Subgroups — C₂⁶×#261 #16809659

Order 3328.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×#261	C₂	1	126	yes	maximal, direct product factor
2	C₂⁶×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁶×C₁₃	C₄	1	1	yes	characteristic, complemented
4	C₂⁵×D₁₃	C₄	1	63	yes	complemented
5	C₂⁵×D₁₃	C₂²	1	63	yes	—
6	C₂⁴×#261	C₂²	1	2604	yes	direct product factor
7	C₂⁵×C₁₃	C₂×C₄	1	63	yes	complemented
8	C₂⁴×D₁₃	C₂×C₄	1	1953	yes	complemented
9	C₂⁴×D₁₃	C₂³	1	651	yes	—
10	C₂³×#261	C₂³	1	11160	yes	direct product factor
11	C₂⁶×C₄	—	13	1	no	maximal, Sylow
12	C₂⁴×C₁₃	C₂²×C₄	1	651	yes	complemented
13	C₂³×D₁₃	C₂²×C₄	1	9765	yes	complemented
14	C₂³×D₁₃	C₂⁴	1	1395	yes	—
15	C₂²×#261	C₂⁴	1	10416	yes	direct product factor
16	C₂⁷	—	13	1	no	—
17	C₂⁵×C₄	—	13	126	no	—
18	C₂³×C₁₃	C₂³×C₄	1	1395	yes	complemented
19	C₂²×D₁₃	C₂³×C₄	1	9765	yes	complemented
20	C₂²×D₁₃	C₂⁵	1	651	yes	—
21	C₂×#261	C₂⁵	1	2016	yes	direct product factor
22	C₂⁶	—	13	63	no	—
23	C₂⁶	—	13	63	no	—
24	C₂⁶	#261	1	1	yes	characteristic, direct product factor
25	C₂⁴×C₄	—	13	2604	no	—
26	C₂²×C₁₃	C₂⁴×C₄	1	651	yes	complemented
27	C₂×D₁₃	C₂⁴×C₄	1	1953	yes	complemented
28	C₂×D₁₃	C₂⁶	1	63	yes	—
29	#261	C₂⁶	1	64	yes	direct product factor
30	C₂⁵	—	13	651	no	—
31	C₂⁵	—	13	1953	no	—
32	C₂⁵	C₂×#261	1	63	yes	direct product factor
33	C₂³×C₄	—	13	11160	no	—
34	C₂×C₁₃	C₂⁵×C₄	1	63	yes	complemented
35	D₁₃	C₂⁵×C₄	1	63	yes	complemented
36	D₁₃	C₂⁷	1	1	yes	characteristic
37	C₂⁴	—	13	1395	no	—
38	C₂⁴	—	13	9765	no	—
39	C₂⁴	C₂²×#261	1	651	yes	direct product factor
40	C₂²×C₄	—	13	10416	no	—
41	C₁₃	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
42	C₂³	—	13	651	no	—
43	C₂³	—	13	9765	no	—
44	C₂³	C₂³×#261	1	1395	yes	direct product factor
45	C₂×C₄	—	13	2016	no	—
46	C₂²	—	13	1953	no	—
47	C₂²	—	13	63	no	—
48	C₂²	C₂⁴×#261	1	651	yes	direct product factor
49	C₄	—	13	64	no	—
50	C₂	—	13	1	no	—
51	C₂	—	13	63	no	—
52	C₂	C₂⁵×#261	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	#261
commutator, hypocenter	C₁₃	C₂⁶×C₄
Frattini	C₁	G
Fitting, socle	C₂⁶×C₁₃	C₄
prime radical	C₂⁶×D₁₃	C₂
cosocle	D₁₃	C₂⁷
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁵×#261	C₂	direct (N × H)
3. C₂⁶×C₁₃	C₄	semidirect
4. C₂⁵×D₁₃	C₄	semidirect
6. C₂⁴×#261	C₂²	direct (N × H)
7. C₂⁵×C₁₃	C₂×C₄	semidirect
8. C₂⁴×D₁₃	C₂×C₄	semidirect
10. C₂³×#261	C₂³	direct (N × H)
12. C₂⁴×C₁₃	C₂²×C₄	semidirect
13. C₂³×D₁₃	C₂²×C₄	semidirect
15. C₂²×#261	C₂⁴	direct (N × H)
18. C₂³×C₁₃	C₂³×C₄	semidirect
19. C₂²×D₁₃	C₂³×C₄	semidirect
21. C₂×#261	C₂⁵	direct (N × H)
24. C₂⁶	#261	direct (N × H)
26. C₂²×C₁₃	C₂⁴×C₄	semidirect
27. C₂×D₁₃	C₂⁴×C₄	semidirect
29. #261	C₂⁶	direct (N × H)
32. C₂⁵	C₂×#261	direct (N × H)
34. C₂×C₁₃	C₂⁵×C₄	semidirect
35. D₁₃	C₂⁵×C₄	semidirect
39. C₂⁴	C₂²×#261	direct (N × H)
41. C₁₃	C₂⁶×C₄	semidirect
44. C₂³	C₂³×#261	direct (N × H)
48. C₂²	C₂⁴×#261	direct (N × H)
52. C₂	C₂⁵×#261	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×#261	2
C₂⁶×D₁₃	2
C₂⁶×C₄	13

Subgroups — C26×#261 #16809659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×#261 #16809659