Subgroups — #20289878

Order 6784.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811551	C₂	1	2	yes	maximal
2	C₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#13133288	—	2	2	no	—
4	C₁₆×D₅₃	C₂²	1	1	yes	characteristic
5	#13133123	C₄	1	1	yes	characteristic
6	C₃₂×C₅₃	C₄	1	1	yes	characteristic
7	#11719936	—	4	2	no	—
8	C₈×D₅₃	D₄	1	1	yes	characteristic
9	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
10	#11719908	Q₈	1	1	yes	characteristic
11	C₄×D₅₃	D₈	1	1	yes	characteristic
12	#88324	—	8	2	no	—
13	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
14	#88322	Q₁₆	1	1	yes	characteristic
15	C₂×D₅₃	Q₃₂	1	1	yes	characteristic
16	C₄×C₅₃	#107	1	1	yes	characteristic
17	Dic₅₃	D₁₆	1	1	yes	characteristic
18	#1425	—	53	1	no	maximal, Sylow
19	C₂×C₅₃	#366	1	1	yes	characteristic
20	D₅₃	—	2	1	no	—
21	C₂×C₃₂	—	53	1	no	—
22	#368	—	53	2	no	—
23	C₅₃	#1425	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₆	—	53	1	no	—
25	#108	—	106	2	no	—
26	C₃₂	—	53	1	no	—
27	C₃₂	#6157	1	1	yes	characteristic
28	M₁₆	—	212	2	no	—
29	C₂×C₈	—	53	1	no	—
30	C₁₆	—	53	1	no	—
31	C₁₆	C₂×#6157	1	1	yes	characteristic
32	C₂×C₄	—	53	1	no	—
33	C₈	—	53	1	no	—
34	C₈	—	424	2	no	—
35	C₈	C₄⋊#6157	1	1	yes	characteristic
36	C₂²	—	53	1	no	—
37	C₄	—	53	1	no	—
38	C₄	#13133286	1	1	yes	characteristic
39	C₂	—	106	1	no	—
40	C₂	#16811549	1	1	yes	characteristic

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

N	H ≅ G/N	type
23. C₅₃	#1425	semidirect