Subgroups — C₅₃×#1369 #20270306

Order 6784.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#364	C₂	1	2	yes	maximal
2	C₅₃×#346	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₅₃	—	2	2	no	—
4	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
9	C₄²×C₅₃	Q₈	1	1	yes	characteristic
10	C₁₆×C₅₃	—	2	1	no	—
11	C₁₆×C₅₃	—	4	2	no	—
12	C₁₆×C₅₃	C₈	1	2	yes	—
13	C₂×C₄×C₅₃	—	2	1	no	—
14	C₂×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₅₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₅₃	M₁₆	1	1	yes	characteristic
17	C₈×C₅₃	SD₁₆	1	2	yes	—
18	C₂²×C₅₃	#108	1	1	yes	characteristic
19	C₄×C₅₃	—	4	1	no	—
20	C₄×C₅₃	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₅₃	#106	1	1	yes	characteristic
22	#1369	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₅₃	—	2	1	no	—
24	C₂×C₅₃	#334	1	1	yes	characteristic
25	#364	C₂×C₅₃	1	2	yes	—
26	#346	C₂×C₅₃	1	1	yes	characteristic
27	C₅₃	#1369	1	1	yes	characteristic, direct product factor, Sylow
28	M₃₂	—	2	2	no	—
29	C₂×C₁₆	C₄×C₅₃	1	1	yes	characteristic
30	C₂×C₁₆	C₄×C₅₃	1	1	yes	characteristic
31	C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
32	C₂×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
33	C₂×C₈	D₄×C₅₃	1	1	yes	characteristic
34	C₄²	Q₈×C₅₃	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	4	2	no	—
37	C₁₆	C₈×C₅₃	1	2	yes	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
40	C₈	C₂×C₈×C₅₃	1	1	yes	characteristic
41	C₈	M₁₆×C₅₃	1	1	yes	characteristic
42	C₈	SD₁₆×C₅₃	1	2	yes	—
43	C₂²	#108×C₅₃	1	1	yes	characteristic
44	C₄	—	4	1	no	—
45	C₄	C₄⋊C₈×C₅₃	1	1	yes	characteristic
46	C₄	#106×C₅₃	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₅₃×#334	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅₃	#106
commutator	C₈	C₂×C₈×C₅₃
Frattini, cosocle	C₄×C₈	C₂²×C₅₃
socle	C₂×C₅₃	#334
prime radical	C₂²×C₅₃	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₃ ◁ C₂×C₈×C₅₃ ◁ C₄×C₈×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
22. #1369	C₅₃	direct (N × H)
27. C₅₃	#1369	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#364	2
C₅₃×#346	2
#1369	53

Subgroups — C53×#1369 #20270306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#1369 #20270306