Subgroups — C₂⁵×C₄×D₁₃ #16776793

Order 3328.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×C₄×D₁₃	C₂	1	124	yes	maximal, direct product factor
4	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
6	C₂⁵×D₁₃	C₄	1	64	yes	direct product factor
7	C₂⁵×D₁₃	C₂²	1	62	yes	—
8	C₂⁴×C₄×C₁₃	C₂²	1	62	yes	complemented
9	C₂⁴×Dic₁₃	C₂²	1	62	yes	complemented
10	C₂³×C₄×D₁₃	C₂²	1	2480	yes	direct product factor
11	C₂⁵×C₁₃	C₂×C₄	1	32	yes	complemented
12	C₂⁵×C₁₃	C₂³	1	31	yes	—
13	C₂⁴×D₁₃	C₂×C₄	1	1984	yes	direct product factor
14	C₂⁴×D₁₃	C₂³	1	620	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	620	yes	complemented
16	C₂³×Dic₁₃	C₂³	1	620	yes	complemented
17	C₂²×C₄×D₁₃	C₂³	1	9920	yes	direct product factor
18	C₂⁶×C₄	—	13	1	no	maximal, Sylow
19	C₂⁴×C₁₃	C₂²×C₄	1	496	yes	complemented
20	C₂⁴×C₁₃	C₂⁴	1	155	yes	—
21	C₂³×D₁₃	C₂²×C₄	1	9920	yes	direct product factor
22	C₂³×D₁₃	C₂⁴	1	1240	yes	—
23	C₂²×C₄×C₁₃	C₂⁴	1	1240	yes	complemented
24	C₂²×Dic₁₃	C₂⁴	1	1240	yes	complemented
25	C₂×C₄×D₁₃	C₂⁴	1	7936	yes	direct product factor
26	C₂⁷	—	13	1	no	—
27	C₂⁵×C₄	—	13	1	no	—
28	C₂⁵×C₄	—	13	124	no	—
29	C₂⁵×C₄	D₁₃	1	1	yes	characteristic, direct product factor
30	C₂³×C₁₃	C₂³×C₄	1	1240	yes	complemented
31	C₂³×C₁₃	C₂⁵	1	155	yes	—
32	C₂²×D₁₃	C₂³×C₄	1	9920	yes	direct product factor
33	C₂²×D₁₃	C₂⁵	1	496	yes	—
34	C₂×C₄×C₁₃	C₂⁵	1	496	yes	complemented
35	C₂×Dic₁₃	C₂⁵	1	496	yes	complemented
36	C₄×D₁₃	C₂⁵	1	1024	yes	direct product factor
37	C₂⁶	—	13	64	no	—
38	C₂⁶	—	13	62	no	—
39	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
40	C₂⁴×C₄	—	13	62	no	—
41	C₂⁴×C₄	—	13	2480	no	—
42	C₂⁴×C₄	C₂×D₁₃	1	62	yes	direct product factor
43	C₂²×C₁₃	C₂⁴×C₄	1	620	yes	complemented
44	C₂²×C₁₃	C₂⁶	1	31	yes	—
45	C₂×D₁₃	C₂⁴×C₄	1	1984	yes	direct product factor
46	C₂×D₁₃	C₂⁶	1	32	yes	—
47	C₄×C₁₃	C₂⁶	1	32	yes	complemented
48	Dic₁₃	C₂⁶	1	32	yes	complemented
49	C₂⁵	—	13	1984	no	—
50	C₂⁵	—	13	620	no	—
51	C₂⁵	C₄×D₁₃	1	32	yes	direct product factor
52	C₂⁵	C₂²×D₁₃	1	31	yes	—
53	C₂³×C₄	—	13	620	no	—
54	C₂³×C₄	—	13	9920	no	—
55	C₂³×C₄	C₂²×D₁₃	1	620	yes	direct product factor
56	C₂×C₁₃	C₂⁵×C₄	1	62	yes	complemented
57	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
58	D₁₃	C₂⁵×C₄	1	64	yes	direct product factor
59	C₂⁴	—	13	9920	no	—
60	C₂⁴	—	13	1240	no	—
61	C₂⁴	C₂×C₄×D₁₃	1	496	yes	direct product factor
62	C₂⁴	C₂³×D₁₃	1	155	yes	—
63	C₂²×C₄	—	13	1240	no	—
64	C₂²×C₄	—	13	7936	no	—
65	C₂²×C₄	C₂³×D₁₃	1	1240	yes	direct product factor
66	C₁₃	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	13	9920	no	—
68	C₂³	—	13	496	no	—
69	C₂³	C₂²×C₄×D₁₃	1	1240	yes	direct product factor
70	C₂³	C₂⁴×D₁₃	1	155	yes	—
71	C₂×C₄	—	13	496	no	—
72	C₂×C₄	—	13	1024	no	—
73	C₂×C₄	C₂⁴×D₁₃	1	496	yes	direct product factor
74	C₂²	—	13	1984	no	—
75	C₂²	—	13	32	no	—
76	C₂²	C₂³×C₄×D₁₃	1	620	yes	direct product factor
77	C₂²	C₂⁵×D₁₃	1	31	yes	—
78	C₄	—	13	32	no	—
79	C₄	C₂⁵×D₁₃	1	32	yes	direct product factor
80	C₂	—	13	64	no	—
81	C₂	C₂⁴×C₄×D₁₃	1	62	yes	direct product factor
82	C₂	C₂⁶×D₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂⁵×Dic₁₃	C₂	semidirect
3. C₂⁴×C₄×D₁₃	C₂	direct (N × H)
4. C₂⁵×C₄×C₁₃	C₂	semidirect
6. C₂⁵×D₁₃	C₄	direct (N × H)
8. C₂⁴×C₄×C₁₃	C₂²	semidirect
9. C₂⁴×Dic₁₃	C₂²	semidirect
10. C₂³×C₄×D₁₃	C₂²	direct (N × H)
11. C₂⁵×C₁₃	C₂×C₄	semidirect
13. C₂⁴×D₁₃	C₂×C₄	direct (N × H)
15. C₂³×C₄×C₁₃	C₂³	semidirect
16. C₂³×Dic₁₃	C₂³	semidirect
17. C₂²×C₄×D₁₃	C₂³	direct (N × H)
19. C₂⁴×C₁₃	C₂²×C₄	semidirect
21. C₂³×D₁₃	C₂²×C₄	direct (N × H)
23. C₂²×C₄×C₁₃	C₂⁴	semidirect
24. C₂²×Dic₁₃	C₂⁴	semidirect
25. C₂×C₄×D₁₃	C₂⁴	direct (N × H)
29. C₂⁵×C₄	D₁₃	direct (N × H)
30. C₂³×C₁₃	C₂³×C₄	semidirect
32. C₂²×D₁₃	C₂³×C₄	direct (N × H)
34. C₂×C₄×C₁₃	C₂⁵	semidirect
35. C₂×Dic₁₃	C₂⁵	semidirect
36. C₄×D₁₃	C₂⁵	direct (N × H)
42. C₂⁴×C₄	C₂×D₁₃	direct (N × H)
43. C₂²×C₁₃	C₂⁴×C₄	semidirect
45. C₂×D₁₃	C₂⁴×C₄	direct (N × H)
47. C₄×C₁₃	C₂⁶	semidirect
48. Dic₁₃	C₂⁶	semidirect
51. C₂⁵	C₄×D₁₃	direct (N × H)
55. C₂³×C₄	C₂²×D₁₃	direct (N × H)
56. C₂×C₁₃	C₂⁵×C₄	semidirect
58. D₁₃	C₂⁵×C₄	direct (N × H)
61. C₂⁴	C₂×C₄×D₁₃	direct (N × H)
65. C₂²×C₄	C₂³×D₁₃	direct (N × H)
66. C₁₃	C₂⁶×C₄	semidirect
69. C₂³	C₂²×C₄×D₁₃	direct (N × H)
73. C₂×C₄	C₂⁴×D₁₃	direct (N × H)
76. C₂²	C₂³×C₄×D₁₃	direct (N × H)
79. C₄	C₂⁵×D₁₃	direct (N × H)
81. C₂	C₂⁴×C₄×D₁₃	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
C₂⁵×Dic₁₃	2
C₂⁴×C₄×D₁₃	2
C₂⁵×C₄×C₁₃	2
C₂⁶×C₄	13

Subgroups — C25×C4×D13 #16776793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₄×D₁₃ #16776793