Subgroups — C₅₃×#1425 #20270362

Order 6784.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#368	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
4	#108×C₅₃	—	2	2	no	—
5	C₃₂×C₅₃	C₄	1	2	yes	—
6	M₁₆×C₅₃	—	4	2	no	—
7	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
8	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
11	C₈×C₅₃	—	8	2	no	—
12	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₅₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₅₃	Q₃₂	1	1	yes	characteristic
15	C₄×C₅₃	#107	1	1	yes	characteristic
16	C₄×C₅₃	D₁₆	1	1	yes	characteristic
17	#1425	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₅₃	—	2	1	no	—
19	C₂×C₅₃	#366	1	1	yes	characteristic
20	C₂×C₃₂	C₂×C₅₃	1	1	yes	characteristic
21	#368	C₂×C₅₃	1	2	yes	—
22	C₅₃	#1425	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₁₆	C₂²×C₅₃	1	1	yes	characteristic
24	#108	—	2	2	no	—
25	C₃₂	C₄×C₅₃	1	2	yes	—
26	M₁₆	—	4	2	no	—
27	C₂×C₈	D₄×C₅₃	1	1	yes	characteristic
28	C₁₆	C₂×C₄×C₅₃	1	1	yes	characteristic
29	C₁₆	Q₈×C₅₃	1	1	yes	characteristic
30	C₂×C₄	D₈×C₅₃	1	1	yes	characteristic
31	C₈	—	8	2	no	—
32	C₈	C₄⋊C₄×C₅₃	1	1	yes	characteristic
33	C₈	Q₁₆×C₅₃	1	1	yes	characteristic
34	C₂²	Q₃₂×C₅₃	1	1	yes	characteristic
35	C₄	#107×C₅₃	1	1	yes	characteristic
36	C₄	D₁₆×C₅₃	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	C₅₃×#366	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅₃	D₁₆
commutator	C₁₆	C₂×C₄×C₅₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₅₃
socle	C₂×C₅₃	#366
prime radical	C₂²×C₅₃	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₃ ◁ C₂×C₄×C₅₃ ◁ C₂×C₈×C₅₃ ◁ C₂×C₁₆×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
17. #1425	C₅₃	direct (N × H)
22. C₅₃	#1425	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₂×C₅₃	2
C₅₃×#368	2
#1425	53

Subgroups — C53×#1425 #20270362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#1425 #20270362