Subgroups — C₂×C₅₃⋊#401 #20278011

Order 6784.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃⋊#401	C₂	1	8	yes	maximal, direct product factor
2	C₂×#13133124	C₂	1	3	yes	maximal
3	C₂×#13133124	C₂	1	3	yes	maximal
4	C₂×#95×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic
6	C₂³×Dic₅₃	C₂²	1	3	yes	—
7	#13133124	C₂²	1	12	yes	—
8	#13133124	C₂²	1	12	yes	—
9	C₂³×C₄×C₅₃	C₂²	1	3	yes	—
10	#95×C₅₃	C₂²	1	4	yes	—
11	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₅₃	—	2	6	no	—
13	C₂²×C₄×C₅₃	—	2	12	no	—
14	C₂²×C₄×C₅₃	C₂³	1	6	yes	—
15	C₂²×Dic₅₃	—	2	6	no	—
16	C₂²×Dic₅₃	—	2	6	no	—
17	C₂²×Dic₅₃	—	2	6	no	—
18	C₂²×Dic₅₃	—	2	6	no	—
19	C₂²×Dic₅₃	C₂³	1	6	yes	—
20	C₂²×Dic₅₃	C₂³	1	2	yes	—
21	C₂³×C₅₃	#41	1	6	yes	—
22	C₂³×C₅₃	#41	1	6	yes	—
23	C₂³×C₅₃	#41	1	2	yes	—
24	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₅₃	—	2	12	no	—
26	C₂×C₄×C₅₃	—	2	6	no	—
27	C₂×C₄×C₅₃	—	4	12	no	—
28	C₂×Dic₅₃	—	2	6	no	—
29	C₂×Dic₅₃	—	2	6	no	—
30	C₂×Dic₅₃	—	2	6	no	—
31	C₂×Dic₅₃	—	2	6	no	—
32	C₂×Dic₅₃	—	4	4	no	—
33	C₂×Dic₅₃	—	4	12	no	—
34	C₂²×C₅₃	#126	1	12	yes	—
35	C₂²×C₅₃	#126	1	4	yes	—
36	C₂²×C₅₃	#126	1	12	yes	—
37	C₂²×C₅₃	C₂×#41	1	3	yes	—
38	C₂²×C₅₃	C₂×#41	1	3	yes	—
39	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
40	C₄×C₅₃	—	4	6	no	—
41	Dic₅₃	—	4	2	no	—
42	Dic₅₃	—	4	6	no	—
43	C₂×#401	—	53	1	no	maximal, Sylow
44	C₂×C₅₃	#401	1	8	yes	complemented
45	C₂×C₅₃	C₂×#126	1	3	yes	—
46	C₂×C₅₃	C₂×#126	1	1	yes	characteristic
47	C₂×C₅₃	C₂×#126	1	3	yes	—
48	#401	—	53	8	no	—
49	C₂×#95	—	53	3	no	—
50	C₂×#95	—	53	3	no	—
51	C₂×#95	D₅₃	1	1	yes	characteristic
52	C₅₃	C₂×#401	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₄	—	53	1	no	—
54	C₂³×C₄	—	53	3	no	—
55	C₂³×C₄	C₂×D₅₃	1	3	yes	—
56	#95	—	53	12	no	—
57	#95	—	53	12	no	—
58	#95	C₂×D₅₃	1	4	yes	—
59	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
60	C₂²×C₄	—	2	6	no	—
61	C₂²×C₄	—	2	12	no	—
62	C₂²×C₄	—	53	6	no	—
63	C₂²×C₄	—	53	2	no	—
64	C₂²×C₄	—	106	6	no	—
65	C₂²×C₄	—	106	6	no	—
66	C₂²×C₄	—	106	6	no	—
67	C₂²×C₄	—	106	6	no	—
68	C₂²×C₄	C₂²×D₅₃	1	6	yes	—
69	C₂³	#11719945	1	6	yes	—
70	C₂³	#11719947	1	6	yes	—
71	C₂³	#11719949	1	2	yes	—
72	C₂³	C₂³×D₅₃	1	1	yes	characteristic
73	C₂×C₄	—	2	12	no	—
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	4	12	no	—
76	C₂×C₄	—	106	6	no	—
77	C₂×C₄	—	106	6	no	—
78	C₂×C₄	—	106	6	no	—
79	C₂×C₄	—	106	6	no	—
80	C₂×C₄	—	212	4	no	—
81	C₂×C₄	—	212	12	no	—
82	C₂²	#13133210	1	12	yes	—
83	C₂²	#13133211	1	4	yes	—
84	C₂²	#13133212	1	12	yes	—
85	C₂²	C₂×#11719947	1	3	yes	—
86	C₂²	C₂×#11719945	1	3	yes	—
87	C₂²	C₂×#11719949	1	1	yes	characteristic
88	C₄	—	4	6	no	—
89	C₄	—	212	2	no	—
90	C₄	—	212	6	no	—
91	C₂	C₅₃⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#13133210	1	3	yes	—
93	C₂	C₂×#13133211	1	1	yes	characteristic
94	C₂	C₂×#13133212	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₅₃
commutator	C₂³×C₅₃	C₂⁴
Frattini	C₂³	C₂³×D₅₃
Fitting	C₂×#95×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂³
hypercenter	C₂×#95	D₅₃
hypocenter	C₅₃	C₂×#401
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₅₃⋊#401	C₂	direct (N × H)
44. C₂×C₅₃	#401	semidirect
52. C₅₃	C₂×#401	semidirect
91. C₂	C₅₃⋊#401	direct (N × H)

Subgroups — C2×C53⋊#401 #20278011

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅₃⋊#401 #20278011