Subgroups — C₂⁵×Dic₁₀ #13013180

Order 1280.

63326 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×Dic₅	C₂	1	2	yes	maximal
3	C₂⁴×Dic₁₀	C₂	1	124	yes	maximal, direct product factor
4	C₂⁶×C₅	C₂²	1	1	yes	characteristic
5	C₂⁴×C₄×C₅	C₂²	1	62	yes	—
6	C₂⁴×Dic₅	C₂²	1	124	yes	—
7	C₂³×Dic₁₀	C₂²	1	2480	yes	direct product factor
8	C₂⁵×Q₈	—	5	1	no	maximal, Sylow
9	C₂⁵×C₅	Q₈	1	32	yes	complemented
10	C₂⁵×C₅	C₂³	1	31	yes	—
11	C₂³×C₄×C₅	C₂³	1	620	yes	—
12	C₂³×Dic₅	C₂³	1	1240	yes	—
13	C₂²×Dic₁₀	C₂³	1	9920	yes	direct product factor
14	C₂⁴×Q₈	—	5	124	no	—
15	C₂⁵×C₄	—	5	2	no	—
16	C₂⁵×C₄	D₅	1	1	yes	characteristic
17	C₂⁴×C₅	C₂×Q₈	1	496	yes	complemented
18	C₂⁴×C₅	C₂⁴	1	155	yes	—
19	C₂²×C₄×C₅	C₂⁴	1	1240	yes	—
20	C₂²×Dic₅	C₂⁴	1	2480	yes	—
21	C₂×Dic₁₀	C₂⁴	1	7936	yes	direct product factor
22	C₂⁶	C₂×D₅	1	1	yes	characteristic
23	C₂³×Q₈	—	5	2480	no	—
24	C₂⁴×C₄	—	5	124	no	—
25	C₂⁴×C₄	C₂×D₅	1	62	yes	—
26	C₂³×C₅	C₂²×Q₈	1	1240	yes	complemented
27	C₂³×C₅	C₂⁵	1	155	yes	—
28	C₂×C₄×C₅	C₂⁵	1	496	yes	—
29	C₂×Dic₅	C₂⁵	1	992	yes	—
30	Dic₁₀	C₂⁵	1	1024	yes	direct product factor
31	C₂⁵	Dic₁₀	1	32	yes	direct product factor
32	C₂⁵	C₂²×D₅	1	31	yes	—
33	C₂²×Q₈	—	5	9920	no	—
34	C₂³×C₄	—	5	1240	no	—
35	C₂³×C₄	C₂²×D₅	1	620	yes	—
36	C₂²×C₅	C₂³×Q₈	1	620	yes	complemented
37	C₂²×C₅	C₂⁶	1	31	yes	—
38	C₄×C₅	C₂⁶	1	32	yes	—
39	Dic₅	C₂⁶	1	64	yes	—
40	C₂⁴	C₂×Dic₁₀	1	496	yes	direct product factor
41	C₂⁴	C₂³×D₅	1	155	yes	—
42	C₂×Q₈	—	5	7936	no	—
43	C₂²×C₄	—	5	2480	no	—
44	C₂²×C₄	C₂³×D₅	1	1240	yes	—
45	C₂×C₅	C₂⁴×Q₈	1	62	yes	complemented
46	C₂×C₅	C₂⁷	1	1	yes	characteristic
47	C₂³	C₂²×Dic₁₀	1	1240	yes	direct product factor
48	C₂³	C₂⁴×D₅	1	155	yes	—
49	Q₈	—	5	1024	no	—
50	C₂×C₄	—	5	992	no	—
51	C₂×C₄	C₂⁴×D₅	1	496	yes	—
52	C₅	C₂⁵×Q₈	1	1	yes	characteristic, complemented, Sylow
53	C₂²	C₂³×Dic₁₀	1	620	yes	direct product factor
54	C₂²	C₂⁵×D₅	1	31	yes	—
55	C₄	—	5	64	no	—
56	C₄	C₂⁵×D₅	1	32	yes	—
57	C₂	C₂⁴×Dic₁₀	1	62	yes	direct product factor
58	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, prime radical	C₂⁶×C₅	C₂²
hypercenter	C₂⁵×C₄	D₅
hypocenter	C₅	C₂⁵×Q₈
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
3. C₂⁴×Dic₁₀	C₂	direct (N × H)
7. C₂³×Dic₁₀	C₂²	direct (N × H)
9. C₂⁵×C₅	Q₈	semidirect
13. C₂²×Dic₁₀	C₂³	direct (N × H)
17. C₂⁴×C₅	C₂×Q₈	semidirect
21. C₂×Dic₁₀	C₂⁴	direct (N × H)
26. C₂³×C₅	C₂²×Q₈	semidirect
30. Dic₁₀	C₂⁵	direct (N × H)
31. C₂⁵	Dic₁₀	direct (N × H)
36. C₂²×C₅	C₂³×Q₈	semidirect
40. C₂⁴	C₂×Dic₁₀	direct (N × H)
45. C₂×C₅	C₂⁴×Q₈	semidirect
47. C₂³	C₂²×Dic₁₀	direct (N × H)
52. C₅	C₂⁵×Q₈	semidirect
53. C₂²	C₂³×Dic₁₀	direct (N × H)
57. C₂	C₂⁴×Dic₁₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₅	2
C₂⁵×Dic₅	2
C₂⁴×Dic₁₀	2
C₂⁵×Q₈	5

Subgroups — C25×Dic10 #13013180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×Dic₁₀ #13013180