Subgroups — C₂⁶×C₅⋊D₅ #72258458

Order 3200.

233696 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁵×C₅⋊D₅	C₂	1	126	yes	maximal, direct product factor
3	C₂⁵×C₅²	C₂²	1	63	yes	complemented
4	C₂⁴×C₅⋊D₅	C₂²	1	2604	yes	direct product factor
5	C₂⁶×D₅	—	5	6	no	maximal
6	C₂⁴×C₅²	C₂³	1	651	yes	complemented
7	C₂³×C₅⋊D₅	C₂³	1	11160	yes	direct product factor
8	C₂⁶×C₅	D₅	1	6	yes	complemented
9	C₂⁵×D₅	—	5	756	no	—
10	C₂³×C₅²	C₂⁴	1	1395	yes	complemented
11	C₂²×C₅⋊D₅	C₂⁴	1	10416	yes	direct product factor
12	C₂⁵×C₅	C₂×D₅	1	378	yes	complemented
13	C₂⁴×D₅	—	5	15624	no	—
14	C₂⁷	—	25	1	no	Sylow
15	C₂²×C₅²	C₂⁵	1	651	yes	complemented
16	C₂×C₅⋊D₅	C₂⁵	1	2016	yes	direct product factor
17	C₂⁴×C₅	C₂²×D₅	1	3906	yes	complemented
18	C₂³×D₅	—	5	66960	no	—
19	C₂⁶	—	25	126	no	—
20	C₂⁶	C₅⋊D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₅²	C₂⁶	1	63	yes	complemented
22	C₅⋊D₅	C₂⁶	1	64	yes	direct product factor
23	C₂³×C₅	C₂³×D₅	1	8370	yes	complemented
24	C₂²×D₅	—	5	62496	no	—
25	C₂⁵	—	25	2604	no	—
26	C₂⁵	C₂×C₅⋊D₅	1	63	yes	direct product factor
27	C₅²	C₂⁷	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₅	C₂⁴×D₅	1	3906	yes	complemented
29	C₂×D₅	—	5	12096	no	—
30	C₂⁴	—	25	11160	no	—
31	C₂⁴	C₂²×C₅⋊D₅	1	651	yes	direct product factor
32	C₂×C₅	C₂⁵×D₅	1	378	yes	complemented
33	D₅	—	5	384	no	—
34	C₂³	—	25	10416	no	—
35	C₂³	C₂³×C₅⋊D₅	1	1395	yes	direct product factor
36	C₅	C₂⁶×D₅	1	6	yes	complemented
37	C₂²	—	25	2016	no	—
38	C₂²	C₂⁴×C₅⋊D₅	1	651	yes	direct product factor
39	C₂	—	25	64	no	—
40	C₂	C₂⁵×C₅⋊D₅	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁶×C₅²	C₂	semidirect
2. C₂⁵×C₅⋊D₅	C₂	direct (N × H)
3. C₂⁵×C₅²	C₂²	semidirect
4. C₂⁴×C₅⋊D₅	C₂²	direct (N × H)
6. C₂⁴×C₅²	C₂³	semidirect
7. C₂³×C₅⋊D₅	C₂³	direct (N × H)
8. C₂⁶×C₅	D₅	semidirect
10. C₂³×C₅²	C₂⁴	semidirect
11. C₂²×C₅⋊D₅	C₂⁴	direct (N × H)
12. C₂⁵×C₅	C₂×D₅	semidirect
15. C₂²×C₅²	C₂⁵	semidirect
16. C₂×C₅⋊D₅	C₂⁵	direct (N × H)
17. C₂⁴×C₅	C₂²×D₅	semidirect
20. C₂⁶	C₅⋊D₅	direct (N × H)
21. C₂×C₅²	C₂⁶	semidirect
22. C₅⋊D₅	C₂⁶	direct (N × H)
23. C₂³×C₅	C₂³×D₅	semidirect
26. C₂⁵	C₂×C₅⋊D₅	direct (N × H)
27. C₅²	C₂⁷	semidirect
28. C₂²×C₅	C₂⁴×D₅	semidirect
31. C₂⁴	C₂²×C₅⋊D₅	direct (N × H)
32. C₂×C₅	C₂⁵×D₅	semidirect
35. C₂³	C₂³×C₅⋊D₅	direct (N × H)
36. C₅	C₂⁶×D₅	semidirect
38. C₂²	C₂⁴×C₅⋊D₅	direct (N × H)
40. C₂	C₂⁵×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
C₂⁶×C₅²	2
C₂⁵×C₅⋊D₅	2
C₂⁶×D₅	5

Subgroups — C26×C5⋊D5 #72258458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₅⋊D₅ #72258458