Subgroups — C₂⁵×D₂₀ #13013178

Order 1280.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₅	C₂	1	2	yes	maximal, complemented
2	C₂⁵×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×D₂₀	C₂	1	124	yes	maximal, direct product factor
4	C₂⁶×C₅	C₂²	1	1	yes	characteristic
5	C₂⁵×D₅	—	2	64	no	—
6	C₂⁵×D₅	C₂²	1	124	yes	complemented
7	C₂⁴×C₄×C₅	C₂²	1	62	yes	complemented
8	C₂³×D₂₀	C₂²	1	2480	yes	direct product factor
9	C₂⁵×D₄	—	5	1	no	maximal, Sylow
10	C₂⁵×C₅	D₄	1	32	yes	complemented
11	C₂⁵×C₅	C₂³	1	31	yes	—
12	C₂⁴×D₅	—	2	1984	no	—
13	C₂⁴×D₅	C₂³	1	1240	yes	complemented
14	C₂³×C₄×C₅	C₂³	1	620	yes	complemented
15	C₂²×D₂₀	C₂³	1	9920	yes	direct product factor
16	C₂⁷	—	5	2	no	—
17	C₂⁴×D₄	—	5	124	no	—
18	C₂⁵×C₄	D₅	1	1	yes	characteristic, complemented
19	C₂⁴×C₅	C₂×D₄	1	496	yes	complemented
20	C₂⁴×C₅	C₂⁴	1	155	yes	—
21	C₂³×D₅	—	2	9920	no	—
22	C₂³×D₅	C₂⁴	1	2480	yes	complemented
23	C₂²×C₄×C₅	C₂⁴	1	1240	yes	complemented
24	C₂×D₂₀	C₂⁴	1	7936	yes	direct product factor
25	C₂⁶	—	5	124	no	—
26	C₂⁶	—	10	64	no	—
27	C₂⁶	C₂×D₅	1	1	yes	characteristic
28	C₂³×D₄	—	5	2480	no	—
29	C₂⁴×C₄	C₂×D₅	1	62	yes	complemented
30	C₂³×C₅	C₂²×D₄	1	1240	yes	complemented
31	C₂³×C₅	C₂⁵	1	155	yes	—
32	C₂²×D₅	—	2	9920	no	—
33	C₂²×D₅	C₂⁵	1	992	yes	complemented
34	C₂×C₄×C₅	C₂⁵	1	496	yes	complemented
35	D₂₀	C₂⁵	1	1024	yes	direct product factor
36	C₂⁵	—	5	1240	no	—
37	C₂⁵	—	10	1984	no	—
38	C₂⁵	D₂₀	1	32	yes	direct product factor
39	C₂⁵	C₂²×D₅	1	31	yes	—
40	C₂²×D₄	—	5	9920	no	—
41	C₂³×C₄	C₂²×D₅	1	620	yes	complemented
42	C₂²×C₅	C₂³×D₄	1	620	yes	complemented
43	C₂²×C₅	C₂⁶	1	31	yes	—
44	C₂×D₅	—	2	1984	no	—
45	C₂×D₅	C₂⁶	1	64	yes	complemented
46	C₄×C₅	C₂⁶	1	32	yes	complemented
47	C₂⁴	—	5	2480	no	—
48	C₂⁴	—	10	9920	no	—
49	C₂⁴	C₂×D₂₀	1	496	yes	direct product factor
50	C₂⁴	C₂³×D₅	1	155	yes	—
51	C₂×D₄	—	5	7936	no	—
52	C₂²×C₄	C₂³×D₅	1	1240	yes	complemented
53	C₂×C₅	C₂⁴×D₄	1	62	yes	complemented
54	C₂×C₅	C₂⁷	1	1	yes	characteristic
55	D₅	—	2	64	no	—
56	C₂³	—	5	992	no	—
57	C₂³	—	10	9920	no	—
58	C₂³	C₂²×D₂₀	1	1240	yes	direct product factor
59	C₂³	C₂⁴×D₅	1	155	yes	—
60	D₄	—	5	1024	no	—
61	C₂×C₄	C₂⁴×D₅	1	496	yes	complemented
62	C₅	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	5	64	no	—
64	C₂²	—	10	1984	no	—
65	C₂²	C₂³×D₂₀	1	620	yes	direct product factor
66	C₂²	C₂⁵×D₅	1	31	yes	—
67	C₄	C₂⁵×D₅	1	32	yes	complemented
68	C₂	—	10	64	no	—
69	C₂	C₂⁴×D₂₀	1	62	yes	direct product factor
70	C₂	C₂⁶×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁷
Frattini	C₂	C₂⁶×D₅
Fitting	C₂⁵×C₄×C₅	C₂
socle	C₂⁶×C₅	C₂²
hypercenter	C₂⁵×C₄	D₅
hypocenter	C₅	C₂⁵×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁶ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₅	C₂	semidirect
2. C₂⁵×C₄×C₅	C₂	semidirect
3. C₂⁴×D₂₀	C₂	direct (N × H)
6. C₂⁵×D₅	C₂²	semidirect
7. C₂⁴×C₄×C₅	C₂²	semidirect
8. C₂³×D₂₀	C₂²	direct (N × H)
10. C₂⁵×C₅	D₄	semidirect
13. C₂⁴×D₅	C₂³	semidirect
14. C₂³×C₄×C₅	C₂³	semidirect
15. C₂²×D₂₀	C₂³	direct (N × H)
18. C₂⁵×C₄	D₅	semidirect
19. C₂⁴×C₅	C₂×D₄	semidirect
22. C₂³×D₅	C₂⁴	semidirect
23. C₂²×C₄×C₅	C₂⁴	semidirect
24. C₂×D₂₀	C₂⁴	direct (N × H)
29. C₂⁴×C₄	C₂×D₅	semidirect
30. C₂³×C₅	C₂²×D₄	semidirect
33. C₂²×D₅	C₂⁵	semidirect
34. C₂×C₄×C₅	C₂⁵	semidirect
35. D₂₀	C₂⁵	direct (N × H)
38. C₂⁵	D₂₀	direct (N × H)
41. C₂³×C₄	C₂²×D₅	semidirect
42. C₂²×C₅	C₂³×D₄	semidirect
45. C₂×D₅	C₂⁶	semidirect
46. C₄×C₅	C₂⁶	semidirect
49. C₂⁴	C₂×D₂₀	direct (N × H)
52. C₂²×C₄	C₂³×D₅	semidirect
53. C₂×C₅	C₂⁴×D₄	semidirect
58. C₂³	C₂²×D₂₀	direct (N × H)
61. C₂×C₄	C₂⁴×D₅	semidirect
62. C₅	C₂⁵×D₄	semidirect
65. C₂²	C₂³×D₂₀	direct (N × H)
67. C₄	C₂⁵×D₅	semidirect
69. C₂	C₂⁴×D₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₅	2
C₂⁵×C₄×C₅	2
C₂⁴×D₂₀	2
C₂⁵×D₄	5

Subgroups — C25×D20 #13013178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₂₀ #13013178