Subgroups — C₂⁵×Dic₂₅₁ #44565155

Order 32128.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₂₅₁	C₂	1	62	yes	maximal, direct product factor
2	C₂⁶×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂³×Dic₂₅₁	C₂²	1	620	yes	direct product factor
4	C₂⁵×C₂₅₁	C₄	1	32	yes	complemented
5	C₂⁵×C₂₅₁	C₂²	1	31	yes	—
6	C₂²×Dic₂₅₁	C₂³	1	1240	yes	direct product factor
7	C₂⁴×C₂₅₁	C₂×C₄	1	496	yes	complemented
8	C₂⁴×C₂₅₁	C₂³	1	155	yes	—
9	C₂×Dic₂₅₁	C₂⁴	1	496	yes	direct product factor
10	C₂³×C₂₅₁	C₂²×C₄	1	1240	yes	complemented
11	C₂³×C₂₅₁	C₂⁴	1	155	yes	—
12	C₂²×C₂₅₁	C₂³×C₄	1	620	yes	complemented
13	C₂²×C₂₅₁	C₂⁵	1	31	yes	—
14	Dic₂₅₁	C₂⁵	1	32	yes	direct product factor
15	C₂×C₂₅₁	C₂⁴×C₄	1	62	yes	complemented
16	C₂×C₂₅₁	C₂⁶	1	1	yes	characteristic
17	C₂₅₁	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂⁵×C₄	—	251	1	no	maximal, Sylow
19	C₂⁶	D₂₅₁	1	1	yes	characteristic
20	C₂⁴×C₄	—	251	62	no	—
21	C₂⁵	Dic₂₅₁	1	32	yes	direct product factor
22	C₂⁵	C₂×D₂₅₁	1	31	yes	—
23	C₂³×C₄	—	251	620	no	—
24	C₂⁴	C₂×Dic₂₅₁	1	496	yes	direct product factor
25	C₂⁴	C₂²×D₂₅₁	1	155	yes	—
26	C₂²×C₄	—	251	1240	no	—
27	C₂³	C₂²×Dic₂₅₁	1	1240	yes	direct product factor
28	C₂³	C₂³×D₂₅₁	1	155	yes	—
29	C₂×C₄	—	251	496	no	—
30	C₂²	C₂³×Dic₂₅₁	1	620	yes	direct product factor
31	C₂²	C₂⁴×D₂₅₁	1	31	yes	—
32	C₄	—	251	32	no	—
33	C₂	C₂⁴×Dic₂₅₁	1	62	yes	direct product factor
34	C₂	C₂⁵×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	D₂₅₁
commutator, hypocenter	C₂₅₁	C₂⁵×C₄
Frattini	C₂	C₂⁵×D₂₅₁
Fitting, socle, prime radical	C₂⁶×C₂₅₁	C₂
cosocle	C₂×C₂₅₁	C₂⁶
LCS	G ▷ C₂₅₁
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Dic₂₅₁	C₂	direct (N × H)
3. C₂³×Dic₂₅₁	C₂²	direct (N × H)
4. C₂⁵×C₂₅₁	C₄	semidirect
6. C₂²×Dic₂₅₁	C₂³	direct (N × H)
7. C₂⁴×C₂₅₁	C₂×C₄	semidirect
9. C₂×Dic₂₅₁	C₂⁴	direct (N × H)
10. C₂³×C₂₅₁	C₂²×C₄	semidirect
12. C₂²×C₂₅₁	C₂³×C₄	semidirect
14. Dic₂₅₁	C₂⁵	direct (N × H)
15. C₂×C₂₅₁	C₂⁴×C₄	semidirect
17. C₂₅₁	C₂⁵×C₄	semidirect
21. C₂⁵	Dic₂₅₁	direct (N × H)
24. C₂⁴	C₂×Dic₂₅₁	direct (N × H)
27. C₂³	C₂²×Dic₂₅₁	direct (N × H)
30. C₂²	C₂³×Dic₂₅₁	direct (N × H)
33. C₂	C₂⁴×Dic₂₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₂₅₁	2
C₂⁶×C₂₅₁	2
C₂⁵×C₄	251

Subgroups — C25×Dic251 #44565155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×Dic₂₅₁ #44565155