Subgroups — C₂²×C₅×C₈×C₁₆₃ #72203233

Order 26080.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₁₆₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈×C₁₆₃	C₂	1	6	yes	maximal, direct product factor
3	C₂³×C₅×C₁₆₃	C₄	1	1	yes	characteristic
4	C₂×C₄×C₅×C₁₆₃	C₄	1	3	yes	—
5	C₂×C₄×C₅×C₁₆₃	C₂²	1	3	yes	—
6	C₅×C₈×C₁₆₃	C₂²	1	4	yes	direct product factor
7	C₂²×C₈×C₁₆₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₅×C₁₆₃	C₈	1	4	yes	direct product factor
9	C₂²×C₅×C₁₆₃	C₂×C₄	1	3	yes	—
10	C₄×C₅×C₁₆₃	C₂×C₄	1	3	yes	—
11	C₄×C₅×C₁₆₃	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₁₆₃	C₂×C₅	1	1	yes	characteristic
13	C₂×C₈×C₁₆₃	C₂×C₅	1	6	yes	direct product factor
14	C₂×C₅×C₁₆₃	C₂×C₈	1	6	yes	direct product factor
15	C₂×C₅×C₁₆₃	C₂²×C₄	1	1	yes	characteristic
16	C₂³×C₁₆₃	C₄×C₅	1	1	yes	characteristic
17	C₂×C₄×C₁₆₃	C₄×C₅	1	3	yes	—
18	C₂×C₄×C₁₆₃	C₂²×C₅	1	3	yes	—
19	C₈×C₁₆₃	C₂²×C₅	1	4	yes	direct product factor
20	C₅×C₁₆₃	C₂²×C₈	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₁₆₃	C₅×C₈	1	4	yes	direct product factor
22	C₂²×C₁₆₃	C₂×C₄×C₅	1	3	yes	—
23	C₄×C₁₆₃	C₂×C₄×C₅	1	3	yes	—
24	C₄×C₁₆₃	C₂³×C₅	1	1	yes	characteristic
25	C₂×C₁₆₃	C₂×C₅×C₈	1	6	yes	direct product factor
26	C₂×C₁₆₃	C₂²×C₄×C₅	1	1	yes	characteristic
27	C₁₆₃	C₂²×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²×C₅×C₈	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂²×C₄×C₅	C₂×C₁₆₃	1	1	yes	characteristic
30	C₂×C₅×C₈	C₂×C₁₆₃	1	6	yes	direct product factor
31	C₂³×C₅	C₄×C₁₆₃	1	1	yes	characteristic
32	C₂×C₄×C₅	C₄×C₁₆₃	1	3	yes	—
33	C₂×C₄×C₅	C₂²×C₁₆₃	1	3	yes	—
34	C₅×C₈	C₂²×C₁₆₃	1	4	yes	direct product factor
35	C₂²×C₈	C₅×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	C₈×C₁₆₃	1	4	yes	direct product factor
37	C₂²×C₅	C₂×C₄×C₁₆₃	1	3	yes	—
38	C₄×C₅	C₂×C₄×C₁₆₃	1	3	yes	—
39	C₄×C₅	C₂³×C₁₆₃	1	1	yes	characteristic
40	C₂²×C₄	C₂×C₅×C₁₆₃	1	1	yes	characteristic
41	C₂×C₈	C₂×C₅×C₁₆₃	1	6	yes	direct product factor
42	C₂×C₅	C₂×C₈×C₁₆₃	1	6	yes	direct product factor
43	C₂×C₅	C₂²×C₄×C₁₆₃	1	1	yes	characteristic
44	C₂³	C₄×C₅×C₁₆₃	1	1	yes	characteristic
45	C₂×C₄	C₄×C₅×C₁₆₃	1	3	yes	—
46	C₂×C₄	C₂²×C₅×C₁₆₃	1	3	yes	—
47	C₈	C₂²×C₅×C₁₆₃	1	4	yes	direct product factor
48	C₅	C₂²×C₈×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	C₅×C₈×C₁₆₃	1	4	yes	direct product factor
50	C₂²	C₂×C₄×C₅×C₁₆₃	1	3	yes	—
51	C₄	C₂×C₄×C₅×C₁₆₃	1	3	yes	—
52	C₄	C₂³×C₅×C₁₆₃	1	1	yes	characteristic
53	C₂	C₂×C₅×C₈×C₁₆₃	1	6	yes	direct product factor
54	C₂	C₂²×C₄×C₅×C₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂³×C₅×C₁₆₃
socle, prime radical	C₂³×C₅×C₁₆₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₈×C₁₆₃	C₂	direct (N × H)
6. C₅×C₈×C₁₆₃	C₂²	direct (N × H)
7. C₂²×C₈×C₁₆₃	C₅	direct (N × H)
8. C₂²×C₅×C₁₆₃	C₈	direct (N × H)
13. C₂×C₈×C₁₆₃	C₂×C₅	direct (N × H)
14. C₂×C₅×C₁₆₃	C₂×C₈	direct (N × H)
19. C₈×C₁₆₃	C₂²×C₅	direct (N × H)
20. C₅×C₁₆₃	C₂²×C₈	direct (N × H)
21. C₂²×C₁₆₃	C₅×C₈	direct (N × H)
25. C₂×C₁₆₃	C₂×C₅×C₈	direct (N × H)
27. C₁₆₃	C₂²×C₅×C₈	direct (N × H)
28. C₂²×C₅×C₈	C₁₆₃	direct (N × H)
30. C₂×C₅×C₈	C₂×C₁₆₃	direct (N × H)
34. C₅×C₈	C₂²×C₁₆₃	direct (N × H)
35. C₂²×C₈	C₅×C₁₆₃	direct (N × H)
36. C₂²×C₅	C₈×C₁₆₃	direct (N × H)
41. C₂×C₈	C₂×C₅×C₁₆₃	direct (N × H)
42. C₂×C₅	C₂×C₈×C₁₆₃	direct (N × H)
47. C₈	C₂²×C₅×C₁₆₃	direct (N × H)
48. C₅	C₂²×C₈×C₁₆₃	direct (N × H)
49. C₂²	C₅×C₈×C₁₆₃	direct (N × H)
53. C₂	C₂×C₅×C₈×C₁₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×C₁₆₃	2
C₂×C₅×C₈×C₁₆₃	2
C₂²×C₈×C₁₆₃	5
C₂²×C₅×C₈	163

Subgroups — C22×C5×C8×C163 #72203233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₈×C₁₆₃ #72203233