Subgroups — C₂³×SD₁₆×C₅₃ #20272512

Order 6784.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×SD₁₆×C₅₃	C₂	1	28	yes	maximal, direct product factor
4	C₂³×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×C₅₃	—	2	1	no	—
6	C₂²×Q₈×C₅₃	—	2	7	no	—
7	C₂²×Q₈×C₅₃	C₂²	1	14	yes	complemented
8	C₂²×D₄×C₅₃	—	2	7	no	—
9	C₂²×D₄×C₅₃	C₂²	1	14	yes	—
10	C₂³×C₄×C₅₃	—	2	1	no	—
11	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×SD₁₆×C₅₃	C₂²	1	112	yes	direct product factor
13	C₂²×C₈×C₅₃	C₂²	1	14	yes	complemented
14	C₂⁴×C₅₃	—	2	14	no	—
15	C₂⁴×C₅₃	—	4	8	no	—
16	C₂⁴×C₅₃	D₄	1	1	yes	characteristic
17	C₂×Q₈×C₅₃	—	2	42	no	—
18	C₂×Q₈×C₅₃	C₂³	1	28	yes	complemented
19	C₂×D₄×C₅₃	—	2	42	no	—
20	C₂×D₄×C₅₃	C₂³	1	28	yes	—
21	C₂²×C₄×C₅₃	—	2	14	no	—
22	C₂²×C₄×C₅₃	D₄	1	7	yes	—
23	C₂²×C₄×C₅₃	C₂³	1	7	yes	—
24	SD₁₆×C₅₃	C₂³	1	64	yes	direct product factor
25	C₂×C₈×C₅₃	C₂³	1	28	yes	complemented
26	C₂³×C₅₃	—	2	28	no	—
27	C₂³×C₅₃	—	4	56	no	—
28	C₂³×C₅₃	SD₁₆	1	8	yes	direct product factor
29	C₂³×C₅₃	C₂×D₄	1	7	yes	—
30	Q₈×C₅₃	—	2	28	no	—
31	Q₈×C₅₃	C₂⁴	1	8	yes	complemented
32	D₄×C₅₃	—	2	28	no	—
33	D₄×C₅₃	C₂⁴	1	8	yes	—
34	C₂×C₄×C₅₃	—	2	28	no	—
35	C₂×C₄×C₅₃	C₂×D₄	1	21	yes	—
36	C₂×C₄×C₅₃	C₂⁴	1	7	yes	—
37	C₈×C₅₃	C₂⁴	1	8	yes	complemented
38	C₂²×C₅₃	—	2	8	no	—
39	C₂²×C₅₃	—	4	56	no	—
40	C₂²×C₅₃	C₂×SD₁₆	1	28	yes	direct product factor
41	C₂²×C₅₃	C₂²×D₄	1	7	yes	—
42	C₄×C₅₃	—	2	8	no	—
43	C₄×C₅₃	C₂²×D₄	1	7	yes	—
44	C₄×C₅₃	C₂⁵	1	1	yes	characteristic
45	C₂³×SD₁₆	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅₃	—	4	8	no	—
47	C₂×C₅₃	C₂²×SD₁₆	1	14	yes	direct product factor
48	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
49	C₂³×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
50	C₂³×D₄	C₂×C₅₃	1	1	yes	characteristic
51	C₂²×SD₁₆	C₂×C₅₃	1	28	yes	direct product factor
52	C₂³×C₈	C₂×C₅₃	1	1	yes	characteristic, complemented
53	C₅₃	C₂³×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
54	C₂⁵	—	2	1	no	—
55	C₂²×Q₈	—	2	7	no	—
56	C₂²×Q₈	C₂²×C₅₃	1	14	yes	complemented
57	C₂²×D₄	—	2	7	no	—
58	C₂²×D₄	C₂²×C₅₃	1	14	yes	—
59	C₂³×C₄	—	2	1	no	—
60	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
61	C₂×SD₁₆	C₂²×C₅₃	1	112	yes	direct product factor
62	C₂²×C₈	C₂²×C₅₃	1	14	yes	complemented
63	C₂⁴	—	2	14	no	—
64	C₂⁴	—	4	8	no	—
65	C₂⁴	D₄×C₅₃	1	1	yes	characteristic
66	C₂×Q₈	—	2	42	no	—
67	C₂×Q₈	C₂³×C₅₃	1	28	yes	complemented
68	C₂×D₄	—	2	42	no	—
69	C₂×D₄	C₂³×C₅₃	1	28	yes	—
70	C₂²×C₄	—	2	14	no	—
71	C₂²×C₄	D₄×C₅₃	1	7	yes	—
72	C₂²×C₄	C₂³×C₅₃	1	7	yes	—
73	SD₁₆	C₂³×C₅₃	1	64	yes	direct product factor
74	C₂×C₈	C₂³×C₅₃	1	28	yes	complemented
75	C₂³	—	2	28	no	—
76	C₂³	—	4	56	no	—
77	C₂³	SD₁₆×C₅₃	1	8	yes	direct product factor
78	C₂³	C₂×D₄×C₅₃	1	7	yes	—
79	Q₈	—	2	28	no	—
80	Q₈	C₂⁴×C₅₃	1	8	yes	complemented
81	D₄	—	2	28	no	—
82	D₄	C₂⁴×C₅₃	1	8	yes	—
83	C₂×C₄	—	2	28	no	—
84	C₂×C₄	C₂×D₄×C₅₃	1	21	yes	—
85	C₂×C₄	C₂⁴×C₅₃	1	7	yes	—
86	C₈	C₂⁴×C₅₃	1	8	yes	complemented
87	C₂²	—	2	8	no	—
88	C₂²	—	4	56	no	—
89	C₂²	C₂×SD₁₆×C₅₃	1	28	yes	direct product factor
90	C₂²	C₂²×D₄×C₅₃	1	7	yes	—
91	C₄	—	2	8	no	—
92	C₄	C₂²×D₄×C₅₃	1	7	yes	—
93	C₄	C₂⁵×C₅₃	1	1	yes	characteristic
94	C₂	—	4	8	no	—
95	C₂	C₂²×SD₁₆×C₅₃	1	14	yes	direct product factor
96	C₂	C₂³×D₄×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅₃	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₅₃
prime radical	C₂³×D₄×C₅₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₃ ◁ C₂³×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×C₅₃	C₂	semidirect
3. C₂²×SD₁₆×C₅₃	C₂	direct (N × H)
4. C₂³×C₈×C₅₃	C₂	semidirect
7. C₂²×Q₈×C₅₃	C₂²	semidirect
12. C₂×SD₁₆×C₅₃	C₂²	direct (N × H)
13. C₂²×C₈×C₅₃	C₂²	semidirect
18. C₂×Q₈×C₅₃	C₂³	semidirect
24. SD₁₆×C₅₃	C₂³	direct (N × H)
25. C₂×C₈×C₅₃	C₂³	semidirect
28. C₂³×C₅₃	SD₁₆	direct (N × H)
31. Q₈×C₅₃	C₂⁴	semidirect
37. C₈×C₅₃	C₂⁴	semidirect
40. C₂²×C₅₃	C₂×SD₁₆	direct (N × H)
45. C₂³×SD₁₆	C₅₃	direct (N × H)
47. C₂×C₅₃	C₂²×SD₁₆	direct (N × H)
49. C₂³×Q₈	C₂×C₅₃	semidirect
51. C₂²×SD₁₆	C₂×C₅₃	direct (N × H)
52. C₂³×C₈	C₂×C₅₃	semidirect
53. C₅₃	C₂³×SD₁₆	direct (N × H)
56. C₂²×Q₈	C₂²×C₅₃	semidirect
61. C₂×SD₁₆	C₂²×C₅₃	direct (N × H)
62. C₂²×C₈	C₂²×C₅₃	semidirect
67. C₂×Q₈	C₂³×C₅₃	semidirect
73. SD₁₆	C₂³×C₅₃	direct (N × H)
74. C₂×C₈	C₂³×C₅₃	semidirect
77. C₂³	SD₁₆×C₅₃	direct (N × H)
80. Q₈	C₂⁴×C₅₃	semidirect
86. C₈	C₂⁴×C₅₃	semidirect
89. C₂²	C₂×SD₁₆×C₅₃	direct (N × H)
95. C₂	C₂²×SD₁₆×C₅₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×Q₈×C₅₃	2
C₂³×D₄×C₅₃	2
C₂²×SD₁₆×C₅₃	2
C₂³×C₈×C₅₃	2
C₂³×SD₁₆	53

Subgroups — C23×SD16×C53 #20272512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×SD₁₆×C₅₃ #20272512