Subgroups — C₂×#16810398 #20276304

Order 6784.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11719908	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	#16810398	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#88322	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₅₃	C₄	1	1	yes	characteristic
7	C₂×#11719908	C₄	1	4	yes	complemented
8	C₂×#11719908	C₂²	1	2	yes	—
9	C₈×Dic₅₃	C₄	1	2	yes	—
10	C₈×Dic₅₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₅₃	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₅₃	C₂²	1	2	yes	—
14	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₅₃	C₈	1	2	yes	—
16	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
20	C₄×Dic₅₃	C₈	1	2	yes	—
21	C₄×Dic₅₃	C₂×C₄	1	2	yes	—
22	C₂×#88322	C₈	1	4	yes	—
23	C₂×#88322	C₂×C₄	1	2	yes	—
24	C₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
25	#11719908	C₂×C₄	1	4	yes	complemented
26	C₂³×C₅₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₅₃	C₄²	1	2	yes	—
28	C₂×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₅₃	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₅₃	—	2	4	no	—
32	C₂×Dic₅₃	C₂×C₈	1	4	yes	—
33	C₈×C₅₃	C₄²	1	2	yes	—
34	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
36	#88322	C₂×C₈	1	4	yes	—
37	C₂²×C₅₃	C₄×C₈	1	2	yes	—
38	C₂²×C₅₃	M₃₂	1	4	yes	—
39	C₂²×C₅₃	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₅₃	C₄×C₈	1	2	yes	—
41	C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
43	Dic₅₃	—	2	4	no	—
44	C₂×#346	—	53	1	no	maximal, Sylow
45	C₂×C₅₃	#346	1	4	yes	complemented
46	C₂×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
47	C₂×C₅₃	C₂×M₃₂	1	2	yes	—
48	C₂²×C₁₆	—	53	1	no	—
49	C₂²×C₁₆	D₅₃	1	1	yes	characteristic
50	C₂×C₄×C₈	—	53	1	no	—
51	#346	—	53	4	no	—
52	C₅₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₈	—	53	1	no	—
54	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
55	C₂×C₄²	—	53	1	no	—
56	C₂×C₁₆	—	53	4	no	—
57	C₂×C₁₆	—	53	2	no	—
58	C₂×C₁₆	Dic₅₃	1	4	yes	complemented
59	C₂×C₁₆	C₂×D₅₃	1	2	yes	—
60	C₄×C₈	—	53	2	no	—
61	C₄×C₈	—	53	2	no	—
62	C₂²×C₄	—	53	2	no	—
63	C₂²×C₄	C₄×D₅₃	1	1	yes	characteristic
64	C₂×C₈	—	53	2	no	—
65	C₂×C₈	—	53	4	no	—
66	C₂×C₈	C₄×D₅₃	1	2	yes	—
67	C₂×C₈	C₄×D₅₃	1	1	yes	characteristic
68	C₂×C₈	C₂×Dic₅₃	1	2	yes	—
69	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
70	C₄²	—	53	2	no	—
71	C₄²	—	53	2	no	—
72	C₁₆	—	53	4	no	—
73	C₁₆	C₂×Dic₅₃	1	4	yes	complemented
74	C₂³	C₈×D₅₃	1	1	yes	characteristic
75	C₂×C₄	—	53	4	no	—
76	C₂×C₄	—	106	4	no	—
77	C₂×C₄	C₈×D₅₃	1	1	yes	characteristic
78	C₂×C₄	C₈×D₅₃	1	2	yes	—
79	C₂×C₄	C₄×Dic₅₃	1	2	yes	—
80	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
81	C₈	—	53	4	no	—
82	C₈	C₄×Dic₅₃	1	2	yes	—
83	C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
84	C₈	C₂²×Dic₅₃	1	1	yes	characteristic
85	C₂²	C₈×Dic₅₃	1	2	yes	—
86	C₂²	#13133156	1	4	yes	—
87	C₂²	C₂×C₈×D₅₃	1	1	yes	characteristic
88	C₄	—	106	4	no	—
89	C₄	C₈×Dic₅₃	1	2	yes	—
90	C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
91	C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
92	C₂	#16810398	1	4	yes	direct product factor
93	C₂	C₂×C₈×Dic₅₃	1	1	yes	characteristic
94	C₂	C₂×#13133156	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×D₅₃
commutator	C₂×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₅₃
Fitting	C₂²×C₁₆×C₅₃	C₂
socle	C₂³×C₅₃	C₂×C₈
hypercenter	C₂²×C₁₆	D₅₃
hypocenter	C₅₃	C₂×#346
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #16810398	C₂	direct (N × H)
7. C₂×#11719908	C₄	semidirect
12. C₂×C₁₆×C₅₃	C₄	semidirect
24. C₁₆×C₅₃	C₂×C₄	semidirect
25. #11719908	C₂×C₄	semidirect
45. C₂×C₅₃	#346	semidirect
52. C₅₃	C₂×#346	semidirect
58. C₂×C₁₆	Dic₅₃	semidirect
73. C₁₆	C₂×Dic₅₃	semidirect
92. C₂	#16810398	direct (N × H)

Subgroups — C2×#16810398 #20276304

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810398 #20276304