Subgroups — #20272926

Order 6784.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810342	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic
4	C₃₂×C₅₃	C₄	1	1	yes	characteristic
5	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₅₃	C₈	1	1	yes	characteristic
7	C₁₆×C₅₃	C₈	1	1	yes	characteristic
8	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅₃	C₁₆	1	1	yes	characteristic
10	C₈×C₅₃	C₁₆	1	1	yes	characteristic
11	C₈×C₅₃	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₅₃	C₃₂	1	1	yes	characteristic
13	C₄×C₅₃	C₃₂	1	1	yes	characteristic
14	C₄×C₅₃	C₂×C₁₆	1	1	yes	characteristic
15	M₁₂₈	—	53	1	no	maximal, Sylow
16	C₂×C₅₃	—	2	1	no	—
17	C₂×C₅₃	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₃₂	D₅₃	1	1	yes	characteristic
19	C₆₄	—	53	2	no	—
20	C₅₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₆	Dic₅₃	1	1	yes	characteristic
22	C₃₂	Dic₅₃	1	1	yes	characteristic
23	C₃₂	C₂×D₅₃	1	1	yes	characteristic
24	C₂×C₈	#88322	1	1	yes	characteristic
25	C₁₆	#88322	1	1	yes	characteristic
26	C₁₆	C₂×Dic₅₃	1	1	yes	characteristic
27	C₂×C₄	#11719908	1	1	yes	characteristic
28	C₈	#11719908	1	1	yes	characteristic
29	C₈	C₂×#88322	1	1	yes	characteristic
30	C₂²	#13133123	1	1	yes	characteristic
31	C₄	#13133123	1	1	yes	characteristic
32	C₄	C₂×#11719908	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#13133123	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16810342	C₂	semidirect
20. C₅₃	M₁₂₈	semidirect