Subgroups — C₅₃×#1840 #20270777

Order 6784.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#376	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#336	C₂	1	6	yes	maximal
3	C₂²×C₈×C₅₃	C₂²	1	4	yes	—
4	C₂×C₄²×C₅₃	C₂²	1	3	yes	—
5	#95×C₅₃	C₄	1	4	yes	—
6	C₂²×C₄×C₅₃	C₂×C₄	1	6	yes	—
7	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
8	C₂×C₈×C₅₃	—	2	12	no	—
9	C₄²×C₅₃	—	2	6	no	—
10	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₅₃	—	2	6	no	—
12	C₂×C₄×C₅₃	—	2	12	no	—
13	C₂×C₄×C₅₃	#41	1	6	yes	—
14	C₈×C₅₃	—	4	4	no	—
15	C₂²×C₅₃	#117	1	3	yes	—
16	C₂²×C₅₃	#131	1	4	yes	—
17	C₄×C₅₃	—	4	6	no	—
18	C₄×C₅₃	#126	1	4	yes	—
19	#1840	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₅₃	#383	1	1	yes	characteristic
21	C₂×C₅₃	#433	1	6	yes	—
22	#376	C₂×C₅₃	1	1	yes	characteristic
23	#336	C₂×C₅₃	1	6	yes	—
24	C₅₃	#1840	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₈	C₂²×C₅₃	1	4	yes	—
26	C₂×C₄²	C₂²×C₅₃	1	3	yes	—
27	#95	C₄×C₅₃	1	4	yes	—
28	C₂²×C₄	C₂×C₄×C₅₃	1	6	yes	—
29	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
30	C₂×C₈	—	2	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×C₄×C₅₃	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#41×C₅₃	1	6	yes	—
36	C₈	—	4	4	no	—
37	C₂²	#117×C₅₃	1	3	yes	—
38	C₂²	#131×C₅₃	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#126×C₅₃	1	4	yes	—
41	C₂	C₅₃×#383	1	1	yes	characteristic
42	C₂	C₅₃×#433	1	6	yes	—

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

N	H ≅ G/N	type
19. #1840	C₅₃	direct (N × H)
24. C₅₃	#1840	direct (N × H)

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