Subgroups — C₄×C₈×Dic₅₃ #20274396

Order 6784.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#88322	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₅₃	C₂	1	4	yes	maximal
3	C₄²×Dic₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#88322	C₂²	1	2	yes	—
6	C₂×C₄×Dic₅₃	C₄	1	4	yes	—
7	C₂×C₄×Dic₅₃	C₂²	1	2	yes	—
8	C₄×#88322	C₄	1	4	yes	complemented
9	C₈×Dic₅₃	C₄	1	16	yes	direct product factor
10	C₂²×C₈×C₅₃	C₂²	1	2	yes	—
11	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₅₃	C₄	1	4	yes	complemented
13	C₂²×C₄×C₅₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₅₃	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₅₃	C₂×C₄	1	8	yes	—
17	C₂×C₈×C₅₃	C₂×C₄	1	4	yes	—
18	C₄²×C₅₃	C₂×C₄	1	2	yes	—
19	C₄²×C₅₃	C₂×C₄	1	2	yes	—
20	C₄×Dic₅₃	C₈	1	16	yes	direct product factor
21	C₄×Dic₅₃	C₂×C₄	1	8	yes	—
22	C₂×#88322	C₂×C₄	1	8	yes	—
23	C₂×#88322	C₂×C₄	1	4	yes	—
24	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₅₃	C₄²	1	4	yes	—
26	C₂×C₄×C₅₃	C₂×C₈	1	8	yes	—
27	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₅₃	C₂²×C₄	1	4	yes	—
29	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₅₃	C₄²	1	8	yes	—
31	C₂×Dic₅₃	C₂×C₈	1	16	yes	—
32	C₈×C₅₃	C₄²	1	8	yes	complemented
33	#88322	C₄²	1	8	yes	complemented
34	C₂²×C₅₃	C₂×C₄²	1	2	yes	—
35	C₂²×C₅₃	C₂×C₄²	1	1	yes	characteristic
36	C₂²×C₅₃	C₂²×C₈	1	4	yes	—
37	C₄×C₅₃	C₄×C₈	1	8	yes	complemented
38	C₄×C₅₃	C₂×C₄²	1	2	yes	—
39	C₄×C₅₃	C₂×C₄²	1	2	yes	—
40	Dic₅₃	C₄×C₈	1	16	yes	direct product factor
41	C₄²×C₈	—	53	1	no	maximal, Sylow
42	C₂×C₅₃	C₄³	1	1	yes	characteristic
43	C₂×C₅₃	C₂×C₄×C₈	1	4	yes	—
44	C₂×C₅₃	C₂×C₄×C₈	1	2	yes	—
45	C₂×C₄×C₈	—	53	4	no	—
46	C₂×C₄×C₈	—	53	1	no	—
47	C₂×C₄×C₈	D₅₃	1	1	yes	characteristic
48	C₄³	—	53	1	no	—
49	C₅₃	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₈	—	53	2	no	—
51	C₂²×C₈	C₂×D₅₃	1	2	yes	—
52	C₂×C₄²	—	53	4	no	—
53	C₂×C₄²	—	53	2	no	—
54	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
55	C₄×C₈	—	53	16	no	—
56	C₄×C₈	—	53	4	no	—
57	C₄×C₈	Dic₅₃	1	4	yes	direct product factor
58	C₂²×C₄	—	53	4	no	—
59	C₂²×C₄	C₄×D₅₃	1	2	yes	—
60	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
61	C₂×C₈	—	53	4	no	—
62	C₂×C₈	—	53	8	no	—
63	C₂×C₈	C₄×D₅₃	1	8	yes	—
64	C₂×C₈	C₂×Dic₅₃	1	4	yes	—
65	C₄²	—	53	8	no	—
66	C₄²	—	53	16	no	—
67	C₄²	C₄×D₅₃	1	2	yes	—
68	C₄²	C₂×Dic₅₃	1	2	yes	—
69	C₂³	C₂×C₄×D₅₃	1	1	yes	characteristic
70	C₂×C₄	—	53	8	no	—
71	C₂×C₄	—	53	16	no	—
72	C₂×C₄	C₈×D₅₃	1	8	yes	—
73	C₂×C₄	C₄×Dic₅₃	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
75	C₂×C₄	C₂×C₄×D₅₃	1	4	yes	—
76	C₂×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
77	C₈	—	53	8	no	—
78	C₈	C₄×Dic₅₃	1	8	yes	direct product factor
79	C₂²	C₄²×D₅₃	1	2	yes	—
80	C₂²	C₂×C₄×Dic₅₃	1	1	yes	characteristic
81	C₂²	C₂×C₈×D₅₃	1	4	yes	—
82	C₄	—	53	16	no	—
83	C₄	C₈×Dic₅₃	1	8	yes	direct product factor
84	C₄	C₄²×D₅₃	1	2	yes	—
85	C₄	C₂×C₄×Dic₅₃	1	2	yes	—
86	C₂	C₄²×Dic₅₃	1	1	yes	characteristic
87	C₂	C₄×C₈×D₅₃	1	4	yes	—
88	C₂	C₂×C₈×Dic₅₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄×C₈	D₅₃
commutator, hypocenter	C₅₃	C₄²×C₈
Frattini	C₂²×C₄	C₂²×D₅₃
Fitting	C₂×C₄×C₈×C₅₃	C₂
socle	C₂³×C₅₃	C₂²×C₄
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×#88322	C₄	semidirect
9. C₈×Dic₅₃	C₄	direct (N × H)
12. C₄×C₈×C₅₃	C₄	semidirect
20. C₄×Dic₅₃	C₈	direct (N × H)
32. C₈×C₅₃	C₄²	semidirect
33. #88322	C₄²	semidirect
37. C₄×C₅₃	C₄×C₈	semidirect
40. Dic₅₃	C₄×C₈	direct (N × H)
49. C₅₃	C₄²×C₈	semidirect
57. C₄×C₈	Dic₅₃	direct (N × H)
78. C₈	C₄×Dic₅₃	direct (N × H)
83. C₄	C₈×Dic₅₃	direct (N × H)

Subgroups — C4×C8×Dic53 #20274396

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₈×Dic₅₃ #20274396