	direct (N × H)
43. C₂×C₅	C₂²×C₅×D₅	semidirect
44. C₂×C₅	C₂²×C₅⋊D₅	direct (N × H)
47. C₂³	C₅×C₅⋊D₅	direct (N × H)
49. C₅	C₂³×C₅×D₅	semidirect
50. C₅	C₂³×C₅⋊D₅	direct (N × H)
52. C₂²	C₂×C₅×C₅⋊D₅	direct (N × H)
54. C₂	C₂²×C₅×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
C₂³×C₅³	2
C₂²×C₅×C₅⋊D₅	2
C₂³×C₅⋊D₅	5
C₂³×C₅×D₅	5

Subgroups — C23×C5×C5⋊D5 #14522998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×C₅⋊D₅ #14522998