Subgroups — #20272925

Order 6784.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#16810342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₅₃	C₄	1	1	yes	characteristic
5	#13133123	C₄	1	1	yes	characteristic
6	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
7	C₈×D₅₃	C₈	1	1	yes	characteristic
8	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
9	#11719908	C₈	1	1	yes	characteristic
10	C₄×D₅₃	C₁₆	1	1	yes	characteristic
11	C₈×C₅₃	C₂×C₈	1	1	yes	characteristic
12	#88322	C₁₆	1	1	yes	characteristic
13	C₂×D₅₃	C₃₂	1	1	yes	characteristic
14	C₄×C₅₃	C₂×C₁₆	1	1	yes	characteristic
15	Dic₅₃	C₃₂	1	1	yes	characteristic
16	M₁₂₈	—	53	1	no	maximal, Sylow
17	C₂×C₅₃	C₂×C₃₂	1	1	yes	characteristic
18	D₅₃	—	2	1	no	—
19	C₂×C₃₂	—	53	1	no	—
20	C₆₄	—	53	1	no	—
21	C₆₄	D₅₃	1	1	yes	characteristic, complemented
22	C₅₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	53	1	no	—
24	C₃₂	—	53	1	no	—
25	C₃₂	C₂×D₅₃	1	1	yes	characteristic
26	C₂×C₈	—	53	1	no	—
27	C₁₆	—	53	1	no	—
28	C₁₆	C₄×D₅₃	1	1	yes	characteristic
29	C₂×C₄	—	53	1	no	—
30	C₈	—	53	1	no	—
31	C₈	C₈×D₅₃	1	1	yes	characteristic
32	C₂²	—	53	1	no	—
33	C₄	—	53	1	no	—
34	C₄	C₁₆×D₅₃	1	1	yes	characteristic
35	C₂	—	106	1	no	—
36	C₂	C₃₂×D₅₃	1	1	yes	characteristic

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