Subgroups — C₂⁵×C₂²⋊D₅₃ #28297969

Order 13568.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₂²⋊D₅₃	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁷×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×D₅₃	—	2	32	no	—
6	C₂⁵×D₅₃	C₂²	1	62	yes	complemented
7	C₂³×C₂²⋊D₅₃	C₂²	1	2480	yes	direct product factor
8	C₂⁴×Dic₅₃	C₂²	1	62	yes	complemented
9	C₂⁶×C₅₃	—	2	32	no	—
10	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
11	C₂⁶×C₅₃	C₂²	1	62	yes	complemented
12	C₂⁴×D₅₃	—	2	992	no	—
13	C₂⁴×D₅₃	C₂³	1	620	yes	complemented
14	C₂²×C₂²⋊D₅₃	C₂³	1	9920	yes	direct product factor
15	C₂³×Dic₅₃	C₂³	1	620	yes	complemented
16	C₂⁵×C₅₃	—	2	992	no	—
17	C₂⁵×C₅₃	D₄	1	32	yes	complemented
18	C₂⁵×C₅₃	C₂³	1	31	yes	—
19	C₂⁵×C₅₃	C₂³	1	620	yes	complemented
20	C₂⁴×C₅₃	—	2	4960	no	—
21	C₂⁴×C₅₃	C₂×D₄	1	496	yes	complemented
22	C₂⁴×C₅₃	C₂⁴	1	155	yes	—
23	C₂⁴×C₅₃	C₂⁴	1	1240	yes	complemented
24	C₂³×D₅₃	—	2	4960	no	—
25	C₂³×D₅₃	C₂⁴	1	1240	yes	complemented
26	C₂×C₂²⋊D₅₃	C₂⁴	1	7936	yes	direct product factor
27	C₂²×Dic₅₃	C₂⁴	1	1240	yes	complemented
28	C₂³×C₅₃	—	2	4960	no	—
29	C₂³×C₅₃	C₂²×D₄	1	1240	yes	complemented
30	C₂³×C₅₃	C₂⁵	1	155	yes	—
31	C₂³×C₅₃	C₂⁵	1	496	yes	complemented
32	C₂²×D₅₃	—	2	4960	no	—
33	C₂²×D₅₃	C₂⁵	1	496	yes	complemented
34	C₂²⋊D₅₃	C₂⁵	1	1024	yes	direct product factor
35	C₂×Dic₅₃	C₂⁵	1	496	yes	complemented
36	C₂⁵×D₄	—	53	1	no	maximal, Sylow
37	C₂²×C₅₃	—	2	992	no	—
38	C₂²×C₅₃	C₂³×D₄	1	620	yes	complemented
39	C₂²×C₅₃	C₂⁶	1	31	yes	—
40	C₂²×C₅₃	C₂⁶	1	32	yes	complemented
41	C₂×D₅₃	—	2	992	no	—
42	C₂×D₅₃	C₂⁶	1	32	yes	complemented
43	Dic₅₃	C₂⁶	1	32	yes	complemented
44	C₂⁷	—	53	1	no	—
45	C₂⁷	D₅₃	1	1	yes	characteristic, complemented
46	C₂⁴×D₄	—	53	124	no	—
47	C₂⁵×C₄	—	53	1	no	—
48	C₂×C₅₃	—	2	32	no	—
49	C₂×C₅₃	C₂⁴×D₄	1	62	yes	complemented
50	C₂×C₅₃	C₂⁷	1	1	yes	characteristic
51	D₅₃	—	2	32	no	—
52	C₂⁶	—	2	32	no	—
53	C₂⁶	—	53	62	no	—
54	C₂⁶	—	106	32	no	—
55	C₂⁶	C₂×D₅₃	1	1	yes	characteristic
56	C₂⁶	C₂×D₅₃	1	62	yes	complemented
57	C₂³×D₄	—	53	2480	no	—
58	C₂⁴×C₄	—	53	62	no	—
59	C₅₃	C₂⁵×D₄	1	1	yes	characteristic, complemented, Sylow
60	C₂⁵	—	2	992	no	—
61	C₂⁵	—	53	620	no	—
62	C₂⁵	—	106	992	no	—
63	C₂⁵	C₂²⋊D₅₃	1	32	yes	direct product factor
64	C₂⁵	C₂²×D₅₃	1	31	yes	—
65	C₂⁵	C₂²×D₅₃	1	620	yes	complemented
66	C₂²×D₄	—	53	9920	no	—
67	C₂³×C₄	—	53	620	no	—
68	C₂⁴	—	2	4960	no	—
69	C₂⁴	—	53	1240	no	—
70	C₂⁴	—	106	4960	no	—
71	C₂⁴	C₂×C₂²⋊D₅₃	1	496	yes	direct product factor
72	C₂⁴	C₂³×D₅₃	1	155	yes	—
73	C₂⁴	C₂³×D₅₃	1	1240	yes	complemented
74	C₂×D₄	—	53	7936	no	—
75	C₂²×C₄	—	53	1240	no	—
76	C₂³	—	2	4960	no	—
77	C₂³	—	53	496	no	—
78	C₂³	—	106	4960	no	—
79	C₂³	C₂²×C₂²⋊D₅₃	1	1240	yes	direct product factor
80	C₂³	C₂⁴×D₅₃	1	155	yes	—
81	C₂³	C₂⁴×D₅₃	1	496	yes	complemented
82	D₄	—	53	1024	no	—
83	C₂×C₄	—	53	496	no	—
84	C₂²	—	2	992	no	—
85	C₂²	—	53	32	no	—
86	C₂²	—	106	992	no	—
87	C₂²	C₂³×C₂²⋊D₅₃	1	620	yes	direct product factor
88	C₂²	C₂⁵×D₅₃	1	31	yes	—
89	C₂²	C₂⁵×D₅₃	1	32	yes	complemented
90	C₄	—	53	32	no	—
91	C₂	—	2	32	no	—
92	C₂	—	106	32	no	—
93	C₂	C₂⁴×C₂²⋊D₅₃	1	62	yes	direct product factor
94	C₂	C₂⁶×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₅₃
commutator, cosocle	C₂×C₅₃	C₂⁷
Frattini	C₂	C₂⁶×D₅₃
Fitting	C₂⁷×C₅₃	C₂
socle	C₂⁶×C₅₃	C₂²
hypercenter	C₂⁷	D₅₃
hypocenter	C₅₃	C₂⁵×D₄
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁶ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₅₃	C₂	semidirect
2. C₂⁴×C₂²⋊D₅₃	C₂	direct (N × H)
3. C₂⁵×Dic₅₃	C₂	semidirect
4. C₂⁷×C₅₃	C₂	semidirect
6. C₂⁵×D₅₃	C₂²	semidirect
7. C₂³×C₂²⋊D₅₃	C₂²	direct (N × H)
8. C₂⁴×Dic₅₃	C₂²	semidirect
11. C₂⁶×C₅₃	C₂²	semidirect
13. C₂⁴×D₅₃	C₂³	semidirect
14. C₂²×C₂²⋊D₅₃	C₂³	direct (N × H)
15. C₂³×Dic₅₃	C₂³	semidirect
17. C₂⁵×C₅₃	D₄	semidirect
19. C₂⁵×C₅₃	C₂³	semidirect
21. C₂⁴×C₅₃	C₂×D₄	semidirect
23. C₂⁴×C₅₃	C₂⁴	semidirect
25. C₂³×D₅₃	C₂⁴	semidirect
26. C₂×C₂²⋊D₅₃	C₂⁴	direct (N × H)
27. C₂²×Dic₅₃	C₂⁴	semidirect
29. C₂³×C₅₃	C₂²×D₄	semidirect
31. C₂³×C₅₃	C₂⁵	semidirect
33. C₂²×D₅₃	C₂⁵	semidirect
34. C₂²⋊D₅₃	C₂⁵	direct (N × H)
35. C₂×Dic₅₃	C₂⁵	semidirect
38. C₂²×C₅₃	C₂³×D₄	semidirect
40. C₂²×C₅₃	C₂⁶	semidirect
42. C₂×D₅₃	C₂⁶	semidirect
43. Dic₅₃	C₂⁶	semidirect
45. C₂⁷	D₅₃	semidirect
49. C₂×C₅₃	C₂⁴×D₄	semidirect
56. C₂⁶	C₂×D₅₃	semidirect
59. C₅₃	C₂⁵×D₄	semidirect
63. C₂⁵	C₂²⋊D₅₃	direct (N × H)
65. C₂⁵	C₂²×D₅₃	semidirect
71. C₂⁴	C₂×C₂²⋊D₅₃	direct (N × H)
73. C₂⁴	C₂³×D₅₃	semidirect
79. C₂³	C₂²×C₂²⋊D₅₃	direct (N × H)
81. C₂³	C₂⁴×D₅₃	semidirect
87. C₂²	C₂³×C₂²⋊D₅₃	direct (N × H)
89. C₂²	C₂⁵×D₅₃	semidirect
93. C₂	C₂⁴×C₂²⋊D₅₃	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×D₅₃	2
C₂⁴×C₂²⋊D₅₃	2
C₂⁵×Dic₅₃	2
C₂⁷×C₅₃	2
C₂⁵×D₄	53

Subgroups — C25×C22⋊D53 #28297969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₂²⋊D₅₃ #28297969