Subgroups — C₂×#401×D₅₃ #27550385

Order 13568.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃⋊#401	C₂	1	7	yes	maximal, complemented
2	#401×D₅₃	C₂	1	16	yes	maximal, direct product factor
3	C₂×#95×D₅₃	C₂	1	7	yes	maximal
4	C₂×C₅₃×#401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×D₅₃	C₂²	1	7	yes	—
6	C₅₃⋊#401	C₂²	1	56	yes	complemented
7	C₂×#13133124	C₂²	1	21	yes	—
8	#95×D₅₃	C₂²	1	56	yes	—
9	C₅₃×#401	C₂²	1	8	yes	complemented
10	C₂×#95×C₅₃	C₂²	1	7	yes	—
11	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
12	C₂³×Dic₅₃	C₂³	1	7	yes	—
13	C₂²×C₄×D₅₃	—	2	84	no	—
14	C₂²×C₄×D₅₃	C₂³	1	28	yes	—
15	#13133124	C₂³	1	84	yes	—
16	C₂³×C₄×C₅₃	C₂³	1	7	yes	—
17	#95×C₅₃	C₂³	1	28	yes	—
18	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
19	C₂³×D₅₃	#41	1	28	yes	—
20	C₂³×D₅₃	C₂⁴	1	2	yes	—
21	C₂²×C₄×C₅₃	—	2	42	no	—
22	C₂²×C₄×C₅₃	C₂⁴	1	14	yes	—
23	C₂²×Dic₅₃	—	2	42	no	—
24	C₂²×Dic₅₃	C₂⁴	1	14	yes	—
25	C₂×C₄×D₅₃	—	2	168	no	—
26	C₂×C₄×D₅₃	—	4	112	no	—
27	C₂³×C₅₃	C₂×#41	1	14	yes	—
28	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
29	C₂²×D₅₃	#126	1	112	yes	—
30	C₂²×D₅₃	C₂×#41	1	28	yes	—
31	C₂×C₄×C₅₃	—	2	42	no	—
32	C₂×C₄×C₅₃	—	4	28	no	—
33	C₂×Dic₅₃	—	2	42	no	—
34	C₂×Dic₅₃	—	4	28	no	—
35	C₄×D₅₃	—	4	112	no	—
36	C₂²×#401	—	53	1	no	maximal, Sylow
37	C₂²×C₅₃	C₂×#126	1	28	yes	—
38	C₂²×C₅₃	C₂²×#41	1	7	yes	—
39	C₂×D₅₃	#401	1	64	yes	direct product factor
40	C₂×D₅₃	C₂×#126	1	56	yes	—
41	C₄×C₅₃	—	4	14	no	—
42	Dic₅₃	—	4	14	no	—
43	C₂×#401	—	53	16	no	—
44	C₂×#401	—	53	7	no	—
45	C₂×#401	D₅₃	1	1	yes	characteristic, direct product factor
46	C₂²×#95	—	53	7	no	—
47	C₂×C₅₃	C₂×#401	1	8	yes	complemented
48	C₂×C₅₃	C₂²×#126	1	7	yes	—
49	D₅₃	C₂×#401	1	16	yes	direct product factor
50	C₂⁴×C₄	—	53	7	no	—
51	#401	—	53	56	no	—
52	#401	C₂×D₅₃	1	8	yes	direct product factor
53	C₂×#95	—	53	21	no	—
54	C₂×#95	—	53	56	no	—
55	C₂×#95	C₂×D₅₃	1	7	yes	—
56	C₅₃	C₂²×#401	1	1	yes	characteristic, complemented, Sylow
57	C₂⁵	—	53	1	no	—
58	C₂³×C₄	—	53	7	no	—
59	C₂³×C₄	—	53	28	no	—
60	C₂³×C₄	—	106	84	no	—
61	C₂³×C₄	C₂²×D₅₃	1	7	yes	—
62	#95	—	53	84	no	—
63	#95	C₂²×D₅₃	1	28	yes	—
64	C₂⁴	—	53	28	no	—
65	C₂⁴	—	53	2	no	—
66	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
67	C₂²×C₄	—	2	42	no	—
68	C₂²×C₄	—	53	14	no	—
69	C₂²×C₄	—	106	168	no	—
70	C₂²×C₄	—	106	42	no	—
71	C₂²×C₄	—	212	112	no	—
72	C₂²×C₄	C₂³×D₅₃	1	14	yes	—
73	C₂³	—	53	112	no	—
74	C₂³	—	53	28	no	—
75	C₂³	#41×D₅₃	1	14	yes	—
76	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
77	C₂×C₄	—	2	42	no	—
78	C₂×C₄	—	4	28	no	—
79	C₂×C₄	—	106	42	no	—
80	C₂×C₄	—	212	112	no	—
81	C₂×C₄	—	212	28	no	—
82	C₂²	—	53	56	no	—
83	C₂²	—	53	64	no	—
84	C₂²	#126×D₅₃	1	28	yes	—
85	C₂²	C₂×#41×D₅₃	1	7	yes	—
86	C₄	—	4	14	no	—
87	C₄	—	212	14	no	—
88	C₂	—	53	16	no	—
89	C₂	#401×D₅₃	1	8	yes	direct product factor
90	C₂	C₂×#126×D₅₃	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂³×C₅₃	C₂⁵
Frattini	C₂³	C₂⁴×D₅₃
Fitting	C₂×C₅₃×#401	C₂
socle	C₂⁴×C₅₃	C₂⁴
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	C₂×#401	D₅₃
hypocenter	C₅₃	C₂²×#401
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃⋊#401	C₂	semidirect
2. #401×D₅₃	C₂	direct (N × H)
4. C₂×C₅₃×#401	C₂	semidirect
6. C₅₃⋊#401	C₂²	semidirect
9. C₅₃×#401	C₂²	semidirect
39. C₂×D₅₃	#401	direct (N × H)
45. C₂×#401	D₅₃	direct (N × H)
47. C₂×C₅₃	C₂×#401	semidirect
49. D₅₃	C₂×#401	direct (N × H)
52. #401	C₂×D₅₃	direct (N × H)
56. C₅₃	C₂²×#401	semidirect
89. C₂	#401×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
C₂×C₅₃⋊#401	2
#401×D₅₃	2
C₂×#95×D₅₃	2
C₂×C₅₃×#401	2
C₂²×#401	53

Subgroups — C2×#401×D53 #27550385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#401×D₅₃ #27550385