Subgroups — #20272919

Order 6784.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810453	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
3	#13133153	—	2	2	no	—
4	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₅₃	C₄	1	2	yes	—
6	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
7	#11719917	—	4	2	no	—
8	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
11	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₅₃	Q₁₆	1	1	yes	characteristic
13	#88322	—	8	2	no	—
14	C₂²×C₅₃	Q₃₂	1	1	yes	characteristic
15	C₄×C₅₃	#107	1	1	yes	characteristic
16	C₄×C₅₃	D₁₆	1	1	yes	characteristic
17	#1425	—	53	1	no	maximal, Sylow
18	C₂×C₅₃	—	2	1	no	—
19	C₂×C₅₃	#366	1	1	yes	characteristic
20	C₂×C₃₂	D₅₃	1	1	yes	characteristic
21	#368	—	53	2	no	—
22	C₅₃	#1425	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
24	#108	—	106	2	no	—
25	C₃₂	Dic₅₃	1	2	yes	—
26	M₁₆	—	212	2	no	—
27	C₂×C₈	D₂₁₂	1	1	yes	characteristic
28	C₁₆	Dic₁₀₆	1	1	yes	characteristic
29	C₁₆	C₂×Dic₅₃	1	1	yes	characteristic
30	C₂×C₄	D₄₂₄	1	1	yes	characteristic
31	C₈	—	424	2	no	—
32	C₈	Dic₂₁₂	1	1	yes	characteristic
33	C₈	C₄⋊Dic₅₃	1	1	yes	characteristic
34	C₂²	Dic₄₂₄	1	1	yes	characteristic
35	C₄	#13133151	1	1	yes	characteristic
36	C₄	D₈₄₈	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#16810449	1	1	yes	characteristic

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

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