Subgroups — C₂⁵×C₂²⋊D₁₃ #16776796

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, complemented
2	C₂⁴×C₂²⋊D₁₃	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁷×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁶×C₁₃	—	2	32	no	—
6	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
7	C₂⁶×C₁₃	C₂²	1	62	yes	complemented
8	C₂⁵×D₁₃	—	2	32	no	—
9	C₂⁵×D₁₃	C₂²	1	62	yes	complemented
10	C₂³×C₂²⋊D₁₃	C₂²	1	2480	yes	direct product factor
11	C₂⁴×Dic₁₃	C₂²	1	62	yes	complemented
12	C₂⁵×C₁₃	—	2	992	no	—
13	C₂⁵×C₁₃	D₄	1	32	yes	complemented
14	C₂⁵×C₁₃	C₂³	1	31	yes	—
15	C₂⁵×C₁₃	C₂³	1	620	yes	complemented
16	C₂⁴×D₁₃	—	2	992	no	—
17	C₂⁴×D₁₃	C₂³	1	620	yes	complemented
18	C₂²×C₂²⋊D₁₃	C₂³	1	9920	yes	direct product factor
19	C₂³×Dic₁₃	C₂³	1	620	yes	complemented
20	C₂⁵×D₄	—	13	1	no	maximal, Sylow
21	C₂⁴×C₁₃	—	2	4960	no	—
22	C₂⁴×C₁₃	C₂×D₄	1	496	yes	complemented
23	C₂⁴×C₁₃	C₂⁴	1	155	yes	—
24	C₂⁴×C₁₃	C₂⁴	1	1240	yes	complemented
25	C₂³×D₁₃	—	2	4960	no	—
26	C₂³×D₁₃	C₂⁴	1	1240	yes	complemented
27	C₂×C₂²⋊D₁₃	C₂⁴	1	7936	yes	direct product factor
28	C₂²×Dic₁₃	C₂⁴	1	1240	yes	complemented
29	C₂⁷	—	13	1	no	—
30	C₂⁷	D₁₃	1	1	yes	characteristic, complemented
31	C₂⁴×D₄	—	13	124	no	—
32	C₂⁵×C₄	—	13	1	no	—
33	C₂³×C₁₃	—	2	4960	no	—
34	C₂³×C₁₃	C₂²×D₄	1	1240	yes	complemented
35	C₂³×C₁₃	C₂⁵	1	155	yes	—
36	C₂³×C₁₃	C₂⁵	1	496	yes	complemented
37	C₂²×D₁₃	—	2	4960	no	—
38	C₂²×D₁₃	C₂⁵	1	496	yes	complemented
39	C₂²⋊D₁₃	C₂⁵	1	1024	yes	direct product factor
40	C₂×Dic₁₃	C₂⁵	1	496	yes	complemented
41	C₂⁶	—	2	32	no	—
42	C₂⁶	—	13	62	no	—
43	C₂⁶	—	26	32	no	—
44	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
45	C₂⁶	C₂×D₁₃	1	62	yes	complemented
46	C₂³×D₄	—	13	2480	no	—
47	C₂⁴×C₄	—	13	62	no	—
48	C₂²×C₁₃	—	2	992	no	—
49	C₂²×C₁₃	C₂³×D₄	1	620	yes	complemented
50	C₂²×C₁₃	C₂⁶	1	31	yes	—
51	C₂²×C₁₃	C₂⁶	1	32	yes	complemented
52	C₂×D₁₃	—	2	992	no	—
53	C₂×D₁₃	C₂⁶	1	32	yes	complemented
54	Dic₁₃	C₂⁶	1	32	yes	complemented
55	C₂⁵	—	2	992	no	—
56	C₂⁵	—	13	620	no	—
57	C₂⁵	—	26	992	no	—
58	C₂⁵	C₂²⋊D₁₃	1	32	yes	direct product factor
59	C₂⁵	C₂²×D₁₃	1	31	yes	—
60	C₂⁵	C₂²×D₁₃	1	620	yes	complemented
61	C₂²×D₄	—	13	9920	no	—
62	C₂³×C₄	—	13	620	no	—
63	C₂×C₁₃	—	2	32	no	—
64	C₂×C₁₃	C₂⁴×D₄	1	62	yes	complemented
65	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
66	D₁₃	—	2	32	no	—
67	C₂⁴	—	2	4960	no	—
68	C₂⁴	—	13	1240	no	—
69	C₂⁴	—	26	4960	no	—
70	C₂⁴	C₂×C₂²⋊D₁₃	1	496	yes	direct product factor
71	C₂⁴	C₂³×D₁₃	1	155	yes	—
72	C₂⁴	C₂³×D₁₃	1	1240	yes	complemented
73	C₂×D₄	—	13	7936	no	—
74	C₂²×C₄	—	13	1240	no	—
75	C₁₃	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
76	C₂³	—	2	4960	no	—
77	C₂³	—	13	496	no	—
78	C₂³	—	26	4960	no	—
79	C₂³	C₂²×C₂²⋊D₁₃	1	1240	yes	direct product factor
80	C₂³	C₂⁴×D₁₃	1	155	yes	—
81	C₂³	C₂⁴×D₁₃	1	496	yes	complemented
82	D₄	—	13	1024	no	—
83	C₂×C₄	—	13	496	no	—
84	C₂²	—	2	992	no	—
85	C₂²	—	13	32	no	—
86	C₂²	—	26	992	no	—
87	C₂²	C₂³×C₂²⋊D₁₃	1	620	yes	direct product factor
88	C₂²	C₂⁵×D₁₃	1	31	yes	—
89	C₂²	C₂⁵×D₁₃	1	32	yes	complemented
90	C₄	—	13	32	no	—
91	C₂	—	2	32	no	—
92	C₂	—	26	32	no	—
93	C₂	C₂⁴×C₂²⋊D₁₃	1	62	yes	direct product factor
94	C₂	C₂⁶×D₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₁₃	C₂	semidirect
2. C₂⁴×C₂²⋊D₁₃	C₂	direct (N × H)
3. C₂⁵×Dic₁₃	C₂	semidirect
4. C₂⁷×C₁₃	C₂	semidirect
7. C₂⁶×C₁₃	C₂²	semidirect
9. C₂⁵×D₁₃	C₂²	semidirect
10. C₂³×C₂²⋊D₁₃	C₂²	direct (N × H)
11. C₂⁴×Dic₁₃	C₂²	semidirect
13. C₂⁵×C₁₃	D₄	semidirect
15. C₂⁵×C₁₃	C₂³	semidirect
17. C₂⁴×D₁₃	C₂³	semidirect
18. C₂²×C₂²⋊D₁₃	C₂³	direct (N × H)
19. C₂³×Dic₁₃	C₂³	semidirect
22. C₂⁴×C₁₃	C₂×D₄	semidirect
24. C₂⁴×C₁₃	C₂⁴	semidirect
26. C₂³×D₁₃	C₂⁴	semidirect
27. C₂×C₂²⋊D₁₃	C₂⁴	direct (N × H)
28. C₂²×Dic₁₃	C₂⁴	semidirect
30. C₂⁷	D₁₃	semidirect
34. C₂³×C₁₃	C₂²×D₄	semidirect
36. C₂³×C₁₃	C₂⁵	semidirect
38. C₂²×D₁₃	C₂⁵	semidirect
39. C₂²⋊D₁₃	C₂⁵	direct (N × H)
40. C₂×Dic₁₃	C₂⁵	semidirect
45. C₂⁶	C₂×D₁₃	semidirect
49. C₂²×C₁₃	C₂³×D₄	semidirect
51. C₂²×C₁₃	C₂⁶	semidirect
53. C₂×D₁₃	C₂⁶	semidirect
54. Dic₁₃	C₂⁶	semidirect
58. C₂⁵	C₂²⋊D₁₃	direct (N × H)
60. C₂⁵	C₂²×D₁₃	semidirect
64. C₂×C₁₃	C₂⁴×D₄	semidirect
70. C₂⁴	C₂×C₂²⋊D₁₃	direct (N × H)
72. C₂⁴	C₂³×D₁₃	semidirect
75. C₁₃	C₂⁵×D₄	semidirect
79. C₂³	C₂²×C₂²⋊D₁₃	direct (N × H)
81. C₂³	C₂⁴×D₁₃	semidirect
87. C₂²	C₂³×C₂²⋊D₁₃	direct (N × H)
89. C₂²	C₂⁵×D₁₃	semidirect
93. C₂	C₂⁴×C₂²⋊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
C₂⁴×C₂²⋊D₁₃	2
C₂⁵×Dic₁₃	2
C₂⁷×C₁₃	2
C₂⁵×D₄	13

Subgroups — C25×C22⋊D13 #16776796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₂²⋊D₁₃ #16776796