Subgroups — C₂×C₄×C₁₆×C₅₃ #20271042

Order 6784.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×C₅₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₅₃	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₅₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₅₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₅₃	C₄	1	8	yes	direct product factor
8	C₂×C₁₆×C₅₃	C₂²	1	4	yes	—
9	C₄×C₈×C₅₃	C₄	1	2	yes	—
10	C₄×C₈×C₅₃	C₂²	1	2	yes	—
11	C₂²×C₄×C₅₃	C₈	1	2	yes	—
12	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₅₃	C₈	1	4	yes	—
14	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₅₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
18	C₄²×C₅₃	C₈	1	2	yes	—
19	C₄²×C₅₃	C₂×C₄	1	2	yes	—
20	C₁₆×C₅₃	C₂×C₄	1	8	yes	direct product factor
21	C₂³×C₅₃	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄×C₅₃	C₁₆	1	8	yes	direct product factor
23	C₂×C₄×C₅₃	C₄²	1	2	yes	—
24	C₂×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₅₃	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₅₃	C₂×C₈	1	4	yes	—
27	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₅₃	C₄²	1	2	yes	—
29	C₈×C₅₃	C₂×C₈	1	4	yes	—
30	C₈×C₅₃	C₂²×C₄	1	2	yes	—
31	C₂²×C₅₃	C₄×C₈	1	2	yes	—
32	C₂²×C₅₃	C₂×C₁₆	1	4	yes	—
33	C₂²×C₅₃	C₂²×C₈	1	1	yes	characteristic
34	C₄×C₅₃	C₄×C₈	1	2	yes	—
35	C₄×C₅₃	C₂×C₁₆	1	8	yes	direct product factor
36	C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
37	C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₆	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₅₃	C₄×C₁₆	1	4	yes	direct product factor
40	C₂×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
41	C₂×C₅₃	C₂²×C₁₆	1	2	yes	—
42	C₂²×C₁₆	C₂×C₅₃	1	2	yes	—
43	C₂×C₄×C₈	C₂×C₅₃	1	1	yes	characteristic
44	C₄×C₁₆	C₂×C₅₃	1	4	yes	direct product factor
45	C₅₃	C₂×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₈	C₄×C₅₃	1	1	yes	characteristic
47	C₂²×C₈	C₂²×C₅₃	1	1	yes	characteristic
48	C₂×C₄²	C₄×C₅₃	1	1	yes	characteristic
49	C₂×C₁₆	C₄×C₅₃	1	8	yes	direct product factor
50	C₂×C₁₆	C₂²×C₅₃	1	4	yes	—
51	C₄×C₈	C₄×C₅₃	1	2	yes	—
52	C₄×C₈	C₂²×C₅₃	1	2	yes	—
53	C₂²×C₄	C₈×C₅₃	1	2	yes	—
54	C₂²×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
55	C₂×C₈	C₈×C₅₃	1	4	yes	—
56	C₂×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
57	C₂×C₈	C₂×C₄×C₅₃	1	2	yes	—
58	C₂×C₈	C₂×C₄×C₅₃	1	4	yes	—
59	C₂×C₈	C₂³×C₅₃	1	1	yes	characteristic
60	C₄²	C₈×C₅₃	1	2	yes	—
61	C₄²	C₂×C₄×C₅₃	1	2	yes	—
62	C₁₆	C₂×C₄×C₅₃	1	8	yes	direct product factor
63	C₂³	C₂×C₈×C₅₃	1	1	yes	characteristic
64	C₂×C₄	C₁₆×C₅₃	1	8	yes	direct product factor
65	C₂×C₄	C₄²×C₅₃	1	2	yes	—
66	C₂×C₄	C₂×C₈×C₅₃	1	1	yes	characteristic
67	C₂×C₄	C₂×C₈×C₅₃	1	2	yes	—
68	C₂×C₄	C₂×C₈×C₅₃	1	4	yes	—
69	C₂×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
70	C₈	C₄²×C₅₃	1	2	yes	—
71	C₈	C₂×C₈×C₅₃	1	4	yes	—
72	C₈	C₂²×C₄×C₅₃	1	2	yes	—
73	C₂²	C₄×C₈×C₅₃	1	2	yes	—
74	C₂²	C₂×C₁₆×C₅₃	1	4	yes	—
75	C₂²	C₂²×C₈×C₅₃	1	1	yes	characteristic
76	C₄	C₄×C₈×C₅₃	1	2	yes	—
77	C₄	C₂×C₁₆×C₅₃	1	8	yes	direct product factor
78	C₄	C₂×C₄²×C₅₃	1	1	yes	characteristic
79	C₄	C₂²×C₈×C₅₃	1	1	yes	characteristic
80	C₂	C₄×C₁₆×C₅₃	1	4	yes	direct product factor
81	C₂	C₂×C₄×C₈×C₅₃	1	1	yes	characteristic
82	C₂	C₂²×C₁₆×C₅₃	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₈	C₂³×C₅₃
socle	C₂³×C₅₃	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₁₆×C₅₃	C₂	direct (N × H)
7. C₂×C₁₆×C₅₃	C₄	direct (N × H)
20. C₁₆×C₅₃	C₂×C₄	direct (N × H)
22. C₂×C₄×C₅₃	C₁₆	direct (N × H)
35. C₄×C₅₃	C₂×C₁₆	direct (N × H)
38. C₂×C₄×C₁₆	C₅₃	direct (N × H)
39. C₂×C₅₃	C₄×C₁₆	direct (N × H)
44. C₄×C₁₆	C₂×C₅₃	direct (N × H)
45. C₅₃	C₂×C₄×C₁₆	direct (N × H)
49. C₂×C₁₆	C₄×C₅₃	direct (N × H)
62. C₁₆	C₂×C₄×C₅₃	direct (N × H)
64. C₂×C₄	C₁₆×C₅₃	direct (N × H)
77. C₄	C₂×C₁₆×C₅₃	direct (N × H)
80. C₂	C₄×C₁₆×C₅₃	direct (N × H)

Subgroups — C2×C4×C16×C53 #20271042

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄×C₁₆×C₅₃ #20271042