Subgroups — #401×D₅₃ #20278010

Order 6784.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃⋊#401	C₂	1	7	yes	maximal, complemented
2	#95×D₅₃	C₂	1	7	yes	maximal
3	C₅₃×#401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₅₃	C₂²	1	7	yes	—
5	#13133124	C₂²	1	21	yes	—
6	#95×C₅₃	C₂²	1	7	yes	—
7	C₂³×D₅₃	C₂³	1	1	yes	characteristic
8	C₂²×C₄×C₅₃	C₂³	1	7	yes	—
9	C₂²×Dic₅₃	C₂³	1	7	yes	—
10	C₂×C₄×D₅₃	—	2	42	no	—
11	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
12	C₂²×D₅₃	#41	1	14	yes	—
13	C₂×C₄×C₅₃	—	2	21	no	—
14	C₂×Dic₅₃	—	2	21	no	—
15	C₄×D₅₃	—	4	28	no	—
16	C₂²×C₅₃	C₂×#41	1	7	yes	—
17	C₂×D₅₃	#126	1	28	yes	—
18	C₄×C₅₃	—	4	7	no	—
19	Dic₅₃	—	4	7	no	—
20	C₂×#401	—	53	1	no	maximal, Sylow
21	C₂×C₅₃	C₂×#126	1	7	yes	—
22	D₅₃	#401	1	8	yes	direct product factor
23	#401	—	53	7	no	—
24	#401	D₅₃	1	1	yes	characteristic, direct product factor
25	C₂×#95	—	53	7	no	—
26	C₅₃	C₂×#401	1	1	yes	characteristic, complemented, Sylow
27	C₂³×C₄	—	53	7	no	—
28	#95	—	53	21	no	—
29	#95	C₂×D₅₃	1	7	yes	—
30	C₂⁴	—	53	1	no	—
31	C₂²×C₄	—	53	7	no	—
32	C₂²×C₄	—	106	42	no	—
33	C₂²×C₄	C₂²×D₅₃	1	7	yes	—
34	C₂³	—	53	14	no	—
35	C₂³	C₂³×D₅₃	1	1	yes	characteristic
36	C₂×C₄	—	2	21	no	—
37	C₂×C₄	—	106	21	no	—
38	C₂×C₄	—	212	28	no	—
39	C₂²	—	53	28	no	—
40	C₂²	#41×D₅₃	1	7	yes	—
41	C₄	—	4	7	no	—
42	C₄	—	212	7	no	—
43	C₂	—	53	8	no	—
44	C₂	#126×D₅₃	1	7	yes	—

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