Subgroups — C₅₃×#1422 #20270359

Order 6784.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×M₆₄	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
6	C₃₂×C₅₃	—	2	2	no	—
7	C₂×C₈×C₅₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₅₃	C₈	1	1	yes	characteristic
10	C₁₆×C₅₃	—	2	1	no	—
11	C₁₆×C₅₃	D₄	1	1	yes	characteristic
12	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₅₃	—	2	1	no	—
14	C₂×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₅₃	C₁₆	1	2	yes	—
16	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₅₃	M₁₆	1	1	yes	characteristic
18	C₂²×C₅₃	M₃₂	1	1	yes	characteristic
19	C₄×C₅₃	—	2	2	no	—
20	C₄×C₅₃	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₅₃	C₂×C₁₆	1	1	yes	characteristic
22	#1422	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₅₃	—	2	1	no	—
24	C₂×C₅₃	C₄⋊C₁₆	1	1	yes	characteristic
25	M₆₄	C₂×C₅₃	1	2	yes	—
26	C₄×C₁₆	C₂×C₅₃	1	1	yes	characteristic
27	C₅₃	#1422	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₆	C₄×C₅₃	1	1	yes	characteristic
29	C₂×C₁₆	C₂²×C₅₃	1	1	yes	characteristic
30	C₄×C₈	C₄×C₅₃	1	1	yes	characteristic
31	C₃₂	—	2	2	no	—
32	C₂×C₈	C₈×C₅₃	1	1	yes	characteristic
33	C₂×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
34	C₄²	C₈×C₅₃	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	D₄×C₅₃	1	1	yes	characteristic
37	C₁₆	Q₈×C₅₃	1	1	yes	characteristic
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×C₈×C₅₃	1	1	yes	characteristic
40	C₈	C₁₆×C₅₃	1	2	yes	—
41	C₈	C₄⋊C₄×C₅₃	1	1	yes	characteristic
42	C₈	M₁₆×C₅₃	1	1	yes	characteristic
43	C₂²	M₃₂×C₅₃	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊C₈×C₅₃	1	1	yes	characteristic
46	C₄	C₂×C₁₆×C₅₃	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₅₃×C₄⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆×C₅₃	D₄
commutator	C₄	C₂×C₁₆×C₅₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₅₃
socle	C₂×C₅₃	C₄⋊C₁₆
prime radical	C₂²×C₅₃	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₅₃ ◁ C₂×C₁₆×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
22. #1422	C₅₃	direct (N × H)
27. C₅₃	#1422	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×M₆₄	2
C₄×C₁₆×C₅₃	2
#1422	53

Subgroups — C53×#1422 #20270359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#1422 #20270359