Subgroups — #28299397

Order 13568.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289530	C₂	1	2	yes	maximal, complemented
2	C₆₄×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₅₃	C₄	1	1	yes	characteristic
4	#16810342	C₂²	1	1	yes	characteristic
5	C₅₃×C₆₄	C₄	1	1	yes	characteristic
6	C₁₆×D₅₃	C₈	1	1	yes	characteristic
7	#13133123	C₈	1	1	yes	characteristic
8	C₃₂×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₈×D₅₃	C₁₆	1	1	yes	characteristic
10	C₁₆×C₅₃	C₂×C₈	1	1	yes	characteristic
11	#11719908	C₁₆	1	1	yes	characteristic
12	C₄×D₅₃	C₃₂	1	1	yes	characteristic
13	C₈×C₅₃	C₂×C₁₆	1	1	yes	characteristic
14	#88322	C₃₂	1	1	yes	characteristic
15	M₂₅₆	—	53	1	no	maximal, Sylow
16	C₂×D₅₃	C₆₄	1	1	yes	characteristic
17	C₄×C₅₃	C₂×C₃₂	1	1	yes	characteristic
18	Dic₅₃	C₆₄	1	1	yes	characteristic
19	C₂×C₆₄	—	53	1	no	—
20	C₁₂₈	—	53	2	no	—
21	C₂×C₅₃	C₂×C₆₄	1	1	yes	characteristic
22	D₅₃	—	2	1	no	—
23	C₂×C₃₂	—	53	1	no	—
24	C₆₄	—	53	1	no	—
25	C₆₄	#6157	1	1	yes	characteristic
26	C₅₃	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₆	—	53	1	no	—
28	C₃₂	—	53	1	no	—
29	C₃₂	C₂×#6157	1	1	yes	characteristic
30	C₂×C₈	—	53	1	no	—
31	C₁₆	—	53	1	no	—
32	C₁₆	D₅₃⋊C₈	1	1	yes	characteristic
33	C₂×C₄	—	53	1	no	—
34	C₈	—	53	1	no	—
35	C₈	D₅₃⋊C₁₆	1	1	yes	characteristic
36	C₂²	—	53	1	no	—
37	C₄	—	53	1	no	—
38	C₄	D₅₃⋊C₃₂	1	1	yes	characteristic
39	C₂	—	106	1	no	—
40	C₂	D₅₃⋊C₆₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #20289530	C₂	semidirect
26. C₅₃	M₂₅₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.