Subgroups — C₂⁵×D₅₂ #16776797

Order 3328.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂⁴×D₅₂	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
5	C₂⁵×D₁₃	—	2	64	no	—
6	C₂⁵×D₁₃	C₂²	1	124	yes	complemented
7	C₂⁴×C₄×C₁₃	C₂²	1	62	yes	complemented
8	C₂³×D₅₂	C₂²	1	2480	yes	direct product factor
9	C₂⁵×C₁₃	D₄	1	32	yes	complemented
10	C₂⁵×C₁₃	C₂³	1	31	yes	—
11	C₂⁴×D₁₃	—	2	1984	no	—
12	C₂⁴×D₁₃	C₂³	1	1240	yes	complemented
13	C₂³×C₄×C₁₃	C₂³	1	620	yes	complemented
14	C₂²×D₅₂	C₂³	1	9920	yes	direct product factor
15	C₂⁵×D₄	—	13	1	no	maximal, Sylow
16	C₂⁴×C₁₃	C₂×D₄	1	496	yes	complemented
17	C₂⁴×C₁₃	C₂⁴	1	155	yes	—
18	C₂³×D₁₃	—	2	9920	no	—
19	C₂³×D₁₃	C₂⁴	1	2480	yes	complemented
20	C₂²×C₄×C₁₃	C₂⁴	1	1240	yes	complemented
21	C₂×D₅₂	C₂⁴	1	7936	yes	direct product factor
22	C₂⁷	—	13	2	no	—
23	C₂⁴×D₄	—	13	124	no	—
24	C₂⁵×C₄	D₁₃	1	1	yes	characteristic, complemented
25	C₂³×C₁₃	C₂²×D₄	1	1240	yes	complemented
26	C₂³×C₁₃	C₂⁵	1	155	yes	—
27	C₂²×D₁₃	—	2	9920	no	—
28	C₂²×D₁₃	C₂⁵	1	992	yes	complemented
29	C₂×C₄×C₁₃	C₂⁵	1	496	yes	complemented
30	D₅₂	C₂⁵	1	1024	yes	direct product factor
31	C₂⁶	—	13	124	no	—
32	C₂⁶	—	26	64	no	—
33	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
34	C₂³×D₄	—	13	2480	no	—
35	C₂⁴×C₄	C₂×D₁₃	1	62	yes	complemented
36	C₂²×C₁₃	C₂³×D₄	1	620	yes	complemented
37	C₂²×C₁₃	C₂⁶	1	31	yes	—
38	C₂×D₁₃	—	2	1984	no	—
39	C₂×D₁₃	C₂⁶	1	64	yes	complemented
40	C₄×C₁₃	C₂⁶	1	32	yes	complemented
41	C₂⁵	—	13	1240	no	—
42	C₂⁵	—	26	1984	no	—
43	C₂⁵	D₅₂	1	32	yes	direct product factor
44	C₂⁵	C₂²×D₁₃	1	31	yes	—
45	C₂²×D₄	—	13	9920	no	—
46	C₂³×C₄	C₂²×D₁₃	1	620	yes	complemented
47	C₂×C₁₃	C₂⁴×D₄	1	62	yes	complemented
48	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
49	D₁₃	—	2	64	no	—
50	C₂⁴	—	13	2480	no	—
51	C₂⁴	—	26	9920	no	—
52	C₂⁴	C₂×D₅₂	1	496	yes	direct product factor
53	C₂⁴	C₂³×D₁₃	1	155	yes	—
54	C₂×D₄	—	13	7936	no	—
55	C₂²×C₄	C₂³×D₁₃	1	1240	yes	complemented
56	C₁₃	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
57	C₂³	—	13	992	no	—
58	C₂³	—	26	9920	no	—
59	C₂³	C₂²×D₅₂	1	1240	yes	direct product factor
60	C₂³	C₂⁴×D₁₃	1	155	yes	—
61	D₄	—	13	1024	no	—
62	C₂×C₄	C₂⁴×D₁₃	1	496	yes	complemented
63	C₂²	—	13	64	no	—
64	C₂²	—	26	1984	no	—
65	C₂²	C₂³×D₅₂	1	620	yes	direct product factor
66	C₂²	C₂⁵×D₁₃	1	31	yes	—
67	C₄	C₂⁵×D₁₃	1	32	yes	complemented
68	C₂	—	26	64	no	—
69	C₂	C₂⁴×D₅₂	1	62	yes	direct product factor
70	C₂	C₂⁶×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂⁷
Frattini	C₂	C₂⁶×D₁₃
Fitting	C₂⁵×C₄×C₁₃	C₂
socle	C₂⁶×C₁₃	C₂²
hypercenter	C₂⁵×C₄	D₁₃
hypocenter	C₁₃	C₂⁵×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁶ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₁₃	C₂	semidirect
2. C₂⁴×D₅₂	C₂	direct (N × H)
3. C₂⁵×C₄×C₁₃	C₂	semidirect
6. C₂⁵×D₁₃	C₂²	semidirect
7. C₂⁴×C₄×C₁₃	C₂²	semidirect
8. C₂³×D₅₂	C₂²	direct (N × H)
9. C₂⁵×C₁₃	D₄	semidirect
12. C₂⁴×D₁₃	C₂³	semidirect
13. C₂³×C₄×C₁₃	C₂³	semidirect
14. C₂²×D₅₂	C₂³	direct (N × H)
16. C₂⁴×C₁₃	C₂×D₄	semidirect
19. C₂³×D₁₃	C₂⁴	semidirect
20. C₂²×C₄×C₁₃	C₂⁴	semidirect
21. C₂×D₅₂	C₂⁴	direct (N × H)
24. C₂⁵×C₄	D₁₃	semidirect
25. C₂³×C₁₃	C₂²×D₄	semidirect
28. C₂²×D₁₃	C₂⁵	semidirect
29. C₂×C₄×C₁₃	C₂⁵	semidirect
30. D₅₂	C₂⁵	direct (N × H)
35. C₂⁴×C₄	C₂×D₁₃	semidirect
36. C₂²×C₁₃	C₂³×D₄	semidirect
39. C₂×D₁₃	C₂⁶	semidirect
40. C₄×C₁₃	C₂⁶	semidirect
43. C₂⁵	D₅₂	direct (N × H)
46. C₂³×C₄	C₂²×D₁₃	semidirect
47. C₂×C₁₃	C₂⁴×D₄	semidirect
52. C₂⁴	C₂×D₅₂	direct (N × H)
55. C₂²×C₄	C₂³×D₁₃	semidirect
56. C₁₃	C₂⁵×D₄	semidirect
59. C₂³	C₂²×D₅₂	direct (N × H)
62. C₂×C₄	C₂⁴×D₁₃	semidirect
65. C₂²	C₂³×D₅₂	direct (N × H)
67. C₄	C₂⁵×D₁₃	semidirect
69. C₂	C₂⁴×D₅₂	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×D₁₃	2
C₂⁴×D₅₂	2
C₂⁵×C₄×C₁₃	2
C₂⁵×D₄	13

Subgroups — C25×D52 #16776797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₅₂ #16776797