Subgroups — C₅₃×#1426 #20270363

Order 6784.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#368	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#367	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
5	#108×C₅₃	—	2	1	no	—
6	#107×C₅₃	—	2	1	no	—
7	C₃₂×C₅₃	C₄	1	2	yes	complemented
8	M₁₆×C₅₃	—	4	1	no	—
9	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₅₃	—	4	1	no	—
11	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₅₃	—	8	1	no	—
14	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
15	C₈×C₅₃	—	8	1	no	—
16	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₅₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₅₃	SD₃₂	1	1	yes	characteristic
19	C₄×C₅₃	—	16	1	no	—
20	C₄×C₅₃	#107	1	1	yes	characteristic
21	C₄×C₅₃	SD₃₂	1	1	yes	characteristic
22	#1426	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₅₃	—	2	1	no	—
24	C₂×C₅₃	#367	1	1	yes	characteristic
25	M₆₄	C₂×C₅₃	1	1	yes	characteristic
26	#368	C₂×C₅₃	1	1	yes	characteristic
27	#367	C₂×C₅₃	1	1	yes	characteristic
28	C₅₃	#1426	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₁₆	C₂²×C₅₃	1	1	yes	characteristic
30	#108	—	2	1	no	—
31	#107	—	2	1	no	—
32	C₃₂	C₄×C₅₃	1	2	yes	complemented
33	M₁₆	—	4	1	no	—
34	C₂×C₈	D₄×C₅₃	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₁₆	C₂×C₄×C₅₃	1	1	yes	characteristic
37	C₁₆	Q₈×C₅₃	1	1	yes	characteristic
38	C₂×C₄	—	8	1	no	—
39	C₂×C₄	D₈×C₅₃	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	C₄⋊C₄×C₅₃	1	1	yes	characteristic
42	C₈	Q₁₆×C₅₃	1	1	yes	characteristic
43	C₂²	SD₃₂×C₅₃	1	1	yes	characteristic
44	C₄	—	16	1	no	—
45	C₄	#107×C₅₃	1	1	yes	characteristic
46	C₄	SD₃₂×C₅₃	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₅₃×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₃	#367
commutator	C₁₆	C₂×C₄×C₅₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₅₃
prime radical	C₂²×C₅₃	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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
7. C₃₂×C₅₃	C₄	semidirect
22. #1426	C₅₃	direct (N × H)
28. C₅₃	#1426	direct (N × H)
32. C₃₂	C₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×M₆₄	2
C₅₃×#368	2
C₅₃×#367	2
#1426	53

Subgroups — C53×#1426 #20270363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#1426 #20270363