Subgroups — #20272748

Order 6784.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810401	C₂	1	2	yes	maximal, complemented
2	C₅₃×#490	C₂	1	1	yes	maximal, characteristic
3	#13133157	—	2	2	no	—
4	#127×C₅₃	C₄	1	1	yes	characteristic
5	#125×C₅₃	C₄	1	1	yes	characteristic
6	#102×C₅₃	—	2	2	no	—
7	#97×C₅₃	C₂²	1	1	yes	characteristic
8	C₂×D₄×C₅₃	—	2	1	no	—
9	C₂×D₄×C₅₃	—	4	1	no	—
10	C₂×C₈×C₅₃	D₄	1	2	yes	—
11	C₄⋊C₄×C₅₃	—	2	1	no	—
12	C₄⋊C₄×C₅₃	—	4	1	no	—
13	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
14	#11719908	—	2	4	no	—
15	C₂³×C₅₃	—	4	1	no	—
16	D₄×C₅₃	—	4	2	no	—
17	D₄×C₅₃	—	8	2	no	—
18	C₂×C₄×C₅₃	—	2	1	no	—
19	C₂×C₄×C₅₃	—	4	1	no	—
20	C₂×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₅₃	—	2	2	no	—
22	C₂²×C₅₃	—	8	2	no	—
23	C₂²×C₅₃	—	8	1	no	—
24	C₂²×C₅₃	#100	1	1	yes	characteristic
25	C₄×C₅₃	—	4	1	no	—
26	C₄×C₅₃	—	8	1	no	—
27	C₄×C₅₃	#104	1	2	yes	—
28	#1355	—	53	1	no	maximal, Sylow
29	C₂×C₅₃	—	2	1	no	—
30	C₂×C₅₃	—	16	1	no	—
31	C₂×C₅₃	#329	1	1	yes	characteristic
32	#490	D₅₃	1	1	yes	characteristic
33	#347	—	53	2	no	—
34	C₅₃	#1355	1	1	yes	characteristic, complemented, Sylow
35	#127	Dic₅₃	1	1	yes	characteristic
36	#125	Dic₅₃	1	1	yes	characteristic
37	M₃₂	—	106	2	no	—
38	#102	—	2	2	no	—
39	#97	C₂×D₅₃	1	1	yes	characteristic
40	C₂×D₄	—	2	1	no	—
41	C₂×D₄	—	4	1	no	—
42	C₂×C₈	C₂²⋊D₅₃	1	2	yes	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×Dic₅₃	1	1	yes	characteristic
46	C₁₆	—	106	4	no	—
47	C₂³	—	4	1	no	—
48	D₄	—	4	2	no	—
49	D₄	—	8	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₂²	—	8	2	no	—
55	C₂²	—	8	1	no	—
56	C₂²	#13133134	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#13133144	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	16	1	no	—
62	C₂	#16810363	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16810363
commutator	C₄²×C₅₃	C₂×C₄
Frattini	#97	C₂×D₅₃
Fitting	C₅₃×#490	C₂
socle	C₂×C₅₃	#329
hypercenter	#490	D₅₃
hypocenter	C₅₃	#1355
LCS	G ▷ C₄²×C₅₃ ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #490

Complements

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

N	H ≅ G/N	type
1. #16810401	C₂	semidirect
34. C₅₃	#1355	semidirect