Subgroups — C₂⁶×Dic₁₃ #16776794

Order 3328.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₁₃	C₂	1	126	yes	maximal, direct product factor
2	C₂⁷×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁶×C₁₃	C₄	1	64	yes	complemented
4	C₂⁶×C₁₃	C₂²	1	63	yes	—
5	C₂⁴×Dic₁₃	C₂²	1	2604	yes	direct product factor
6	C₂⁵×C₁₃	C₂×C₄	1	2016	yes	complemented
7	C₂⁵×C₁₃	C₂³	1	651	yes	—
8	C₂³×Dic₁₃	C₂³	1	11160	yes	direct product factor
9	C₂⁶×C₄	—	13	1	no	maximal, Sylow
10	C₂⁴×C₁₃	C₂²×C₄	1	10416	yes	complemented
11	C₂⁴×C₁₃	C₂⁴	1	1395	yes	—
12	C₂²×Dic₁₃	C₂⁴	1	10416	yes	direct product factor
13	C₂⁷	D₁₃	1	1	yes	characteristic
14	C₂⁵×C₄	—	13	126	no	—
15	C₂³×C₁₃	C₂³×C₄	1	11160	yes	complemented
16	C₂³×C₁₃	C₂⁵	1	651	yes	—
17	C₂×Dic₁₃	C₂⁵	1	2016	yes	direct product factor
18	C₂⁶	Dic₁₃	1	64	yes	direct product factor
19	C₂⁶	C₂×D₁₃	1	63	yes	—
20	C₂⁴×C₄	—	13	2604	no	—
21	C₂²×C₁₃	C₂⁴×C₄	1	2604	yes	complemented
22	C₂²×C₁₃	C₂⁶	1	63	yes	—
23	Dic₁₃	C₂⁶	1	64	yes	direct product factor
24	C₂⁵	C₂×Dic₁₃	1	2016	yes	direct product factor
25	C₂⁵	C₂²×D₁₃	1	651	yes	—
26	C₂³×C₄	—	13	11160	no	—
27	C₂×C₁₃	C₂⁵×C₄	1	126	yes	complemented
28	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
29	C₂⁴	C₂²×Dic₁₃	1	10416	yes	direct product factor
30	C₂⁴	C₂³×D₁₃	1	1395	yes	—
31	C₂²×C₄	—	13	10416	no	—
32	C₁₃	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂³	C₂³×Dic₁₃	1	11160	yes	direct product factor
34	C₂³	C₂⁴×D₁₃	1	651	yes	—
35	C₂×C₄	—	13	2016	no	—
36	C₂²	C₂⁴×Dic₁₃	1	2604	yes	direct product factor
37	C₂²	C₂⁵×D₁₃	1	63	yes	—
38	C₄	—	13	64	no	—
39	C₂	C₂⁵×Dic₁₃	1	126	yes	direct product factor
40	C₂	C₂⁶×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁷	D₁₃
commutator, hypocenter	C₁₃	C₂⁶×C₄
Frattini	C₂	C₂⁶×D₁₃
Fitting, socle, prime radical	C₂⁷×C₁₃	C₂
cosocle	C₂×C₁₃	C₂⁷
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Dic₁₃	C₂	direct (N × H)
3. C₂⁶×C₁₃	C₄	semidirect
5. C₂⁴×Dic₁₃	C₂²	direct (N × H)
6. C₂⁵×C₁₃	C₂×C₄	semidirect
8. C₂³×Dic₁₃	C₂³	direct (N × H)
10. C₂⁴×C₁₃	C₂²×C₄	semidirect
12. C₂²×Dic₁₃	C₂⁴	direct (N × H)
15. C₂³×C₁₃	C₂³×C₄	semidirect
17. C₂×Dic₁₃	C₂⁵	direct (N × H)
18. C₂⁶	Dic₁₃	direct (N × H)
21. C₂²×C₁₃	C₂⁴×C₄	semidirect
23. Dic₁₃	C₂⁶	direct (N × H)
24. C₂⁵	C₂×Dic₁₃	direct (N × H)
27. C₂×C₁₃	C₂⁵×C₄	semidirect
29. C₂⁴	C₂²×Dic₁₃	direct (N × H)
32. C₁₃	C₂⁶×C₄	semidirect
33. C₂³	C₂³×Dic₁₃	direct (N × H)
36. C₂²	C₂⁴×Dic₁₃	direct (N × H)
39. C₂	C₂⁵×Dic₁₃	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×Dic₁₃	2
C₂⁷×C₁₃	2
C₂⁶×C₄	13

Subgroups — C26×Dic13 #16776794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×Dic₁₃ #16776794