Subgroups — C₂⁶×C₄×C₆₁ #29566527

Order 15616.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₄×C₆₁	C₂	1	126	yes	maximal, direct product factor
3	C₂⁶×C₆₁	C₄	1	64	yes	direct product factor
4	C₂⁶×C₆₁	C₂²	1	63	yes	—
5	C₂⁴×C₄×C₆₁	C₂²	1	2604	yes	direct product factor
6	C₂⁵×C₆₁	C₂×C₄	1	2016	yes	direct product factor
7	C₂⁵×C₆₁	C₂³	1	651	yes	—
8	C₂³×C₄×C₆₁	C₂³	1	11160	yes	direct product factor
9	C₂⁴×C₆₁	C₂²×C₄	1	10416	yes	direct product factor
10	C₂⁴×C₆₁	C₂⁴	1	1395	yes	—
11	C₂²×C₄×C₆₁	C₂⁴	1	10416	yes	direct product factor
12	C₂³×C₆₁	C₂³×C₄	1	11160	yes	direct product factor
13	C₂³×C₆₁	C₂⁵	1	651	yes	—
14	C₂×C₄×C₆₁	C₂⁵	1	2016	yes	direct product factor
15	C₂⁶×C₄	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂²×C₆₁	C₂⁴×C₄	1	2604	yes	direct product factor
17	C₂²×C₆₁	C₂⁶	1	63	yes	—
18	C₄×C₆₁	C₂⁶	1	64	yes	direct product factor
19	C₂⁷	C₂×C₆₁	1	1	yes	characteristic
20	C₂⁵×C₄	C₂×C₆₁	1	126	yes	direct product factor
21	C₂×C₆₁	C₂⁵×C₄	1	126	yes	direct product factor
22	C₂×C₆₁	C₂⁷	1	1	yes	characteristic
23	C₂⁶	C₄×C₆₁	1	64	yes	direct product factor
24	C₂⁶	C₂²×C₆₁	1	63	yes	—
25	C₂⁴×C₄	C₂²×C₆₁	1	2604	yes	direct product factor
26	C₆₁	C₂⁶×C₄	1	1	yes	characteristic, direct product factor, Sylow
27	C₂⁵	C₂×C₄×C₆₁	1	2016	yes	direct product factor
28	C₂⁵	C₂³×C₆₁	1	651	yes	—
29	C₂³×C₄	C₂³×C₆₁	1	11160	yes	direct product factor
30	C₂⁴	C₂²×C₄×C₆₁	1	10416	yes	direct product factor
31	C₂⁴	C₂⁴×C₆₁	1	1395	yes	—
32	C₂²×C₄	C₂⁴×C₆₁	1	10416	yes	direct product factor
33	C₂³	C₂³×C₄×C₆₁	1	11160	yes	direct product factor
34	C₂³	C₂⁵×C₆₁	1	651	yes	—
35	C₂×C₄	C₂⁵×C₆₁	1	2016	yes	direct product factor
36	C₂²	C₂⁴×C₄×C₆₁	1	2604	yes	direct product factor
37	C₂²	C₂⁶×C₆₁	1	63	yes	—
38	C₄	C₂⁶×C₆₁	1	64	yes	direct product factor
39	C₂	C₂⁵×C₄×C₆₁	1	126	yes	direct product factor
40	C₂	C₂⁷×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁷×C₆₁
socle, prime radical	C₂⁷×C₆₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₄×C₆₁	C₂	direct (N × H)
3. C₂⁶×C₆₁	C₄	direct (N × H)
5. C₂⁴×C₄×C₆₁	C₂²	direct (N × H)
6. C₂⁵×C₆₁	C₂×C₄	direct (N × H)
8. C₂³×C₄×C₆₁	C₂³	direct (N × H)
9. C₂⁴×C₆₁	C₂²×C₄	direct (N × H)
11. C₂²×C₄×C₆₁	C₂⁴	direct (N × H)
12. C₂³×C₆₁	C₂³×C₄	direct (N × H)
14. C₂×C₄×C₆₁	C₂⁵	direct (N × H)
15. C₂⁶×C₄	C₆₁	direct (N × H)
16. C₂²×C₆₁	C₂⁴×C₄	direct (N × H)
18. C₄×C₆₁	C₂⁶	direct (N × H)
20. C₂⁵×C₄	C₂×C₆₁	direct (N × H)
21. C₂×C₆₁	C₂⁵×C₄	direct (N × H)
23. C₂⁶	C₄×C₆₁	direct (N × H)
25. C₂⁴×C₄	C₂²×C₆₁	direct (N × H)
26. C₆₁	C₂⁶×C₄	direct (N × H)
27. C₂⁵	C₂×C₄×C₆₁	direct (N × H)
29. C₂³×C₄	C₂³×C₆₁	direct (N × H)
30. C₂⁴	C₂²×C₄×C₆₁	direct (N × H)
32. C₂²×C₄	C₂⁴×C₆₁	direct (N × H)
33. C₂³	C₂³×C₄×C₆₁	direct (N × H)
35. C₂×C₄	C₂⁵×C₆₁	direct (N × H)
36. C₂²	C₂⁴×C₄×C₆₁	direct (N × H)
38. C₄	C₂⁶×C₆₁	direct (N × H)
39. C₂	C₂⁵×C₄×C₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁷×C₆₁	2
C₂⁵×C₄×C₆₁	2
C₂⁶×C₄	61

Subgroups — C26×C4×C61 #29566527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₄×C₆₁ #29566527